# Additive Manufacturing of functionalised atomic vapour cells for next-
generation quantum technologies

F. Wang  Faculty of Engineering, University of Nottingham, University Park,
Nottingham, NG7 2RD, UK<EMAIL_ADDRESS>N. Cooper  School of
Physics and Astronomy, University of Nottingham, University Park, Nottingham,
NG7 2RD, UK<EMAIL_ADDRESS>Y. He1 Faculty of Engineering,
University of Nottingham, University Park, Nottingham, NG7 2RD, UK  B. Hopton
School of Physics and Astronomy, University of Nottingham, University Park,
Nottingham, NG7 2RD, UK  D. Johnson  School of Physics and Astronomy,
University of Nottingham, University Park, Nottingham, NG7 2RD, UK  P. Zhao
Faculty of Engineering, University of Nottingham, University Park, Nottingham,
NG7 2RD, UK  T. M. Fromhold  School of Physics and Astronomy, University of
Nottingham, University Park, Nottingham, NG7 2RD, UK  C. J. Tuck  Faculty of
Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD,
UK  R. Hague  Faculty of Engineering, University of Nottingham, University
Park, Nottingham, NG7 2RD, UK  R. D. Wildman  Faculty of Engineering,
University of Nottingham, University Park, Nottingham, NG7 2RD, UK  L.
Turyanska  Faculty of Engineering, University of Nottingham, University Park,
Nottingham, NG7 2RD, UK  L. Hackermüller  School of Physics and Astronomy,
University of Nottingham, University Park, Nottingham, NG7 2RD, UK

###### Abstract

Atomic vapour cells are an indispensable tool for quantum technologies (QT),
but potential improvements are limited by the capacities of conventional
manufacturing methods. Using an additive manufacturing (AM) technique - vat
polymerisation by digital light processing - we demonstrate, for the first
time, a 3D-printed glass vapour cell. The exploitation of AM capacities allows
intricate internal architectures, overprinting of 2D optoelectronical
materials to create integrated sensors and surface functionalisation, while
also showing the ability to tailor the optical properties of the AM glass by
in-situ growth of gold nanoparticles. The produced cells achieve ultra-high
vacuum of $2\times 10^{-9}$ mbar and enable Doppler-free spectroscopy; we
demonstrate laser frequency stabilisation as a QT application. These results
highlight the transformative role that AM can play for QT in enabling compact,
optimised and integrated multi-material components and devices.

††preprint: APS/123-QED

##  I Introduction

Growing understanding of fundamental quantum processes offers benefits in
multiple sectors, from medicine [1, 2] and sensing applications [3, 4, 5],
positioning and security [6, 7] to quantum computing [8]. However, realising
these benefits requires innovations in quantum technology (QT) hardware, which
must become smaller, lighter, cheaper, and better suited to the needs of
specific applications. Additive manufacturing (AM) has the potential to
transform QT [9, 10] by enabling miniaturised, robust devices that can be
fabricated on demand with advanced architectures for enhanced operation, such
as the innovative ultra-high vacuum apparatus [11] previously reported. AM
also presents opportunities for integration, both of novel hardware with
existing equipment [12, 13] or of functionalised components within a larger
device.

A critical QT component is the atomic vapour cell [14, 15], it underpins many
technologies, spanning laser frequency stabilisation [16, 17], atom, molecule
and ion-trapping [18, 19, 20] thermal vapour magnetometers [21], medical
imaging [1, 2] and industrial scanning applications [22, 23]. However, vapour
cells are difficult to manufacture, rely on the art of glass-blowing and are
consequently limited in size and shape. They are usually cylindrical with
dimensions on the order of centimetres, and have only limited scope for
miniaturisation or customisation.

Planar lithographic processes [24, 25] and microelectromechanical systems
(MEMS) with anodic bonding [26, 27, 28] can produce microfabricated cells with
great potential for miniaturisation, but lack 3D-versatility and offer only
two optical interfaces, which is insufficient for some applications; nor do
they have the same transformative potential for integration and customisation
as AM.

Additive manufacturing can provide the means to overcome these limitations. AM
of glass was demonstrated using fused filament fabrication of molten glass
[29, 30], selective laser melting with silica powder [31, 32] and direct ink
writing using silica sol-gel inks [33]. However, significant technological
challenges such as limited building resolution, evident surface roughness,
cracking and low optical transparency have also been identified. Glass
printing via the use of photocurable polymer / silica nanoparticle composites
has led to optically useful constructs [34, 35, 36, 37, 38, 39], but to date,
the use of these formulations has been limited to structural ornaments,
classical optics and fluidics.

Here we provide the first demonstration of an ultra-high vacuum (UHV)
compatible AM glass QT component and show that, by modifying the inks and
printing procedures, transparent printed structures with integrated active
elements (i.e. electronics, photodetectors) can be realised. These structures
are of high optical quality, have the potential to transform vapour cell based
QTs and open a route to the scalable manufacture of key components for
spectroscopy and quantum sensing (Figure 1a)).

Figure 1: Additive manufacturing of a vapour cell for QT applications. a
Schematic diagram of the AM vapour cell for QT applications. Left:
Illustration of the design of the cell mounted on an ultra-high vacuum flange
via a copper tube. Middle: The photo of AM cell mounted for pumping to a
pressure of $2\times 10^{-9}$ mbar and loading with Rb atomic vapour. Right:
Doppler-free pump-probe absorption spectroscopy of Rb vapour in the AM vapour
cell and applications for QT. b Vat polymerisation of glass vapour cells via
DLP and optical images of the printed green, brown and final parts following
debinding and sintering steps. c Photograph of the printed cell with red and
green laser beams propagating through the cell. d New structures are
achievable: photograph of two inter-connected cells. e Integrated
functionalisation: Inkjet printed graphene and silver inter-digit electrodes
for direct photon detection on the cell. Figure 2: Absorption spectroscopy of
Rb vapour in the AM vapour cell. a Rb fluorescence image inside the cell under
exposure to $\lambda_{ex}=780$ nm laser light. b and c CAD model and a scheme
of the vacuum and optical setups. d Single beam absorption spectroscopy. The
scale of the reference signal (yellow) is vertically offset by 0.02 for
clarity. The frequency scale in d and e is set relative to the 87Rb
$F=2\rightarrow F^{\prime}=2\times 3$ transition. e Doppler-free pump-probe
absorption spectroscopy. For clarity, the scale of the reference signal
(yellow) is vertically offset by -0.05.

We describe the fabrication of glass vapour cells with sizes $<1~{}$cm3 by a
vat polymerisation method based on digital light processing (DLP) of high
loading silica nanoparticles resins (Figure 1b). As a QT application, the
cells are used to demonstrate atomic spectroscopy and show excellent vacuum
performance, with pumped cells reaching pressures below $2\times 10^{-9}$ mbar
and sustaining this pressure throughout the experiments. The cells were
thermally tested up to $150^{\circ}$C and were not noticeably degraded by
exposure to high-temperature Rb vapour.

We performed atomic vapour spectroscopy within the cells and demonstrated its
application to laser frequency stabilisation [40] on the D2 line of 85Rb.

The fabrication methodology is further applied to create complex cell
geometries, while in-situ growth of metal nanoparticles is used to selectively
tune the optical transmission of the produced glass, providing a clear
demonstration of the versatility and transformative potential of such a method
for creating optical materials for QT.

These functionalised cells enable exciting applications, e.g. for the creation
of sub-cm sized optically pumped magnetometers incorporating magnetic-field
shielding conductors and photodetectors directly printed on the cell, thereby
providing a significant jump in system flexibility and imaging resolution for
non-invasive magnetoencephalography [41].

##  II Results and Discussion

###  II.1 Additive manufacturing of a vapour cell

To manufacture the glass vapour cell (Figure 1), a resin was formulated based
on [34] containing fumed silica nanoparticles with an average size of 40 nm,
dispersed in a mixture of 2-hydroxyethyl methacrylate (HEMA), tetra(ethylene
glycol) diacrylate (TEGDA) and phenoxyethanol (POE). HEMA forms a solvation
layer on the nanoparticles, hence allowing high silica loading of the resin.
TEGDA is used to improve cross-linking, thus strengthening the mechanical
structure of the printed part. A concentration of 50 wt% silica nanoparticles
was achieved following a multi-step homogenising process [42]. The viscosity
of the resin was measured to be 297 mPa$\cdot$s at a shear rate of 1000 s-1.
For demonstration purposes, and to facilitate comparison with existing vapour
cells used in commercial QTs, our cells have a cuboid shape featuring two
pairs of parallel optical interfaces, in contrast to the single pair of
parallel interfaces in wafer-based cells [43] and most glass-blown cells. The
intended cell dimensions were 7.2 mm (L) $\times~{}7.2$ mm (W) $\times~{}7.2$
mm (H) with 1.5 mm wall thickness; the initial print was therefore 1 cm3 with
2 mm thick walls, to allow for shrinkage. An inlet on one side (Figure 1b)
enables vapour loading and connection to our experimental apparatus.

To optimise the degree of curing during printing and obtain a high shape
fidelity between the printed part and the design, the exposure time of each
layer and the concentration of the absorber was adjusted by measuring the
curing depth with different absorber concentrations (Appendix A1, Figure A1).
The optimal degree of polymerisation, curing depth and shape fidelity, was
achieved with 6.5 s exposure time, 45 mW/cm2 intensity and 0.035 wt% absorber
content. A simulation of light-scattering from the silica nanoparticles showed
an anisotropic distribution, however an isotropic degree of polymerisation can
be achieved using this resin composition (Appendix A2, Figure A2).
The residual uncured resin was removed in washing and post-curing steps,
resulting in a green part with good mechanical strength. Thermal debinding
followed, with a gradual and uniform release of the internal mechanical
stress, which was tailored to avoid cracking or collapse of the structure. The
resulting debound porous brown part maintained the same geometry as the green
part without volume shrinkage, but with a 51% weight loss as a consequence of
the debinding process.
To eliminate porosity, the part was sintered in an inert argon atmosphere at a
temperature of $T=1150\,^{\circ}$C for 12 h. This process allows the silica
nanoparticles to merge and form amorphous glass (Figure A3). We note that the
argon atmosphere prevents the risk of crystallisation, which was previously
observed in synthesis of parts in the presence of oxygen [44]. X-ray
diffraction (XRD) analysis confirmed the amorphous structure of the printed
material (Figure A3a) [45]. The density of the sintered part is 2.2 gcm-3 and
the sintered part had no observable porosity (see SEM images in Figure A3b)).
The cells printed using this formulation show high mechanical stability under
external pressures and good optical flatness/transparency (see below) and
enabled us to achieve and retain vacuum down to $2\times 10^{-9}$ mbar.

For our formulation, we observed $\sim 27\%$ linear shrinkage, both
horizontally and vertically. The shrinkage of the part matched the estimation
based on the solid weight concentration of the silica [42] and was accounted
for in the design. The two pairs of parallel transparent flat surfaces of the
cells allow two perpendicular beams to pass through with minimal distortion
(Figure A1c). An additional polishing step (Grit 1000 polishing paper) was
introduced to reduce outer wall roughness.

###  II.2 QT sensing with an additively manufactured cell

To demonstrate the suitability of the printed cells for quantum technology
applications, we performed rubidium spectroscopy in the cell. For this, the
cell was mounted to an ultra-high vacuum (UHV) flange via an annealed copper
tube (Figure 2a) and connected to a vacuum test system (Figure 2b). The cells
were leak tested and found to retain pressures down to $2\times 10^{-9}$ mbar.
The annealed copper tube allows for a separation of the cells from the vacuum
apparatus after evacuation and use of the cell as a stand-alone device, via a
standard copper pinch-off technique. The cell was then filled with a mixture
of 85Rb and 87Rb via atomic dispensers. The geometry of the cell is also
compatible with alternative filling methods, reported previously [46, 43]. The
cell performance was first characterised through single-pass absorption
spectroscopy. A single-mode, Gaussian laser beam with a diameter of 1.25 mm, a
wavelength of 780 nm and a power of 0.06 mW was passed through the printed
cell and detected on a photodiode (see Figure 2c). The transmission through
the cell without Rb vapour is $>90\,$%.

The frequency of the laser light was scanned across the D2 resonance of
rubidium 85 and fluorescence observed (inset of Figure 2a). The single-pass
transmission spectrum (Figure 2d) displays the typical Voigt-profiles with all
expected features. The yellow line shows Doppler-free absorption spectroscopy
for comparison - this was obtained with a standard, commercial 75 mm long
glass cell. The Doppler-valleys corresponding to the D2 absorption lines of
85Rb and 87Rb are clearly resolved, showing single pass absorption along the
87Rb $F=2$ transition manifold and the 87Rb $F=3$ transition manifold (Figure
2d). The frequency axis in Figure 3e is given relative to the 87Rb
$F=2\rightarrow F’=2\times 3$ transition. As an example of QT-sensing,
Doppler-free saturated absorption spectroscopy was demonstrated with the cell
at room temperature. Counter-propagating linearly polarised beams with powers
of 0.06 mW (probe) and 0.3 mW (pump) were set up as shown in Figure 2c. The
transmission of the probe beam (blue line in Figure 2e) shows the Doppler-free
spectrum that allows the resolution of the hyperfine states, 87Rb
$F=2\rightarrow F^{\prime}=1,2,3$ and 85Rb $F=3\rightarrow F^{\prime}=2,3,4$
(Figure 5e).

Figure 3: Allan deviation of the unlocked laser, and with the laser locked
using the printed vapour cell. Inset: The error signal (red) is shown for
reference. Figure 4: Transmission and polarisation measurement of the AM
vapour cell. a Beam profile of a 780 nm test laser beam with and without
passing through the cell.b Azimuth and ellipticity measured using a
polarisation analyser for varying angles of polarisation, with and without the
presence of the printed vapour cell, for initially linearly polarised light. c
The Azimuth and ellipticity for varying angles of a preceding quarter-
waveplate, with and without the presence of the printed vapour cell, for
initially linearly polarised light. Figure 5: Functionalisation of AM glass -
AuNP doping and graphene tracks. a Photographs of printed glass slabs of
$1.25\times 1.25$ cm, with different concentrations of AuNP dopant, positioned
over the University of Nottingham logo. b Measured absorbance of glass printed
with different concentrations of AuNP dopant. c Representative I(V) dependence
of a graphene track (10 mm by 2 mm) inkjet printed onto the 0.5 mM AuNP doped
glass and (inset) optical microscopy image of the printed graphene track. d
Electrical resistance, Rgr, of the graphene track printed onto an AuNP doped
glass slab (0.5mM) measured in the dark and under continuous illumination with
green laser light ($\lambda=550$ nm, $P=25$ mW). Inset: Schematic of the
measurement scheme.

Doppler-free spectroscopy enables laser frequency stabilisation (“locking”) to
the hyperfine transitions. We stabilised a laser to the 85Rb $F=3\rightarrow
F^{\prime}=3\times 4$ crossover transition and thus demonstrated that the cell
can be used as a frequency standard. The laser current was modulated with a
frequency of 100 kHz, the photodiode signal was demodulated and an error
signal obtained that corresponds to the derivative of the spectroscopy signal.
This signal was used to frequency-stabilise the laser through feedback to the
laser diode drive current.

To analyse the resulting frequency stability, the error signal was recorded
over a period of twenty minutes, while the laser was frequency locked via the
signal from the printed vapour cell. By analysing the error signal, the Allan
deviation was obtained for the locked laser and compared to the unlocked or
free-running laser (see Figure 3).

The stabilisation based on the printed vapour cell reaches $\Delta F/F=2\times
10^{-10}$ at long interrogation times ($t\sim 1\,s$), an improvement of 1-2
orders of magnitude in comparison with the free-running laser, and provides
significant stability improvements on all time scales. This demonstrates that
the printed vapour cell can provide stable, Doppler-free laser locking. A
similar setup based on polarisation can be used to operate the cell as a
magnetometer [43, 47]. We compared the locking performance to a standard 75 mm
long commercial vapour cell (Thorlabs, made by conventional glass blowing);
taking the 15 times difference in optical path length into account, the Allan
deviation normalised to optical path length is similar or slightly better for
the printed cell (Figure A5).

To evaluate the applicability of printed vapour cells for magnetometry and
polarisation dependent QT applications, the effect of the printed cell on beam
shape and the polarisation of laser light (780 nm) was investigated with an
internal vacuum of $2\times 10^{-9}$ mbar. By analysing the Gaussian beam
profile with and without the cell in the optical path, negligible distortion
and a slight increase of the beam waist from the horizontally printed faces as
shown in Figure 4a. For the vertically printed faces, the beam waist increased
by $\sim 50\%$ [$\omega_{\mathrm{no\\_cell}}=(0.51\pm 0.1)$ mm and
$\omega_{\mathrm{cell}}=(0.78\pm 0.1)$ mm] most likely due to curvature of the
internal surface, which can be considered in future designs. Small undulations
are caused by the layer-by-layer printing process.

The effect of the printed vapour cell on polarisation was analysed, for
linearly polarised light, for various input polarisation angles obtained via
tuning of a half-wave plate, with a measurement of the azimuth and ellipticity
taken every $4^{\circ}$ using a polarisation analyser. The measurements with
and without the printed vapour cell (Figure 4b) revealed negligible change
(comparable to the resolution of the instrument) of azimuth and ellipticity
when the cell is present in the optical path. The half-wave plate was then
switched for a quarter-wave plate and the same measurement technique was
repeated, to study the effect of the cell on elliptically polarised light. The
results are shown in Figure 5c.

###  II.3 Functionalisation of AM vapour cell

Our method of 3D-printing vapour cells offers exceptional opportunities for
improved quantum technologies. We are able to demonstrate a range of desirable
features for vapour cell performance that are only made possible through
additive manufacturing. The geometric design freedom of AM enabled printing of
two inter-connected cells with a variable length tube (two 4.5 mm cuboid cells
connected with a 3 mm channel, Figure 1d), thus offering increased optical
depth, while by overprinting the cell with conductive materials (Figure 1e) we
demonstrate integration and compactification potential for sensors and
detectors. Tuneable modification of the optical transparency of 3D printed
glass has previously been achieved by dipping the brown part into solutions
containing metal salts [34, 48, tabellion2006]. We propose a facile method
where AuNP are formed in situ to modify the glass absorption in the visible
wavelength range.
Gold salt, AuCl3, was added to the resin before printing to form Au
nanoparticles (AuNPs) in situ by a photothermal reduction process, thereby
causing the glass to acquire a cranberry-red colour [49]. An absorption peak,
characteristic of AuNPs, was observed at a wavelength of $\sim 565\,$nm
(Figure 5b) for the glass produced with 1 mM of AuCl3, indicating the
formation of AuNPs with a size of $\sim 20\,$nm. By varying the AuCl3
concentration from 0 to 2 mM, the colour of the resulting glass changes to
dark deep red (Figure 5a), indicating the formation of larger size AuNPs, and
the absorption peak shifts to a longer wavelength from 562 nm for 0.5 mM to
567 nm for 2 mM (Figure 5b). Importantly, the doped glass retains sufficient
optical transparency in the near infrared range, as required for Rb atomic
spectroscopy, while filtering out shorter wavelength visible light from
environmental sources. In the context of magnetometer cells, doped glass
offers the exciting exploitation of surface plasmon resonances (SPR) of AuNP
for local optically-activated heating, which can be used to achieve higher
vapour pressure in the cell faster than standard current-based heating methods
[50].

To demonstrate SPR, we inkjet printed a graphene (iGr) track (10 mm (L) × 2 mm
(W)) onto one side of the glass slab as shown in Figure 5c. Upon exposure of
the undecorated side of the AuNP-glass to green laser light ($\lambda=550$
nm), the resistance of the graphene track decreased by 2% in 60 s (Figure 5d),
which is a typical change in resistance expected for a temperature increase of
$30\,^{\circ}$C. An equivalent track on undoped glass produced no detectable
response under the same conditions (Figure A4a), confirming that the localised
heating was generated by SPR of AuNPs. For medical sensing applications, e.g.
magnetometry for brain imaging, this is a very relevant feature as the vapour
pressure can be increased without heating coils and without raising the
temperature of the environment; this reduces power dissipation and the need
for thermal insulation, hence allowing the sensor to be brought closer to the
tissues being studied. The technique also enables glass with a customisable
optical absorption range within one glass structure (see Figure A4 b)).

Similarly to the overprinted graphene path, the vapour cell can be surface-
decorated with other functional materials, including conductive layers/devices
that can be inkjet printed onto the cell. A pair of 300 µm wide interdigitated
conductive tracks was deposited using inkjet printing of silver nanoparticle
ink and graphene inks (Figure 1e), with a sheet resistance of
$0.53\,\Omega/$sq and $207\,\Omega/$sq respectively, which is comparable to
the values achieved on other substrates [51, 52]. The conductive tracks
exhibit good adhesion to the printed glass cell, enabling e.g. heating or
magnetic field shielding elements that are co-manufactured with, and integral
to, the vapour cell. The AM build process also facilitates integration of
other active components, such as inkjet-printed perovskite photon sensors
[53], which can be used for in situ monitoring.

##  III Conclusions

Additive manufacturing of transparent glass elements has immense potential to
improve components for quantum technologies. A glass vapour cell has been
produced by digital light processing and a wide range of functionalisation
capabilities have been demonstrated, including integrated 3D printed
electronics and active optoelectronic components for enhanced device
functionality, and wavelength-selective absorption for surface plasmonic
heating.

The printed vapour cell was successfully pumped to the UHV regime ($2\times
10^{-9}$ mbar) and loaded with atomic rubidium vapour. The cell exhibits high
transparency and polarisation stability, enabling the observation of atomic
spectroscopy, including signature Doppler-valley and sub-Doppler features.
Used as a frequency reference, laser stabilisation has been achieved with an
Allan deviation $\Delta F/F<10^{-9}$, limited by electronic feedback hardware,
not the AM vapour cell.

This work will inspire new AM-QT research directions, for example, how the
sensitivity of a spin-exchange relaxation-free magnetometer based on modified
surfaces in a 3D printed vapour cell compares to established designs [27]. The
process could enable manufacture of $>40$ glass cells (green parts) per lab-
based printer per hour and the times required for debinding and sintering each
cell could be effectively shortened with large volume furnaces.

Our methods open the way for the creation of novel, high-performance sensors
based on functionalised glass vapour cells for enhanced quantum technology
devices, such as magneto-encephalography sensors or atomic clocks. The
upscalability of the AM process, together with good optical quality and high
vacuum performance, makes such devices a scalable, convenient and customisable
fabrication solution for many QT application sectors.

## Data availability statement

The data used in this work are available from the corresponding author upon
reasonable request.

## Acknowledgements

The fabrication work of the glass vapour cell was supported by EPSRC grants
EP/P031684/1, EP/T001046/1 and EP/M013294/1. The characterisation work was
supported by IUK project No.133086, EPSRC grants EP/T001046/1, EP/R024111/1
and EP/M013294/1, and by the European Comission grant ErBeStA (no. 800942).

## Experimental Methods

Resin formulation: A mixture of 60 vol% 2-hydroxyethyl methacrylate (HEMA), 10
vol% tetra (ethylene glycol) diacrylate (TEGDA) and 30 vol% phenoxyethanol
(POE) was prepared, and blended with 0.2 wt% of bis (2,4,6
trimethylbenzoyl)phenylphosphineoxide as a photoinitiator, 0.1 wt% of
hydroquinone monomethyl ether as an inhibitor and 0.035 wt% of Sudan Orange UV
absorber. Aerosil OX50 silica nanopowder (50 wt%) was added in 10 small doses
with 15 min bath sonication to prevent agglomeration. The final slurry was
further bath sonicated for 30 mins and then degassed at a low pressure of 200
mbar for 3 min.

Additive manufacturing process: The design was printed on a Cellink Lumen X
printer (45 mW/cm2 UV power intensity at 405 nm) with $50\,\mu$m hatching
distance and 6.5 s exposure time for each layer. The printed part was immersed
in propylene glycol methyl ether acetate (PGMEA) and washed using a tube
roller at 80 rpm for 5 minutes to remove the residual non-polymerised
material. The washing cycle was repeated three times. Then the part was
exposed to ultraviolet floodlight using a Wicked Curebox for 10 minutes for
post-curing.

Post-process debinding and sintering: The green part was debound in a high-
temperature furnace (Carbolite HRF 7/22 box furnace) with the ambient
temperature being increased at 0.35∘C/min to $T=130^{\circ}$C, held at this
temperature for 2 hours, then increased at the same rate to $320^{\circ}$C for
4 hours and $600^{\circ}$C for 2 hours. The resulting brown part was further
sintered at $T=1150^{\circ}$C for 12 hours with $3^{\circ}$C/min heating and
cooling rates under 1 bar argon flow using a tube furnace (Carbolite STF
15/50).

Functionalisation: Doping with Au nanoparticles was achieved by adding AuCl3
to the resin, with final concentrations of 0.5 mM, 1 mM and 2 mM, before
adding fumed silica powder. Conductive tracks were deposited with a
$300\,\mu$m wide interdigitated design using a Dimatix DMP-2831 inkjet printer
and a Samba cartridgeof 2.4 pL drop volume. Three layers of AgNP ink (XTPL
IJ36) were deposited using a $20\,\mu$m drop spacing and ten layers of
graphene ink (Merck 793663) were printed using $10\,\mu$m drop spacings.

Electrical and optical characterisation: The sheet resistance of the printed
silver and graphene samples was measured using a Keithley 2400 sourcemeter and
a micromanipulator with a four-probe method, also known as the Kelvin
technique, to eliminate contact resistance. Each I-V curve was measured three
times using both forward and backwards scanning. The derivative of the I-V
curve reveals the conductivity of the printed line with the exact geometry
measured by an optical microscope.

Characterisation of polarised light: The laser beam was set up to pass through
a linear polariser and a waveplate (either quarter-wave or half-wave as
appropriate), before passing through the printed vapour cell, which was under
internal vacuum so that no gases in the cell could alter the polarisation.

Atomic spectroscopy: The cell was connected to a UHV-flange via an annealed
copper tube and attached to the tube using UV-curing glue (Dymax OP-67-LS).
The system shown in Fig. 2b was used to demonstrate the vacuum compatibility
of the cells. Following bake-out for 24hrs at $150^{\circ}$C and leak-testing,
pressures down to $2\times 10^{-9}$ mbar were achieved. Laser light resonant
with the rubidium absorption lines from a Toptica 110 tapered amplifier laser
was then guided into the cell and the resulting absorption measured on a
Thorlabs DET10A amplified photodiode. Doppler-free spectroscopy was obtained
using a pump-probe setup as shown in Fig. 2b with 0.06 mW probe beam power and
0.3 mW pump beam power in beams with a diameter of 1.25 mm. The commercial
reference vapour cell of ⌀$25.4\mathrm{mm}\times 71.8$ mm was purchased from
Thorlabs (GC25075-RB). For laser locking with this commercial cell, the probe
beam is retro-reflected back through the cell, instead of separate probe and
pump beams.

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## Appendix

###  A1 Optimisation of printing parameters for the resin

By comparing the curing depth of the resins containing different
concentrations of UV absorbers of 0.01 wt%, 0.02 wt%, 0.035 wt% and 0.05%, as
shown in Figure A1, the 0.035 wt% was chosen as the optimum for the $50\mu$m
layer thickness used by the Lumen X printer, which results in a high
geometrical fidelity at short printing times.

Figure A1: Measured curing depth versus exposure time under irradiance of 45
mW/cm2 UV light for resins with concentrations of UV absorbers of 0.01%,
0.02%, 0.035% and 0.05%.

###  A2 Modelling of scattered light of nanoparticles in the resin

Previous studies have highlighted that the existence of nanoparticles in UV
curable resins promotes the curing depth due to the light scattered from the
nanoparticles [54], and the extra energy overcures the photocurable material
in the curing layer which reduces the printing resolution or even interferes
with the curing of the next layer in DLP printing (A2a)). Following previous
work on the modelling of polymerisation kinetics[55], the degree of curing
caused by scattering in our resin formulation was calculated and confirmed
that the formulated resin successfully suppressed the curing inhomogeneity
caused by scattered light around the nanoparticles.

The scattered light intensity distribution, $I(\theta)$, due to Rayleigh
scattering of one OX 50 nanoparticle can be calculated by

$I(\theta)=I_{0}\frac{1+\cos\theta}{2R^{2}}\left(\frac{2\pi}{\lambda}\right)^{4}\left(\frac{n^{2}-1}{n^{2}+2}\right)^{2}\left(\frac{d}{2}\right)^{6}$
(1)

where $I_{0}=45$ mW/cm2 is the intensity of the Lumen X printer used in this
work, $R$ is the mean distance between the particles, $\theta$ is the
scattering angle, $n=1.45$ is the refractive index of the resin, $d=40$ nm is
the average diameter of the particle and $\lambda=405\,$nm is the wavelength
of the light.
Taking $R=1.02\,d$, which matches the 50 wt% of nanoparticles in the resin,
the distribution of the scattered light intensity $I(\theta)$ is anistropic
and the scattered light is 1.9 times stronger along the direction of the
incoming UV light (z-direction) than the perpendicular x-y-plane (Figure
A1b)).

Figure A2: a) Sketch showing the light scattering by the silica nanoparticles
in the resin. b) Light scattering power density distribution from a silica
nanoparticle when $R=1.02d$ from equ. (1). c) The resulting, homogeneous
consumption of the vinyl group $\chi$ due to scattering around the
nanoparticle from equ. (2), when $R=1.02d$ is chosen.

Despite the anistropic angular distribution of the scattered light intensity,
the formulated resin exhibits an isotropic degree of polymerisation. The total
consumption of the vinyl groups during polymerisation, $\chi$, can be
described by a model developed in [55], which combines classical theory of
free radical polymerisation with consumption $\chi_{p}$, and an
autoacceleration effect with consumption $\chi_{a}$,

$\chi=\chi_{p}+\chi_{a}=\chi_{\mathrm{max,p}}\left(1-e^{k_{p}\Lambda}\right)+\frac{\chi_{\mathrm{max,a}}}{1+e^{k_{a}(\Lambda-\Lambda_{C})}},$
(2)

where $\Lambda=\sqrt{I}t$ is the UV radiation dose ($t$ = 6.5 s is the
exposure time), $\chi_{\mathrm{max,p}}=0.2079$ and
$\chi_{\mathrm{max,a}}=0.5729$ are the maximum degrees of vinyl group
consumption that can be achieved by the classical radical polymerisation and
the autoacceleration polymerisation respectively. The rate constant of free
radical polymerisation $k_{p}=-0.0083\mathrm{(kg/s)^{-1/2}}$, the rate
constant for the autoacceleration stage $k_{a}=-0.1258\mathrm{(kg/s)^{-1/2}}$
and the required UV radiation dose to achieve half of the maximum degree of
vinyl group consumption at the autoacceleration stage
$\Lambda_{C}=14.0719\mathrm{(kg/s)^{1/2}}$ are parameters determined by the
compositions of the monomers, photoinitiators and absorbers in the formulation
utilising the method described in [55]. For the used resin formulation, the
expected angular distribution for the degree of curing $\chi$ has an isotropic
distribution as shown in Fig.A2, which indicates a similar degree of curing
along all directions.

###  A3 Characterisation of printed and functionalised glass structures

Figure A3: a) X-ray diffraction (XRD) pattern and b) a representative, cross-
section scanning electron microscope (SEM) image of the final printed glass
part showing an amorphous structure after sintering. Figure A4: a) Resistance
change of a graphene track printed onto a non-doped glass slab during exposure
to continuous illumination with green laser light (550 nm, P = 25 mW). b)
Printed glass structures with two different colours. The base is without
doping and the standing surfaces are doped with 0.5 mM AuNP.

###  A4 Laser locking comparison to Thorlabs 75 mm vapour cell

For laser frequency stabilisation, we compared the performance of our printed
vapour cell to a standard Thorlabs 75 mm vapour cell. For laser locking with
this cell, the probe beam is retro-reflected back through the cell, instead of
separate probe and pump beams. Note that the total path length is 15 times
that for the printed vapour cell. The resulting Allen deviation is shown in
Figure A5.

Figure A5: Allan deviation comparison of the printed vapour cell and the
commercial vapour cell, adjusted for the ratio of the corresponding optical
path lengths.

###  A5 Polarisation characterisation of the printed vapour cell

The stability of the polarisation was also measured by analysing the
polarisation over time (Figure A6). No time-dependent change (e.g. through a
local temperature change) in polarisation was detected.

Figure A6: The azimuth and ellipticity measured on a polarisation analyser
over time, with and without the presence of the printed vapour cell, for a
given incident polarisation.