# Femtosecond laser micromachining for integrated quantum photonics

Giacomo Corrielli1,2 Andrea Crespi2,1 Roberto Osellame1,2,
<EMAIL_ADDRESS>1Consiglio Nazionale delle Ricerche, Istituto di
Fotonica e Nanotecnologie, piazza Leonardo da Vinci 32, 20133 Milano, Italy
2Dipartimento di Fisica, Politecnico di Milano, piazza Leonardo da Vinci 32,
20133 Milano, Italy

###### Abstract

Integrated quantum photonics, i.e. the generation, manipulation and detection
of quantum states of light in integrated photonic chips, is revolutionizing
the field of quantum information in all applications, from communications to
computing. Although many different platforms are being currently developed,
from silicon photonics to lithium niobate photonic circuits, none of them has
shown the versatility of femtosecond laser micromachining (FLM) in producing
all the components of a complete quantum system, encompassing quantum sources,
reconfigurable state manipulation, quantum memories and detection. It is in
fact evident that FLM has been a key enabling tool in the first-time
demonstration of many quantum devices and functionalities. Although FLM cannot
achieve the same level of miniaturization of other platforms, it still has
many unique advantages for integrated quantum photonics. In particular, in the
last five years, FLM has greatly expanded its range of quantum applications
with several scientific breakthroughs achieved. For these reasons, we believe
that a review article on this topic is very timely and could further promote
the development of this field by convincing end-users of the great potentials
of this technological platform and by stimulating more research groups in FLM
to direct their efforts to the exciting field of quantum technologies.

##  I Introduction

Great expectations are currently placed on the second quantum revolution
Dowling03 , where quantum technologies promise to dramatically change the way
we process information for practical applications. This revolution encompasses
all aspects of information, from how we retrieve it with sensing, to how we
elaborate it through computing and simulation, to the way we transfer it with
communications.

The focus of the second quantum revolution is mainly on developing new
quantum-enabled technologies, in contrast to the first one that mainly aimed
at developing new science (to the extent that the two aspects can be
considered separately). The emphasis put on practical applications of quantum
devices is important to understand the global effort specifically devoted to
advancing the technological aspects. In fact, system scalability and
engineering are the most important keywords in evaluating and selecting
possible quantum platform. The range of physical systems that are currently
available to implement the qubit (the elementary unit of quantum information)
are several and very different. The most advanced ones include superconducting
circuits, trapped ions or atoms, defects in various materials, and photons.
Each of them has specific advantages and disadvantages and lends itself
particularly to a specific task in quantum information.

Photonics has unique properties for quantum communications Gisin07 , but also
has great potentials in sensing pira18 , simulation aspuru12  and computing
rudolph17 . Although amazing results have been achieved with extremely complex
bulk optics set-up Zhong20 , user-friendly, scalable, portable and reliable
photonic devices can only be achieved with integrated optics. The latter is a
well developed approach for applications in classical information and could
thus be leveraged for a rapid growth of quantum technologies.

However, different emphasis is put on some aspects of the photonic circuits by
classical and quantum operation. In particular, photon losses (that can be
easily compensated classically by optical amplifiers) are a key aspect for
quantum photonics, where the no-cloning theorem means that some information is
irreversibly destroyed with each lost photon. In addition, specific components
as single photon sources, memories and detectors need to be developed for a
complete quantum photonic system. These aspects motivate on-going and future
research in integrated quantum photonics.

The aim of this review is not to cover the whole field of integrated quantum
photonics, which has been the topic of a recent review paper wang20 , but to
summarize the contribution given to this important field by a specific
microfabrication technology, i.e. femtosecond laser micromachining (FLM) of
transparent materials osellame12 . In fact, this technological platform has
produced a wealth of new and significant contributions to the field since the
first results discussed in a previous review meany15 .

The article is organized in the following way: Section 2 gives a broader view
on integrated quantum photonics, describing the main architecture of a quantum
photonic system and the most relevant competitors to FLM for its
implementation. Section 3 focuses on FLM and its processing possibilities,
from waveguide writing, to selective removal of material, to additive
manufacturing at the nano/micro-scale with two-photon polymerization. This
unique portfolio of processing capabilities (that can be easily combined) is
implemented with the same experimental setup and can enable unique quantum
devices that are detailed in the following sections. Section 4 focuses on the
use of FLM to directly fabricate single photon sources in different materials.
If a source is produced with a different technology, FLM can still be useful
in devising an efficient interconnection of the source with integrated
photonic circuits as described in Section 5. Section 6 deals with the most
exploited application of FLM in quantum photonics, i.e. the fabrication of
complex integrated photonic circuits for manipulation of quantum states of
light, both in static devices and in dynamically-reconfigurable ones.
Integrated quantum memories, discussed in Section 7, are very important
components that received a significant boost by the adoption of FLM for rare-
earth-doped crystals. Finally, in Section 8 we discuss the perspectives of FLM
in combining single-photon detectors with integrated photonic circuits.

##  II Integrated quantum photonics

Photons are very promising carriers of quantum information, in fact they can
operate at room temperature and can propagate for long distances with very
limited interactions with the environment, thus preserving the quantum state
for a long time. On the other hand, their main limitations are that they can
be lost along their propagation and that they are mainly suitable for linear
manipulation (until strong interactions between individual photons become easy
to implement chang14 ).

Integrated quantum photonics is the synergic combination of quantum photonics
with integrated optics Politi08 ; wang20 . It enables dramatic improvements
with respect to bulk optic quantum experiments in terms of compactness,
scalability, control and phase stability. In addition, integrated quantum
photonics enables a seamless connection with optical fibers yielding robust
and alignment-free devices that can be field-deployable.

The importance of integrated quantum photonics is evident for quantum
communications where their suitability as ’flying qubits’ is unique, but they
are also finding increasing importance in all other quantum information tasks.
Recent work has shown the possibility to simulate vibrational quantum dynamics
of molecules in integrated photonic circuits sparrow18 . Quantum computation
hardware has also been demonstrated in integrated photonics, both at the level
of probabilistic two-qubit quantum gates Politi08 ; Crespi11 ; zhang19 ;
zhang21 , as well as complex reconfigurable linear photonic processors
Carolan15 ; Taball19 . In particular, different variants of measurement-based
quantum computation hold promise for fault-tolerant photonic quantum computers
takeda19 ; bourassa21 .

It is worth noting that even when photons are not used as qubits, they are
still relevant actors in the quantum architecture, for example in the read out
of the state of the quantum system, being it an ion, an atom or a
superconducting circuit; also in this case integrated photonics can play an
important role mehta16 ; leung19 .

###  II.1 Architecture for a universal integrated quantum photonic system

Figure 1: A quantum photonic system is typically built of three blocks. A
first block generates a quantum state $\left|\Psi\right\rangle$ of one or more
photons, which is useful for further elaboration. A second block manipulates
the state, most often by means of a linear unitary transformation $U$. The
final block performs the detection, which equals to measuring the projection
on the elaborated state on one or more quantum states
$\left|\Phi\right\rangle$.

For most, if not all, applications, a quantum photonic system can be
schematized into three main blocks (Fig. 1): the block for the generation of
single photons or more complex quantum states of light, the block for the
manipulation of the information encoded in such quantum states (where the
actual quantum protocol is implemented) and a final block for the measurement
through photodetectors. All three block are undergoing a process of
miniaturization and integration to improve their portability and scalability.
In particular, a significant effort has been devoted to the integration of the
second block, where the information is manipulated according to the quantum
protocol.

A current limitation of quantum photonics is that only linear manipulation of
the quantum state is typically viable, although nonlinearities can be
simulated with measurements of ancillary photons in linear circuits knill01 .
Nevertheless, many tasks can be implemented with linear operations, as well as
reaching a computational hardness Aaron11  that recently led to a quantum
advantage demonstration Zhong20 . In particular, the time evolution of a
quantum system under a given Hamiltonian gives rise to a unitary
transformation of the initial state that can be accurately mapped in a linear
photonic circuit. Thanks to the fine control of the photonic circuit
properties, quantum devices implementing specific unitary transformations can
be fabricated, with the possibility of having different devices for each
quantum manipulation task. However, the main trend nowadays is to produce
fully reconfigurable photonic circuits to implement multiple, arbitrary
unitary transformations in the same circuit.

A final comment on the overall architecture, points to the two current
alternatives to combine the three blocks in a complete quantum system. One
possibility is to combine all of them monolithically on a single substrate
with significant advantages in the long-term for scalability and mass
production, but with greater technical difficulties in optimizing all the
functionalities on the same material. A second possibility is the modular
approach, where each block is developed and optimized in a dedicated module
and then the different modules are optically interconnected. This may prove as
an advantageous approach in the short term as it can harvest immediately all
the results achieved on the different functionalities without having to worry
about how to transfer them on the same technological platform. On the other
hand, assembly of these modular systems may be complicated and not so easily
scalable to very complex devices.

###  II.2 Available integrated photonic platforms

Miniaturization of quantum photonic devices in integrated optics can leverage
from all the work done in classical photonics for other applications.
Different integrated photonic platforms have been developed and each of them
is being explored for its potential in quantum information applications. Each
platform has advantages and disadvantages and thus no clear winner is yet
established in integrated quantum photonics. Silicon photonics silverstone14 ,
silicon nitride Taball19 , and silica on silicon Politi08  are well-
consolidated platforms, listed according to a decreasing level of
miniaturization. Nonclassical single photon sources can be embedded on-chip
exploiting nonlinear four-wave-mixing processes silverstone14 ; harris14  and
superconducting nanowire detectors have been integrated on a few of these
platforms mattioli20 . Reconfigurability of the photonic circuits is mainly
achieved with thermal phase shifters, providing stable but slow phase control.
Lithium niobate is another interesting platform as it provides second order
nonlinearity and electro-optic properties. Photon sources based on parametric
down conversion have been demonstrated on this material krapick13 , as well as
very fast phase control bonneau12 . This last platform is also gaining
significant interest in a new form, i.e. lithium niobate on insulator (LNOI),
where the above properties are combined with an increased miniaturization
capability boes18 . A further integrated photonic platform is femtosecond
laser micromachining (FLM) in transparent materials gattass08 ; osellame12 ;
meany15 . Although less extreme in terms of device miniaturization if compared
to lithographic processes, FLM is a powerful microfabrication technology which
shows the distinctive features of three-dimensional capabilities, versatility
in terms of kind of processable materials, and rapid prototyping. In fact, low
costs and fast fabrication turnaround times of FLM often allow designing the
devices by an iterative process of fabrication and characterization, rather
than relying on complex numerical simulation. This platform has enabled many
breakthroughs in quantum photonics and it will be discussed more in details in
the following sections.

##  III Femtosecond laser micromachining

In FLM, femtosecond laser pulses are exploited to machine transparent
dielectric materials with high spatial resolution in the three dimensions. To
the purpose, the femtosecond laser beam is focused by suitable optics (e.g. an
aspheric lens or a microscope objective) on the surface or into the bulk of
the transparent material (Fig. 2a). The high peak intensity, enabled by the
combination of short pulse length and tight focusing, triggers nonlinear
absorption processes in the transparent material, which can result in a
permanent and localized modification around the focal region. Three-
dimensional machining is achieved by translating the substrate with respect to
the laser focus during irradiation, typically by means of high-precision
translation stages.

The microscopic modification processes are complex, and originate from an
intricate interplay among different phenomena, which include electronic
excitation or relaxation, and thermal effects gattass08 . Indeed,
modifications can be of different nature, encompassing refractive index
variations, chemical/structural changes, ablation and creation of micro-voids,
depending on the specific material and of on the adopted irradiation
parameters. Generally, for increasing pulse energy, one observe the passage
from a regime of smooth modification of the optical properties, to the
creation of more invasive structural changes, ending with cracks and voids if
the deposited energy is too high.

It is also noted that, while the nonlinear absorption phenomena that trigger
the modification process occurs well confined in the focal region, the size of
the modified region can be quite larger, because of the influence of thermal
diffusion or accumulation eaton08 .

We will now discuss in more details the processing portfolio of FLM, from
waveguide writing to 3D structuring, to two-photon polymerization, and will
then conclude emphasising how the specific features of FLM can be beneficial
for integrated quantum photonics.

###  III.1 Waveguide writing

The possibility of producing positive refractive index changes in glass by
means of FLM for writing optical channel waveguides has been originally
discovered by Davis et al. in 1996 davis96 . Since then, numerous research
groups worldwide have extensively worked for improving the guiding features of
laser-written waveguides in many transparent materials, ranging from various
kind of glasses, to dielectric crystalline substrates osellame12 ; chen14 .

In the femtosecond-laser direct-writing process, waveguides are defined by
translating the substrate at constant speed with respect to the laser focus,
according to arbitrary three-dimensional paths. The optical performance of the
fabricated waveguides depends in a non-trivial way on the irradiation
parameters and on the specific substrate. In general, a higher deposited
energy (e.g., via a lower translation speed, a higher pulse energy or a higher
repetition rate) is typically associated with a larger waveguide cross-section
and a higher refractive-index difference of the modified region with respect
to the pristine material. Typical waveguides fabricated by FLM have a
transverse cross section of few $\mu$m2 and show a refractive index change
between core and cladding in the order of $10^{-2}-10^{-3}$, which reflects in
their excellent connectivity with standard optical fibers.

Waveguide inscription in glass is performed by writing directly the waveguide
core, i.e. producing a positive refractive index change with the laser
irradiation (type I waveguide, see Fig. 2b,c). The most employed substrates,
especially for integrated quantum photonics applications, are pure fused
silica and commercial borosilicate glasses, e.g. Corning EagleXG and Eagle2000
or Schott AF32. Single mode waveguides have been fabricated in these materials
covering the whole visible and near infrared spectrum of light, from 400 nm,
up to the telecom C-band, demonstrating propagation losses in the range 0.1-1
dB/cm and negligible bending losses for radii above 30 mm will02 ; day21 ;
ferna20 . The most favorable inscription regime for the processing of pure
fused silica is with low repetition rates, from 1 kHz to 100 kHz, and low scan
speeds (up to few mm/s). Single-scan waveguides fabricated in fused silica
typically present a strongly elongated cross section and a moderate degree of
modal birefringence, up to 10-4. Multiple and partially overlapped scans can
be employed for engineering the waveguide cross section, thus producing more
circular intensity profiles of the guided mode nasu05 . For the fabrication of
waveguides in borosilicate glasses, instead, higher repetition rates (500 kHz
to 5 MHz), and scan speeds from 10 mm/s to 100 mm/s are preferred. In this
regime, thermal accumulation effects importantly contribute to the material
modification eaton05 ; eaton08 , resulting in a more symmetric waveguide cross
section and low birefringence (in the order of 10-5), mostly given by the
residual mechanical stress accumulated in the substrate during the
fabrication. Recently, it has been demonstrated that a thermal annealing
treatment performed on borosilicate waveguides after fabrication improves the
optical mode confinement, allowing for radii of curvature of 10 mm arriola13 ,
and quench waveguide birefringence almost completely (in the order of 10-6),
thus giving rise to fully polarization insensitive integrated photonic
circuits Corr18 .

Concerning the waveguide writing in transparent dielectric crystals, the most
commonly adopted approach is that of inscribing by laser irradiation two
parallel tracks of damaged and amorphized material, separated by a distance
from 10 $\mu$m to 30 $\mu$m, which form the waveguide cladding. Waveguides
fabricated in this way are called type II waveguides, and have been
demonstrated for a great variety of crystals, including many rare earth doped
matrices, several nonlinear crystals and diamond chen14 . More complex
cladding-irradiation strategies have also been explored, with the aim of
improving the vertical confinement of the light, or for creating photonic
band-gap guiding structures (type III waveguides) rodenas19 . Finally, another
possibility for fabricating channel waveguides in crystals by FLM consists in
fabricating two parallel ablation trenches at the crystal surface for
producing a guiding region between them (Type IV waveguide) chen14 . Instead,
the creation of a positive refractive index change in crystals, usually
associated to a local material densification, is very hard to achieve with
direct laser irradiation. Therefore, the demonstration of type I waveguides
has been successful only in a limited number of cases, e.g. lithium nibate
atzeni18 , yttrium orthosilicate Seri18  and potassium dihydrogen phosphate
huang15 .

Crystal waveguides fabricated by FLM typically show worse optical properties
than what attainable in glass, suffering from higher propagation losses (¿ 1
dB/cm) and lower light confinement, with guided-mode field diameters ranging
from 10 $\mu$m to 20 $\mu$m. This holds especially true in the case of type
II-IV structures, preventing the use of these kinds of waveguides in curved
geometries. Nevertheless, the possibility of writing optical waveguides in
crystals remains of very high scientific interest, including for integrated
quantum photonics applications, because they allow to take advantage of the
peculiar physical properties that many transparent dielectric crystals offer.

Figure 2: Graphical summary of the capabilities of FLM. Irradiation of a
transparent substrate with a focused femtosecond laser beam, to produce buried
modified tracks, is represented pictorially in (a); boxes report examples of
the different available fabrication processes (b-g). For direct waveguide
writing, microscope pictures of FLM waveguides in two different materials are
reported: (b) Single-mode waveguide operating in the visible, realized in
fused silica substrate by a single femtosecond laser scan at 50 kHz pulse
repetition rate (authors’ own work, scalebar is 10 $\mu$m); (c) Single-mode
waveguide operating at 1550 nm, inscribed in Eagle2000 (Corning Inc.) alumino-
borosilicate glass by multiple overlapped laser scans at 5 MHz, followed by
thermal annealing (adapted from Ref. arriola13 , scalebar is 10 $\mu$m). For
3D microstructuring, cross-sections of different excavated structures,
produced by water-assisted laser ablation in EagleXG (Corning Inc.) alumino-
borosilicate glass, are reported (both adapted from Ref. Cecca20 ): (d)
Microtrenches realized on both sides of an optical waveguide (scalebar is 200
$\mu$m); (e) U-shaped hollow microstructure, surrounding a thin glass beam
where an optical waveguide has also been inscribed (scalebar is 100 $\mu$m).
For two-photon polymerization, pictures taken with an electronic microscope of
fabricated microstructures are shown: (f) Crossed-arc polymeric waveguides,
each crossing contains one pre-characterized single-photon emitter (adapted
from Ref. shi16 , scalebar is 20 $\mu$m); (g) 3D structure containing several
key photonic elements, such as waveguides, couplers and microdisc resonators
(adapted from Ref. schell2013 , scalebar is 10 $\mu$m).

###  III.2 3D microstructuring

Femtosecond laser pulses are capable of machining the surface of the
dielectric, transparent substrate with ablation processes, which are driven by
the same nonlinear absorption exploited to inscribe waveguide tracks in the
bulk. By focusing the laser beam on the top surface of the substrate it is
possible to drill precise holes, or excavate microtrenches. If low pulse-
repetition rates are adopted, the ablation process is mainly non-thermal and
may yield high resolution and no damage of the surrounding region. However,
during the ablation process debris can deposit close to or just upon the
ablated region, which makes it difficult to realize clean microstructures. In
addition, both the presence of the debris and the presence of the ablated
structure itself modify the focusing conditions while the ablation proceeds
deeper: this limits the depth and the achievable complexity of the realized
structures.

An alternative approach is to perform laser ablation with the substrate
immersed in water, or simply with water wetting the surface to be machined,
and starting from the bottom surface instead of the top one Li01 . In this
way, while the ablation process proceeds towards the middle of the substrate,
the laser beam always propagates through the clean substrate volume, without
being affected by the microstructure that is being formed. In addition, the
presence of water facilitates debris removal and makes it possible to excavate
clean microchannels, where water can flow. This water-assisted laser ablation
technique has enabled to fabricate microfluidic channels with an articulated
path, drawn in the three-dimensions inside the substrate Hwang04 . Hollow
chambers connected to the surface only by means of small passages An06 , or
even microthreads in glass Dega17  have also been reported.

A water-immersion objective can be used conveniently to perform, in the same
session, both the inscription of waveguides and the fabrication of hollow
microstructures by ablation. Only the irradiation parameters, such as pulse
energy and translation speed, need to be changed between one kind of
processing and the other, without the need of realigning the sample.
Waveguides and microstructures are in this way perfectly positioned one
relative to the other. Using this method, mechanical microcantilevers have
been machined in borosilicate glass, with embedded optical waveguides, to
realize optical-intensity modulators and switches working at a frequency of
tens of kilohertz Spagn20 . In addition, deep microtrenches and suspended
glass structures have been incorporated in reconfigurable waveguide circuits,
controlled by thermo-optic phase shifters (see also the discussion in Section
5.2). In this case, the hollow microstructures guide the heat diffusion
processes inside the substrate and enable a highly efficient thermal control
of the circuit Cecca20  (see Fig. 2d,e).

A further, widely adopted method to perform femtosecond laser-assisted glass
microstructuring is the so-called FLICE technique (femtosecond laser
irradiation followed by chemical etching), which exploits the enhanced
sensitivity of laser-irradiated regions to chemical etching, in certain
materials Marci01 . According to this method, tracks are irradiated in the
bulk glass, terminating at one of the facets of the sample. The glass sample
is later immersed in a chemical etching solution, such as an aqueous solution
of hydrofluoric acid or potassium hydroxide. The etching agent preferentially
attacks the irradiated region, giving rise to hollow microstructures along the
irradiated lines Sugi05 ; Hnato06 .

As mentioned, this technique does not work well in all kinds of substrate, but
preeminently in specific materials such as fused silica Marci01 ; Hnato06 . or
photosensitive glass Sugi05  (e.g. Schott Foturan). In these substrates the
high etching selectivity enables to machine three-dimensional microstructures
with complex shapes. In particular, femtosecond-laser written waveguides with
reasonably low losses can also be fabricated in fused silica. It becomes thus
possible to realize, in the same irradiation step and with a simple adjustment
of the irradiation parameters, both optical waveguides and tracks that will be
etched in a subsequent process, forming microfluidic channels that will be
intrinsically aligned with the waveguides Osell07 . This technique have
allowed to demonstrate optofluidic devices for sensing or other biological
applicationsBellini10 ; Crespi10 ; Bragheri12 ; Crespi12 , and even to
integrate fluidic functionalities within the cladding of silica optical fibers
Haque14 .

###  III.3 Two-photon polymerization

In the previous Sections we have seen how FLM can modify the properties of a
transparent material (particularly its refractive index) or can selectively
remove arbitrary portions of the material. Here we will see that FLM can also
be used for additive manufacturing tasks through a process known as two-photon
polymerization (2PP) lee06 . The fundamental physical mechanism is again based
on the exploitation of focused ultrashort pulses to trigger a nonlinear
absorption process. However, this time the nonlinear absorption is performed
inside a negative tone photoresist that absorbs in the UV. Using a near-
infrared femtosecond laser source, a two-photon absorption process triggers a
local photopolymerization of the resist. Moving the focus inside the resist it
is thus possible to polymerize 3D structures of arbitrary shape (see Fig.
2f,g), while the unirradiated resin is removed in a subsequent developing
step. The nonlinear dependence of the absorption process on the intensity
profile, as well as the fact that photopolymerization happens only above a
given threshold of absorbed energy density, make it possible to achieve sub-
diffraction-limit feature sizes with a careful tuning of the laser fluence
tan07 . In addition, it is a maskless process that can be easily combined with
preliminary optical inspection of the sample, enabling the possibility of in-
situ lithography of photonic structures in specific locations where, e.g.,
single photon emitters have been found and characterized shi16 . Finally,
although 2PP is applied to photosensitive resins, while the previous
micromachining processes regard glasses and crystals, all of them can be
implemented on the same femtosecond laser micromachining equipment, by
carefully designing the process workflow Wu2014 .

###  III.4 Advantages of FLM for integrated quantum photonics

It is evident from the previous discussion that FLM has many unique features
with respect to all the other integrated photonic platforms. Such features
have clear advantages also for quantum photonic applications.

Let’s first discuss the versatility of the process. Not only it encompasses
transformative, subtractive and additive technologies in the same tool, but
those technologies can also be easily combined to produce complex 3D quantum
devices with a very limited number of processing steps as compared to
photolithographic technologies. In addition, the versatility also regards the
different materials that can be processed with FLM. It has been shown that
almost all materials have a suitable processing window that allow the
waveguide writing process. This flips the usual way of thinking in designing a
photonic component, i.e. from how to integrate a given functionality in the
material of the integrated photonic platform, to finding the processing window
to produce an integrated photonic circuit in the best material for that
functionality. Naturally, this approach has a perfect match with the modular
architecture of the quantum system described in Section 2.1, where one can
envisage the optical interconnection of separately optimized components
without the constraint of a common substrate material.

Focusing more specifically on the properties of the laser written photonic
circuits as compared to the other platforms, we should first emphasize that
FLM has the unique possibility of writing 3D photonic circuits, while the
other technological platforms are mainly confined to 2D layouts. This feature
can be exploited in devising more compact devices or in removing the usual
limitation of first-neighbour interaction in designing quantum protocols on a
photonic chip.

Laser-written waveguides have mode sizes and refractive indices very close to
those of optical fibers, therefore extremely low-loss edge coupling can be
easily achieved. This is an important feature that further supports a modular
architecture. Not only coupling losses are low, but also propagation losses
are typically around 0.1 dB/cm or better. The downside of the similarity of
the waveguide confinement to that of an optical fiber is the limited minimum
radius of curvature that can be implemented without additional losses. This
brings the miniaturization capability of FLM circuits at the level of the
silica-on-silicon platform, but significantly worse than most of the
alternative ones. Another important advantage of the FLM platform is the low
birefringence of the written waveguides and the possibility to produce
polarization insensitive couplers. This allows the manipulation of the quantum
information encoded in the photons irrespectively of their polarization state,
while other platforms require a fixed polarization for proper operation. This
is a great simplification in the global system, in particular in the modular
architecture, where it may be complicated to preserve the polarization state
in the optical interconnections.

Finally, all the versatility that we have emphasized has a cost in terms of
mass-production capability. In fact, FLM is a serial writing technique and
cannot compete with parallel photolithographic microfabrication for very large
volume of devices. The gap is progressively reducing thanks to the much
smaller number of steps required to produce a complete photonic circuit, to
the increasing processing speeds that have now reached several cm/s, and to
the various strategies that are being developed to parallelize the irradiation
process Pospiech2009 ; Mauclair2009 ; Zandrini2019 ; Manousidaki2020 . In
addition, mass production is not yet an issue in quantum technologies, since
potentially commercial devices are still under development, whereas the
capability of providing custom-tailored components that can be prototyped
rapidly and at low cost is a very relevant feature.

In the following we will discuss several examples where all these advantages
have been exploited.

##  IV Single photon sources

Nonclassical states of light are the core quantum resource that lie at the
heart of quantum photonic technologies. Most of current experiments involving
FLM integrated photonic circuits rely on external single photon sources of
various kinds, from spontaneous parametric down-conversion sources Crespi13a
to quantum dots anton19  or defect-based white20  sources. This is made
possible by the excellent connectivity of laser-written devices with standard
optical fibers. However, the direct on-chip generation of quantum states of
light is a very important functionality, subject of extensive research
activity by several groups for a twofold motivation: on the one hand,
generating quantum light directly inside the photonic circuit allows
eliminating the coupling losses that unavoidably occur when interfacing a
device with an external source; on the other hand, waveguide-based single
photon sources permit quantum state engineering with multiplexed parallel
sources in an interferometrically stable and scalable fashion, for creating
complex quantum states of light which are out of reach for bulk setups.

Integrated single photon sources can be classified in two distinct categories
eisa11 : i) probabilistic sources, where a bright pump beam is coupled to a
waveguide fabricated in a nonlinear medium, for the generation of photon pairs
either by spontaneous parametric down conversion (SPDC) or spontaneous four
wave mixing (SFWM) processes; ii) deterministic sources, which exploit the
fluorescence of single quantum emitters, e.g. individual quantum dots or point
defects in crystals. FLM contributed to the development of both types of
integrated sources, by providing the necessary circuitry for manipulating the
pump light and the generated photons, by fabricating the nonlinear waveguides,
and also by creating the emitting defects with a deterministic control of
their position in the host matrix.

Figure 3:  (a) Schematic of the integrated single photon source presented in
atzeni18 . A first reconfigurable glass chip is used for pump splitting. The
PPLN chip is used for photon pairs generation. The third stage can be
interchanged between device 3a and 3b in order to engineer different type of
biphoton states. (b) Results of the quantum state tomography performed on the
biphoton states produced by the device presented in atzeni18 , when set to
generate the polarization-entangled $|\phi^{-}\rangle$ state. Reported
fidelity with the theoretical state is 93 %. (c) Schematic of the 2-photon
polymerization process employed in schell2013  for fabricating integrated
nanophotonic devices with embedded nanodiamonds. (d) Fluorescence map obtained
from a 5 x 5 square lattice of NV centers fabricated by FLM in chen19 .
Lattice parameter is 2 $\mu$m. (e) Histogram showing the second order
autocorrelation results obtained for the fluorescence light of all NV centers
shown in panel (d). In the inset, a whole $g^{(2)}(t)$ trace measured for a
single defect is shown. (f) Transverse cross section and near field image of
the guided mode of the type II waveguide fabricated in diamond and presented
in hadden18 . (g) Photoluminescence image of the longitudinal profile of the
same waveguide as in panel (f), where it can be clearly noticed the presence
of an individual NV center localized within the core. The panels of this
figure contain pictures adapted from Refs. atzeni18 , schell2013 , chen19  and
hadden18 .

###  IV.1 Photon generation based on nonlinear phenomena in waveguides

Probabilistic sources are relatively easy to implement. However, they suffer
from the drawback of producing photons randomly distributed in time. This
limits their employment for creating complex quantum states involving a large
number of photons. Nevertheless, the possibility of exploiting heralding or
post-selection mechanisms makes this kind of sources highly appealing for
applications. In addition, having the pump beam tightly confined over the
whole waveguide length helps in increasing the overall efficiency of the
generation process, thus resulting in enhanced brightness of the source
tanzilli01 .

The first demonstration of heralded single photon generation in a FLM-written
waveguide is due to Spring et al. in 2013 spring13Source . In this experiment
the authors fabricated a 4 cm long waveguide in fused silica, and exploited
the weak glass $\chi^{(3)}$ non-linearity for generating non-degenerate photon
pairs by SFWM, with the signal and idler photons at the wavelengths of 676 nm
and 790 nm respectively. Notably, the waveguide was fabricated by shaping the
writing beam through adaptive optics elements in order to increase the
ellipticity of the waveguide cross section and to enhance the value of
waveguide birefringence up to $10^{-4}$. This allowed to phase-match the SFWM
process at wavelengths where the photonic noise generated by spontaneous Raman
scattering of the pump in the silica substrate becomes negligible. The
measured purity of the quantum states reached 0.86 without performing spectral
filtering at the waveguide output, and this value was limited by residual
birefringence fluctuations along the waveguide, estimated as $\delta(\Delta
n)<3\cdot 10^{-6}$. In 2014, a different integrated single photon source,
based on photonic circuits written in borosilicate glass, was proposed for the
generation of spatially multiplexed, heralded single photons by SPDC meany14 .
In this case, the nonlinear stage was made with a periodically poled lithium
niobate (PPLN) chip, fabricated by soft proton exchange, containing four
identical waveguides. A laser-written 1 x 4 beam divider was directly butt-
coupled to the PPLN chip input, in order to pump coherently the four PPLN
waveguides with a single laser source. The generation process was phase
matched for producing non-degenerate photon pairs at the wavelengths of 1550
nm (signal) and 1312 nm (idler). A second FLM-written photonic chip was
cascaded after the generation stage, containing four dichroic directional
couplers, capable of separating the signal and the idler photons in distinct
spatial modes with an average extinction ratio of 10 dB. The chip was then
connected to an external filtering stage, in order to suppress the pump light
and for increasing the photons purity. Finally, a bulk system of fast optical
switches was used to route the generated photons to a single spatial mode, and
to demonstrate a fourfold enhancement of the generation rate with respect to a
single source. A similar hybrid approach, where a lithographic PPLN chip is
combined with FLM-written borosilicate circuits, was used in a subsequent
experiment in 2016, for the demonstration of an integrated source of
indistinguishable photon pairs in the telecom C-band verg16 . A first glass
chip was employed to split the pump light and route it to two PPLN waveguides,
for generating pairs of non-degenerate photons. A second glass chip was
cascaded afterwards, containing the required elements for separating the
signal (1560 nm) and the idler (1310 nm) photons, and for engineering the
quantum state of the signal photon pairs. In particular, a thermally
reconfigurable Mach-Zehnder interferometer was used as a variable beam
splitter, in order to combine the signal photons, and produce either a
separable state $\psi=|1\rangle_{1}|1\rangle_{2}$ or an entangled state in the
photon number basis of the form
$\psi\propto|2\rangle_{1}|0\rangle_{2}-|0\rangle_{1}|2\rangle_{2}$ (a two-
photon NOON state) depending on the Mach-Zehnder setting and by post-selecting
the cases where the photons are generated simultaneously in the two PPLN
waveguides. Finally, in another experiment from 2018, a hybrid glass-PPLN-
glass device was used for the on-chip generation of different quantum states
of light, based on the creation of degenerate pairs of photons at 1560 nm by
SPDC atzeni18 . A modular approach was adopted, where the second glass chip
after the PPLN waveguides could be exchanged, in order to engineer different
two-photon quantum states, ranging from product and NOON states, to
polarization-entangled pairs (see Fig. 3a,b). In this case, all components
have been entirely fabricated by FLM. In particular, two identical type I
waveguides have been written within the bulk of a z-cut PPLN sample at the
depth of 100 $\mu$m by employing a multiscan approach. This allowed to finely
control the waveguide cross section and obtain single mode guidance at both
the pump (780 nm) and photons wavelengths. In addition, the two waveguides
exhibited identical spectral behavior, as measured with second harmonic
generation experiments performed with classical light.

###  IV.2 Photon generation based on induced defects in diamond

Among the different types of individual quantum emitters currently studied as
deterministic sources of quantum light, single negatively-charged Nitrogen-
Vacancy (NV) centers, i.e. optically active point defects that form in diamond
when a substitutional nitrogen atom bounds together with a carbon vacancy, are
particularly appealing. In fact, they show a very high room-temperature
radiative quantum efficiency upon optical excitation, as well as a short decay
time of the excited state. The antibunched nature of single NV center
fluorescence has been widely demonstrated kurts00 , and this makes this system
a very attractive candidate to realize deterministic single photon sources.

The first attempt of integrating an NV center source within a laser-written
device is due to Schell et al. in 2013 schell2013 . In particular, the authors
fabricated a set of 3D arch-shaped waveguides and microdisc resonators using
the two-photon polymerization technique (see Fig. 3c), employing an acrylate
polymer photoresist (PETTA) mixed with an ethanol-based nanodiamonds
suspension (mean diamond diameter of 25 nm). Such nanodiamonds naturally
contained NV centers, which remained photostable even after the laser
irradiation for the FLM process, and resulted dispersed within the volume of
the photonic devices. A confocal microscope setup was then used for exciting
individual defects. The analysis of the fluorescence emission, collected at
the waveguides output and fed into a Hanbury-Brown-Twiss interferometer,
clearly confirmed its single-photon nature. In a subsequent experiment, the
same authors showed that this approach is compatible also with a waveguide-
based excitation of the NV centers shi16 . In this case, a peculiar 3D
crossed-waveguide coupler configuration was employed, in order to separate the
excitation mode from the collection mode, and suppress the photonic noise
created in the waveguide by Raman scattering and from fluorescence of the
polymerized photoresist. Remarkably, in this experiment the photonic devices
have been fabricated around pre-characterized defects, selecting those with
best quantum emission features.

FLM can be used also for the direct writing of NV centers at the surface
kono17  and inside the volume of bulk diamond liu13 ; pimenov16 ; chen17 ;
hadden18 ; chen19 . In particular, the first demonstration of this capability,
together with the accurate characterization of the single photon nature of the
fluorescence emitted by the fabricated defects, is due to Chen and co-workers
chen17  in 2017. They employed single pulse irradiation followed by a 1000 ∘C
thermal annealing (few hours duration) of the whole sample for creating single
NV centers per irradiated point with $\approx$ 45 % yield. This process
allowed inscribing high-quality single defects with an in-depth positioning
accuracy of 700 nm and a transverse positioning accuracy of 200 nm. In a
subsequent work chen19 , this inscription method has been improved by
substituting the thermal annealing process with a second laser irradiation
step, in order to heat locally the diamond substrate at the NV center
location. In addition, the FLM setup was modified by adding an in-line
confocal microscope, exploiting the fabrication microscope objective also for
collecting in real time the fluorescence of the defects during the heating
step, thus providing an online feedback for tailoring the irradiation time for
obtaining high quality single NV centers. In this way, the authors
significantly improved the defect fabrication yield, up to 96 %, and the
positioning accuracy (33 nm in-plan accuracy and 200 nm in-depth accuracy). In
Fig. 3c the fluorescence traces from a $5\times 5$ matrix of NV centers
fabricated in this way are shown. Second order autocorrelation measurements
resulted in $g^{(2)}(0)<0.2$ (see Fig. 3e) for all of them, confirming the
antibunched nature of the emission. In addition, the authors have shown that
such defects can be arranged in large 3D matrices, containing up to 2000 NV
centers. Beside quantum light generation, such defects can also be employed as
long lived spin qubits, with a spin excitation coherence time greater than 500
$\mu$s step19 . The direct FLM writing of optically active single defects is a
particularly interesting method, since it has been demonstrated that it can be
applied to other materials besides diamond, including silicon carbide castel18
, cubic boron nitride buividas15  and gallium nitride saleem18 .

Finally, ultrafast laser writing is also suitable for the inscription of
buried type-II and type-III optical waveguides in diamond courvo16 ; sotillo16
(see Fig. 3f). Interestingly, in 2018 Hadden et al. hadden18  have shown that
waveguides and NV centers writing by FLM are two complementary techniques that
can be combined for the inscription of the NV centers directly coupled with
the waveguide mode. In particular, they first fabricated a type II optical
waveguide in the bulk of a diamond sample, and then inscribed a set of NV
centers, employing the same procedure presented in chen17 , precisely
localized within the waveguide core (see Fig. 3g). It was then shown that the
thermal annealing step did not alter the waveguide properties, and that the
waveguide could be used both for exciting the NV center and for collecting its
fluorescence emission. These results proved that FLM has a significant
potential in developing diamond-based integrated quantum photonics platforms.

##  V On-chip manipulation of quantum states of light

Integrated photonic circuits are made of straight or bent waveguide segments,
directional couplers and integrated waveplates. Combinations of these elements
indeed allow to perform a unitary transformation on the state of the injected
photons (neglecting photon losses or post-selecting output states with the
same number of photons as the input).

From a physical point of view, the operation of these devices is based on a
combination of classical and quantum interference of photons. A striking
advantage of the adoption of an integrated platform lies in its inherent
interferometric stability, which together with the miniaturization properties,
makes it possible to realize optical circuits that would be too large to
assemble, or very hard to operate, with bulk components on an optical table.

In the following we will review the main achievements in the on-chip
manipulation of quantum states, which have been accomplished by FLM waveguide
circuits. We will broadly distinguish between static and dynamically-
reconfigurable photonic circuits. The former cannot actively modify their
function, which is thus fixed upon fabrication. The latter ones, on the other
hand, contain components whose operation is governed by external signals (e.g.
electrical currents), and can actively change in time the performed unitary
transformation.

###  V.1 Static photonic circuits

Manipulation of path-encoded photonic qubits, which essentially requires to
interfere identical photons on many different paths, comes natural in the
integrated setting Politi09 , and is indeed perfectly possible with
femtosecond-laser-written devices. Shortly after the first demonstration of
the operation of a silica-on-silicon optical chip in the quantum regime
Politi08 , it was shown that quantum interference could be reliably observed
also in femtosecond-laser written waveguide circuits Marsh09 .

Static circuits, written by femtosecond lasers, have proved capable to prepare
and characterize high-order single-photon entangled states on many paths
Grafe14 , to produce two-photon path-encoded Bell-states Li20 , or to
efficiently perform quantum state tomography of single and multi-photon states
involving several optical modes Titch18 . By interfacing a waveguide Mach-
Zehnder interferometer with an etched microchannel, in a single optical chip
fully fabricated by femtosecond laser pulses, it was possible to perform two-
photon quantum interferometry and experimentally retrieve the concentration of
biological solutions Crespi12 .

Special multi-port interferometers Spagn13t ; Spagn13b ; Tillm15 ; Crespi16 ;
Viggia18njp ; Viggia18sb ; munz21  have allowed to investigate fundamental
aspects of multi-photon quantum interference. In particular, symmetric multi-
ports Crespi16 ; Viggia18njp ; Viggia18sb ; munz21  were employed to
demonstrate experimentally massive effects of quantum destructive
interference, which suppress many of the possible output states; these
integrated devices could also find application in assessing the quality of
multi-photon sources.

It is worth noting that, in an integrated platform, continuously-coupled
waveguide arrays allow to implement interactions among optical modes that have
no analogous in the bulk realm Spagn13t ; Grafe14 ; Titch18 . In addition, the
FLM technology yields the unique capability of inscribing circuits with three-
dimensional layouts, which further enhances stability and compactness. In
fact, waveguides can pass one over the other, if needed, without intersecting
Meany16  (see Fig. 4a), and circuit architectures, impossible to realize with
a planar technology, are made feasible Grafe14 ; Crespi16 ; Viggia18njp ;
Viggia18sb . Interestingly, special three-dimensional arrangements of
directional couplers have been reported, inspired to the Cooley-Tukey Fast-
Fourier-Transform algorithm Cooley65 ; Barak07 ; Crespi16 ; Viggia18njp ;
Viggia18sb  (see Fig. 4b): such architecture can be used to realize a
significant class of linear optical networks with a substantial reduction in
the number of needed components, and notable resilience to losses and
fabrication tolerances Flam17 .

In addition, static multi-port interferometers, fabricated by femtosecond
laser pulses, have played a significant role in the recent years as hardware
for Boson Sampling experiments. Boson Sampling, a kind of experiment conceived
by Aaronson and Arkhipov in 2011 Aaron11 , consists in sampling from the
output distribution of multiple interfering bosons, evolved along a random
unitary transformation. Such task is of interest because it is deemed
intractable for classical computers as the system size scales up; thus, it can
provide a route to demonstrate a quantum experiment that is hard to simulate
with classical resources, showcasing a kind of quantum advantage Zhong20 . In
the photonic version, Boson Sampling consists in sampling the output
distribution of multiple photons that have propagated in a large random
interferometer Brod19 .

FLM indeed provided the photonic hardware (in detail, five-mode integrated
interferometers) for two Tillm13 ; Crespi13b  of the four Tillm13 ; Crespi13b
; Broome13 ; Spring13  first-time demonstrations of Boson Sampling experiments
in 2013. Following experiments, which investigated different aspects of the
Boson Sampling problem, harnessed fetmosecond-laser-written interferometers
with up to 13 optical modes Spagn14 ; Benti15 ; Giorda18 ; Agre19 . Note that
an interferometer that realizes a random arbitrary unitary transformation may
not be trivial to design in practice. Theoretical schemes are known, by Reck
Reck94  and Clements Clem16 , which implement an arbitrary unitary by
cascading directional couplers with different power-splitting ratios, and
different phase shifts in between them. However, in a planar network of
waveguide components, changes in the coupler geometry (to modulate the
splitting ratio) will produce changes also to the length of the
interconnections, thus modulating also the phase shifts, making it difficult
to control independently all the parameters. Of note, Ref. Crespi13b
demonstrated a novel design technique for the optical circuit to overcome this
problem, by exploiting the unique three-dimensionality given by femtosecond
laser waveguide inscription (see Fig. 4c). Different phase shifts are produced
in the circuit by properly deforming the S-bends that connects the cascaded
couplers. Instead, the splitting ratios are modulated by rotating one arm of
the directional coupler out of the plane, thus making the two waveguides
closer or farther in the interaction region without changing the length of the
connecting waveguides.

In all the experiments described above, photons have fixed polarization
states, and the only degree of freedom that the integrated circuit is
manipulating is in which spatial mode the photon is propagating. Actually,
femtosecond-laser-written waveguides conceal a more peculiar potential for the
manipulation of photons in multiple degrees of freedom. Shortly after the
first demonstration of a quantum application of a femtosecond laser written
circuit Marsh09 , Sansoni et al. reported Sans10  that a femtosecond-laser-
written directional coupler in borosilicate glass could safely interfere also
polarization entangled photons. Ciampini et al. Ciamp16 , using a pair of
analogous directional couplers, demonstrated that hyperentangled states of two
photons could be successfully manipulated (i.e. photons entangled both in the
polarization and path degrees of freedom). Recently, Chen et al. Chen18  were
even able to propagate single-photon states with orbital angular momentum in
specially tailored waveguides, again inscribed in borosilicate glass by
juxtaposing irradiated tracks to form a ring-shaped core (Fig. 4g).

The capability of supporting and manipulating the polarization degrees of
freedom make femtosecond-laser-written circuits suitable for quantum protocols
based on polarization encoding. On the one hand, by using specific geometries
for the directional couplers Sans12  or special irradiation recipes ensuring
ultra-low birefringence Corr18 , polarization-transparent circuits can be
produced Sans12 ; Crespi13a ; Chap16 ; Pitsios17p ; Zeuner21 . On the other
hand, by harnessing waveguide birefringence, partially-polarizing Crespi11
and polarizing Ferna11 ; Pitsios17g ; Zeuner18  integrated beam splitters
(directional couplers) can be inscribed, enabling the realization of
integrated two-qubit CNOT gates either working in post-selection Crespi11  or
with heralding Zeuner18 . In addition, the birefringence axis of the waveguide
can be locally tilted to produce integrated waveplates, either by juxtaposing
laser-irradiated tracks that produce stress oriented at the desired angle in
the substrate Heil14  (Fig. 4e) or by employing asymmetric focusing of the
writing laser beam Corr14  (Fig. 4f). The latter components can implement
arbitrary one-qubit gates Heil14  and, together with the above-mentioned two-
qubit ones, constitute an in-principle complete toolbox for integrated quantum
computing with polarization-encoded qubits. Further devices based on quantum
information encoded in the photon polarization are an integrated QKD
transmitter Vest14 , demonstrated by exploiting a polarization insensitive
network of directional couplers, and an integrated apparatus for polarization
full state tomography of two-qubit states, realized by combining integrated
waveplates and polarization insensitive couplers on chip Corr14 .

A different set of applications of static photonic circuits are disclosed by
the observation that, within the paraxial approximation lax75 , light
propagation in dielectric structures is described by a Schroedinger-type
equation Marte97 ; Longhi09 ; Szameit10 . In this picture, an array of
femtosecond-laser written waveguides implement a lattice of quantum sites,
whose mutual coupling is described by a tight-binding model Chen21 , and time
evolution is mapped onto the propagation coordinate. In addition, proper
bending of the waveguides implement effective external forces Longhi09 ;
Corr13 ; Rechtsm13 . In the realm of quantum optics, the optical modes of a
set of waveguides, populated by single- or multi-photon states, represent
effectively discrete quantum states populated by bosonic particles. By
tailoring the array geometry and the optical properties of the waveguides, it
is indeed possible to implement diverse Hamiltonians and, by injecting single
or multi-photon light states, perform quantum simulation of different physical
systems. In fact, by this method, quantum walks of one Tang18e ; Tang18h ;
Shi20  and two Owens11 ; Sans12 ; Crespi13a ; DiGiu13 ; Poulios14  particles
were demonstrated on different kind of graphs. Furthermore, this setting
allows for fundamental studies, such as investigating the influence of noise
on quantum coherence Perez18 , probing dynamics due to PT symmetry Klauck19 ,
demonstrating the properties of photonic topological insulators Tamb18 ;
Wang19t ; Wang19d ; Klauck21 . As a matter of fact, the range of simulatable
phenomena is indeed wide and encompasses, among the examples present in the
literature, also quantum decay dynamics Crespi15  (Fig. 4d), Bloch
oscillations of NOON states Lebugle15 , perfect state transfer protocols on a
spin chain Chap16 .

Figure 4: Examples of static, femtosecond-laser-written photonic circuits
adopted for quantum applications. (a) Heralded controlled-Z gate for path-
encoded photonic qubits: the bulk-components schematic is depicted on the top-
left; on the right a pictorial representation of the femtosecond-laser written
circuit. The optical waveguides pass one over the other without crossing, at
the center of the circuit. (b) Three-dimensional circuit implementing the
quantum Fourier transform of eight optical modes. The circuit is composed of
three sections and coupling between modes in each step ($L_{i}$) are shown in
the inset. The implemented phase shifts in each step ($P_{i}$) are also
indicated. (c) Concept scheme and three-dimensional representation of a 5-mode
circuit, realized according to the Reck’s layout, which implements an
arbitrary unitary transformation between the input and output modes. (d)
Example of circuit for analogical quantum simulation: the quantum system
represented on the left, consisting of two discrete sites
($\left|1\right\rangle$ and $\left|2\right\rangle$) coupled to a linear chain
of sites, can be simulated by the photonic circuit depicted on the right. (e)
Cross-section of an integrated waveplate (microscope picture): the
birefringence axis of the waveguide (on the left) can be rotated by writing an
additional track (on the right) which induces stress on the former. (f) An
alternative approach to tilt the birefringence axis of a waveguide of an angle
$\theta$ (see cross-sections on the right) is to employ, for the laser
inscription, a large-numerical aperture objective: the writing laser beam,
which must not fill the objective completely, impinges on the objective
entrance at a distance $d\propto\tan\theta$ from the optical axis. (g) A ring-
core waveguide is inscribed by juxtaposing irradiated tracks, to describe a
circle. A straight waveguide segment with such shape is able to propagate
optical modes with non-vanishing values $l_{m}$ of orbital angular momentum.
Pictures in the panels have been adapted respectively from Refs. Meany16 ,
Crespi16 , Crespi13a , Crespi15 , Heil14 , Corr14  and Chen18 .

We note that the three-dimensional capabilities of the FLM technique indeed
allow to implement graph topologies that would not be possible in a planar
circuit setting Owens11 ; Poulios14 ; Perez18 ; Crespi15 . In addition, if the
circuit is polarization transparent, a polarization-entangled photon pair can
be used, depending on the specific entangled state, to simulate the dynamics
of anyonic or fermionic particles Sans12 ; Crespi13a ; Crespi15 . A further
advantage of this fabrication technology is that circuits implementing systems
with slightly different parameters can be fabricated with rapid turnaround and
in a cost-effective way Crespi13a ; Crespi15 ; Perez18 ; Tang18e ; Tang18h ;
Shi20 , thus allowing to conveniently explore different conditions or infer
statistical quantities from the experiments.

###  V.2 Dynamically-reconfigurable photonic circuits

Dynamic operation and reconfiguration of integrated waveguide circuits is
typically achieved by externally controllable phase elements. Depending on the
substrate, diverse physical effects may be exploited to provide localized and
reversible changes of the refractive index of the waveguide structure, which
in turn provide an additional phase delay to the propagating light. To date,
active phase control in femtosecond-laser written waveguide circuits has been
reported by exploiting the electro-optic Li06 , elasto-optic Humphr14 , or
thermo-optic effectChabo15 ; Flami15 . Indeed, such active phase elements are
essential components in a complete quantum-photonics platform Politi09 ;
Matthews09 , as even few dynamic phase shifters applied on a quantum waveguide
circuit tremendously increase its potentials, by allowing to perform quantum
protocols with parameters dynamically changing in time.

The first quantum-optics experiment which included femtosecond-laser written
waveguides with actively-modulated optical properties was reported by
Humphreys et al. Humphr14 . In that work, the birefringence of an optical
waveguide, inscribed at shallow depth in a fused silica substrate, was
modulated by a mechanical pressure on the chip surface. The change in
birefringence was visualized as a two-photon interference fringe exploiting a
bulk polarization interferometer. Exploitation of the elasto-optic effect
yields interesting potential in the quantum-photonics framework. In fact,
mechanical piezo-electric actuators have low power consumption, which would
make their use possible even in a cryostatic environment. Time response is
dictated by the elastic properties of the material and can be in the order of
microseconds or better Humphr14 . Furthermore, the applied mechanical stresses
could be localized in a tight volume and cross-talks between neighbouring
devices could be negligible.

However, it is not trivial to integrate on a glass substrate mechanical micro-
actuators with adequate features, both in terms of developed force and device
miniaturization. As a matter of fact, to our knowledge and with the exception
of Ref. Humphr14 , all quantum photonics experiments to date, which involve
reconfigurable femtosecond-laser written circuits, have exploited thermo-optic
phase shifters. The latter devices are indeed much simpler to fabricate. A
thermo-optic phase shifter is based on a metallic resistive heater, which is
realized above a given waveguide segment, on the top surface of the optical
chip (see Fig. 5a). Heat dissipation on the resistor, by Joule effect,
provokes a localized temperature increase in the substrate. This results in a
localized refractive index variation, and thus a phase shift, which is
typically proportional to the dissipated electrical power, and hence easily
controllable in a dynamic way.

Thermo-optic phase shifters were demonstrated for the first time in
femtosecond-laser written optical circuits in 2015, in two independent papers
by Chaboyer et al. Chabo15  and Flamini et al. Flami15 . In the former Chabo15
, a three-dimensional three-arm interferometer was realized in a borosilicate
glass substrate, and localized heating was provided by an array of alumina
thick-film resistor mounted onto the chip. In the latter work Flami15 , Mach-
Zehnder interferometers were laser-written in the glass substrate and, after
waveguides inscription, a gold layer was deposited on top of the glass
substrate. Resistors were patterned on such metallic layer using again
femtosecond laser pulses, precisely aligned to the underlying waveguides. Both
these works demonstrated circuit operation in the quantum regime, showing two-
photon interference fringes as a function of the dissipated thermal power.

Following these two first demonstrations, a few quantum experiments were
reported, which exploited femtosecond-laser-written circuits with dynamic
elements.

Crespi et al. Crespi17  demonstrated non-classical features of single photons
(in detail, the single-particle quantum contextuality), using two cascaded
optical chips (see Fig. 5b). The first one contained a ramified circuit,
equipped with four distinct thermal phase shifters realized as in Ref. Flami15
. These phase shifters enabled the preparation of different states of a single
photon delocalized on four optical paths (effectively encoding two qubits),
and ensured phase adjustment at the chip interface. The second chip had static
functioning and contained distinct waveguide circuits to perform different
measurements on this prepared state, which were selected by properly aligning
the preparation circuit in the first chip with the chosen measurement circuit
in the second one. The possibility to select a given circuit in the second
chip, only by relative translation between the two, provided indeed another
degree of reconfigurability to the experiment.

A similar cascaded-chips approach was employed also in Ref. Pitsios17p  by
Pitsios et al., to perform a quantum simulation experiment. Here the first
circuit, operating statically, simulated the dynamics of a spin chain with
five sites, exploiting the discrete-time quantum walk of two entangled
photons. The second chip, featuring two thermo-optic phase shifters, allowed
to interfere the output modes and characterize the output state in different
bases (depending on the values of the actively-controlled phases). By such
second chip it was thus possible to certify the presence of entanglement in
the quantum state after the evolution in the first chip.

Three-arm interferometers, equipped with up to eight distinct phase shifters,
were reported more recently Polino19 ; Valeri20 . In these devices, the
dynamic components were employed to tune the interferometer operation and to
implement different phases in the three arms (see Fig. 5b-c). Such
interferometers represent suitable testbeds to benchmark innovative quantum
metrology algorithms, allowing in particular for the simultaneous estimation
of two unknown parameters.

Figure 5: (a) 3D section of a reconfigurable Mach-Zehnder interferometer: a
metallic heater is patterned on top of one of the interferometer’s arms. (b)
Pictorial scheme of the two cascaded photonic chips employed in Ref. Crespi17
. The first one encodes a two-qubit path-encoded state of a single photon. The
second chip, in conjunction with the four single-photon detectors at the
output, enables to perform different measurements on the two-qubit state.
Thermo-optic phase shifters, fabricated as metallic resistors on the first
chip, allow to sweep through several different two-qubit states (R1) and to
calibrate the phase terms at the interface (R2, R3, and R4). (c) Scheme of the
reconfigurable three-arm interferometer reported in Ref. Polino19 . Three
straight waveguide segments are included between two multiport splitters,
which implement unitary transformations $U_{A}$ and $U_{B}$. The device is
equipped with six thermo-optic phase shifters, which dynamically control phase
terms inside the unitary transformations $U_{A,B}$ and in the interferometers
arm. The panels of this figure contain pictures adapted respectively from
Refs. Cecca19 , Crespi17  and Polino19 .

Actually, the potentials of reconfigurable integrated circuits would be fully
exploited in a completely reconfigurable interferometer realized according to
the Reck Reck94  or Clements Clem16  scheme, which constitutes a universal
linear photonic processor Carolan15 ; Taball19  able to implement arbitrary
quantum algorithms. In the femtosecond-laser-written platform, a 4-mode
universal circuit following the Clements layout, including twelve distinct
thermo-optic phase shifters, was demonstrated in 2018 by Dyakonov et al.
Dyak18 . Here, the resistors were engraved by femtosecond laser ablation on a
Nickel-Chromium layer deposited on the fused silica chip, in which the
photonic circuit was previously inscribed using the same femtosecond laser.
However, operation of that circuit was shown only with classical light.

We ought to note that the use of the thermal phase shifting technology with
femtosecond-laser-written circuits may encounter additional practical
difficulties with respect to its use in other waveguide platform. In fact,
planar technologies typically fabricate the waveguides inside a thin
dielectric layer, placed on top of a much thicker silicon substrate which, due
to its high thermal conductivity, stabilizes the temperature and quenches heat
diffusion far from the heaters. On the contrary, in laser-written devices
waveguides are fabricated in a thick glass substrate where heat can slowly
diffuse also far from the heater. This decreases the efficiency of the thermal
phase shifters, increases cross-talks between neighbouring devices and slows
down their time response Penta21 . However, recent works have shown that
thermal efficiency can be enhanced by a careful design of the metallic layer
and with an optimized geometry of the microheater Cecca19 . In addition, the
surface of the optical chip can be machined three-dimensionally by the same
femtosecond laser to guide the heat diffusion Chabo17 ; Cecca20 . In
particular, by excavating deep insulation trenches between waveguides, or by
embedding the waveguide segment in a suspended glass microbeam, thermal
efficiency can be highly increased, and cross-talks diminished, reaching and
even surpassing the state-of-art of other waveguide platforms Cecca20 . Taking
advantage of these technological improvements, a new generation of
reconfigurable laser-written waveguide circuits will enable more complex
quantum photonic experiments in the close future.

##  VI Integrated quantum memories

Figure 6:  (a) Measurement of the Rabi frequency vs pump power performed in
bulk Pr3+:Y2SiO5 (blue squares) and in a Type II waveguide (red circles)
fabricated by FLM in the same material. Experimental details are reported in
Ref. Corr16 . (b) Microscope pictures of the longitudinal profile (scale bar
is 20 $\mu$m) and the transverse cross section (scale bar is 10 $\mu$m) of a
type-I and a type-II waveguides in Pr3+:Y2SiO5, together with the near field
images of the corresponding guided modes at 606 nm. See Ref. Seri18  for a
complete comparison between the two platforms. (c) Spectrum of the frequency-
multiplexed single photons measured before (brown trace) and after (yellow
trace) the storage in a type-I waveguide, as described in Ref. Seri19 . (d)
Transverse cross section of a type-IV waveguide fabricated by FLM in
Eu3+:Y2SiO5 reported in Ref. Zhu20 , and the corresponding guided mode profile
measured at 580 nm. The panels of this figure contain pictures adapted from
Refs. Corr16 , Seri18 , Seri19  and Zhu20 .

Quantum light storage devices are crucial in the development of large scale
quantum technologies. Optical quantum memories (QMs) are, in fact, the
building block of most schemes for long distance quantum communications, and
play a major role also in photonic quantum computing Buss13 ; Hesh16 . Current
QM realizations rely on engineered light-matter interfaces, where single
photons are absorbed in an optically active medium, and then are re-emitted
after a controllable amount of time, while preserving their original quantum
state.

Cryogenically-cooled rare-earth-doped crystals are among the most studied
systems for developing efficient and long-lived QMs, thanks to the high
coherence offered by the dopant ions, the large inhomogeneous broadening of
the optical transitions of interest, which allows tailoring the absorption
profile by optical pumping, and the possibility to integrate optical
waveguides. The latter feature is particularly important in the light of
implementing practical QMs in real world applications, which require the
simultaneous storage of a very high number of optical modes in a compact and
stable fashion. Moreover, the field confinement arising from guided-wave
propagation improves the interaction between light and matter, which is highly
beneficial for the efficiency of the QM protocols. However, the fabrication of
optical waveguides in rare-earth-doped crystals without perturbing their
coherence properties is challenging. In this sense, FLM has shown in recent
years to be an excellent tool for carrying out this task.

The first pioneering experiment demonstrating a coherent optical memory based
on a laser-written optical waveguide was reported in 2016 by Corrielli et al.
Corr16 . A type-II waveguide was inscribed within the bulk of a Pr3+:Y2SiO5
crystal, and it was used for the storage and the on-demand recall of classical
light pulses at 606 nm employing the atomic frequency comb (AFC) protocol (see
Ref. Afze09  for details on this protocol). In this work it was shown that
type-II waveguides fully preserve the coherence properties of the bulk
material, since the light propagates in a region which is not directly
modified by the laser exposure during the fabrication process. Moreover, the
authors explicitly showed that the light matter-interaction in waveguide,
quantified as the Rabi frequency of the transition of interest, resulted
drastically increased with respect to what measured in bulk under similar
focussing conditions (see. Fig. 6a).

In a successive experiment, the same authors have demonstrated that, by
tailoring very carefully the laser irradiation parameters, it is possible to
inscribe also type-I waveguides in Pr3+:Y2SiO5 Seri18 . In this case, the
optical performance in terms of guided-mode dimensions, waveguide propagation
losses and bending losses, resulted greatly improved with respect to the type-
II counterpart (see. Fig. 6b). In addition, also in this case it was shown
that the spectroscopic and the coherence properties of the material were
largely unaffected by the inscription process. This enabled to show, for the
first time, the quantum storage of heralded single photons in a laser-written
waveguide, which outperformed all previous integrated QM demonstrations in
terms of storage time, AFC retrieval efficiency and coupling efficiency with
the external quantum light source. The same type-I waveguide was then employed
for the quantum storage of heralded single photons prepared in the
superposition of 15 discrete frequency modes Seri19 . The strong light-matter
interaction in waveguide, in fact, enabled to prepare, by optical pumping, 15
independent AFC frequency bins with a moderate amount of pump power, and to
demonstrate the storage and the retrieval of all frequency modes
simultaneously. In Fig. 6c) the spectra of the photons before and after the
storage are reported. By taking advantage also of the intrinsic temporal
multimodality of the AFC protocol, the authors have shown the quantum storage
of more than 130 independent optical modes in a single waveguide, thus
confirming that FLM offers excellent perspectives towards the practical
utilization of QMs in real world scenarios.

More recently, Zhu et al. Zhu20  have shown that type IV waveguides can be
fabricated by FLM in Er3+:Y2SiO5. A microscope picture of the type IV
waveguide and its guided mode profile are reported in Fig. 6d). Also in this
case, it was shown that the coherence properties of the dopant ions inside the
waveguide remained unchanged with respect to the bulk crystal. This device was
used to demonstrate the coherent storage of classical light pulses at the
wavelength of 580 nm adopting the AFC protocol. Since type IV waveguides are
fabricated at the crystal surface, this result opens interesting perspectives
in coupling laser-written QMs with other surface structures, e.g. coplanar
waveguides and/or electrodes, for the coherent driving of the memory
operations with external fields. Finally, the same group has demonstrated the
inscription of type II waveguides in Er3+:Y2SiO5 Liu20 , and has used it to
implement the storage of classical light pulses employing both the AFC
protocol and the Revival Of Silenced Echo protocol (ROSE, see Ref. damo11  for
details).

##  VII Integrated detection

The integration of single photon detectors with laser-written photonic
circuits is, so far, the less developed capability among those required for
realizing a complete photonic quantum architecture. Encouraging results have
already been demonstrated for several integrated lithographic platforms, e.g.
silicon pernice12 ; akhlaghi15 ; shibata19 ; martini21 , silicon nitride
ferrari15 ; kahl15 ; schuck16  and gallium arsenide spreng11 ; mcdonald19 ;
mattioli20  circuits, where superconducting nanowire detectors have been
lithographically machined directly on top of the waveguides. Pursuing a
similar approach with FLM circuits is more challenging, since laser-written
waveguides are buried within the substrate, thus limiting the possibility of
interaction between the photons and the detection medium. Further difficulties
arise from the non-straightforward applicability of lithographic processes on
the glass substrates already machined by FLM. A first attempt in this
direction has been demonstrated very recently, in 2021, by Hou and coworkers
hou21 . In this experiment, the authors fabricated, in a borosilicate glass
substrate, a set of buried waveguides that bend vertically in a 3D fashion for
reaching and crossing the chip top surface. After this step, they performed a
sample polishing in order to obtain a sub-nm flatness of the top surface,
making it compatible with the process of deposition of a superconducting
niobium nitride (NbN) film. Lastly, superconducting NbN nanowires, together
with the proper electrical connection pads, were lithographically defined on
top of the glass portion where the waveguides cross the surface. This device
was then fiber-pigtailed and used as single photon detector, demonstrating an
overall detection efficiency of 1.7%.

In other two recent experiments heilmann16 ; Porto18 , FLM optical circuits
have been used for the implementation of advanced detection schemes of non-
classical states of light. In heilmann16 , a fused silica FLM chip has been
used for sampling the statistics of multiphoton states of light. This device
contained a $1\times 8$ beam divider, fiber-coupled to an array of eight
standard avalanche photodiode single photon detectors. In Porto18 , instead,
the authors performed an integrated homodyne tomography of coherent and
squeezed light states by means of a laser-written circuit containing a
balanced beam splitter and a thermo-optic phase shifter. Although in these
experiments the actual photon detecting elements were not integrated within
the photonic chip, they show the potential of FLM in developing advanced
quantum light analysis. However, incorporating on-chip all the elements for
performing a high-efficient and multiplexed single photon detection remains a
crucial challenge to overcome for scaling the complexity of laser-written
photonic quantum processors, especially for quantum computing and quantum
simulation scenarios, where the large number of optical modes makes bulk
detection a prohibitive perspective. Therefore, we expect that in the near
future this aspect will be studied more and more.

##  VIII Conclusion and outlook

FLM is a prominent microfabrication technology for integrated quantum
photonics as demonstrated by the large amount of experiments and breakthroughs
made possible by this technology. Its role has been important in all domains
of quantum information, from computation to simulation, sensing and
communication. Its success has been motivated, so far, by its versatility and
rapid prototyping capabilities that make it an excellent tool for scientific
experiments and proof of principle demonstrations.

With the increasing effort in developing quantum technologies beyond lab
demonstrations, FLM will have to face a new challenge in competing with
traditional photolithographic technologies for the development of commercial
quantum devices, where scaling of components, packaging and reliability become
important features. Fortunately, FLM is following a parallel evolution in
becoming an industrially viable technology, with an increasing number of
companies that rely on FLM to produce their products. Most likely, FLM has not
yet achieved its full maturity, in fact many improvements are still possible,
from the development of new physical processes to engineering, and
industrialization of the technology.

We believe that the most interesting perspectives for quantum information
applications lie in the development of a complete and customizable quantum
platform combining many interconnected modules produced by FLM, each dedicated
to specific functionalities. The unique three-dimensional capabilities of this
technology will be essential to enhance circuit compactness and to explore new
paradigms, such as topological photonics Kremer21 . Finally, the possibility
to exploit FLM to combine photonic circuits with microchannels, widely
exploited for lab-on-a-chip applications osellame11 , makes this fabrication
technology extremely interesting for the development of integrated quantum
sensors and integrated atom and ion traps with embedded photonic circuits.

###### Acknowledgements.

R.O. acknowledges funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (project
CAPABLE — Grant agreement No. 742745 - www.capable-erc.eu). A.C. acknowledges
funding from the Ministero dell’Istruzione, dell’Universita e della Ricerca
(http://dx.doi.org/10.13039/501100003407, PRIN 2017 programme, QUSHIP project
- id. 2017SRNBRK).

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