# Comprehensive Characterization of a State-of-the-Art Apparatus for Cold
Electromagnetic Dysprosium Dipoles

Gregor Anich  Institut für Quantenoptik und Quanteninformation,
Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria  Institut
für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria  Rudolf
Grimm  Institut für Quantenoptik und Quanteninformation, Österreichische
Akademie der Wissenschaften, 6020 Innsbruck, Austria  Institut für
Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria  Emil
Kirilov  Institut für Quantenoptik und Quanteninformation, Österreichische
Akademie der Wissenschaften, 6020 Innsbruck, Austria  Institut für
Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria

###### Abstract

We developed a new advanced ultra-cold Dysprosium (Dy) apparatus, which
incorporates a quantum gas microscope (QGM) with a resolution of a quarter
micrometer. The QGM and the cooling and trapping regions are within the same
vacuum glass vessel assuring simple atom transport between them. We
demonstrate the essential experimental steps of laser and evaporative cooling,
lattice loading, transporting and precise positioning of a cloud of the
bosonic isotope 164Dy at the QGM focal plane. Preliminary basic
characterization of the QGM and future plans in enabling its full capacity are
outlined. We also present a feasible platform for simulating complex spin
models of quantum magnetism, such as XYZ model, by exploiting a set of closely
spaced opposite parity levels in Dy with a large magnetic and electric dipole
moment. We isolate a degenerate isospin-1/2 system, which possesses both
magnetic and electric dipole-dipole coupling, containing Ising, exchange and
spin-orbit terms. The last gives rise to a spin model with asymmetric tunable
rates, dependable on the lattice geometry.

##  I Introduction

Low-temperature systems with dominant dipole-dipole interaction (DDI), which
is both long range and anisotropic [1], have recently sparked an enormous
interest because of intriguing prospects related to the simulation of
condensed matter systems, quantum information and ultracold chemistry [2]. A
simple example already containing remarkably complex physics is a system of
free dipoles in a 2D geometry [3], with a direct resemblance to the behavior
of a 2D electron gas in metal-oxide-semiconductor field-effect transistors
[4]. At higher temperatures the system presents a unique opportunity to study
the Berezinskii-Kosterlitz-Thouless (BKT) transition, expected to take place
between a normal fluid and superfluid [3]. Another unique phase, coined micro-
emulsion phase [4], should at low temperatures mediate the transition between
a Fermi liquid and a Wigner crystal.

Models of quantum magnetism are a paradigms of key importance in strongly
correlated many-body physics [5]. The theoretical outset when one tries to
recast those models with cold dipolar particles, occupying the sites of an
optical lattice, lies in the projection of the DDI operator among a few
isolated magnetic sublevels. This results in spin-spin coupling, which can
simulate a plethora of lattice spin models utilized to describe quantum
magnetism such as the generalized XXZ [6], generalized XYZ model [7, 8], or
models of high-Tc superconductivity [9] such as the t-J model [10].

To give an instance, some of the above experimental platforms allow for
precise tuning of the mutual weights of the spin exchange and Ising terms
comprising the XXZ Hamiltonian. This is essential in order to map out the full
phase diagram, and possibly observe the expected phase transition from
paramagnetic spin fluid to Néel-ordered antiferromagnet. The possibility to
quench the system across the different regions of its phase diagram should
spontaneously break global symmetries and therefore enable the Kibble-Zurek
mechanism [11, 12].

Furthermore of particular interest are magnetic systems with implemented
competing interactions that cannot be simultaneously fulfilled, and therefore
generate frustration [13]. Because of the anisotropy of the DDI itself or
lattice geometry, which conspire with quantum fluctuations, classical order
even at zero temperature is prevented. Such systems, coined quantum spin
liquids [13, 14, 15], exemplify some of the most demanding problems in quantum
magnetism [16, 17]. Adding disorder to the periodic lattice, either by
projecting a disordered potential landscape or relying on random vacancies
naturally driving disorder in the system, opens up an opportunity to
investigate many-body localization, a phenomena largely unexplored [18].
Lastly, naturally embedded in the DDI is also spin-orbit coupling (SOC) with a
novel many-body character [19]. The excitations generated by such SOC possess
non-trivial topology and a Berry phase reminiscent to the one responsible for
the unconventional quantum Hall effect in bilayer graphene [20]. Uncovering
the above phenomena in the laboratory will elucidate their exotic properties,
challenging their theoretical description and most probably will also lead to
unexpected findings.

Under the ultra-cold atomic physics umbrella, there exist a few experimental
platforms to tackle the above physics. One of the most mature approaches is
based on ultacold diatomic molecules, exploiting the existence of nearby
rotational opposite parity states (OPS) in the ground electronic manifold
(${}^{1}\Sigma$) of such linear rigid rotor molecules. The atomic constituents
of these diatomic molecules are typically chosen from the alkali family due to
the ability to prepare them at degeneracy [21, 22, 23, 24, 25, 26]. The OPS
can subsequently be polarized with static electric fields or a microwave (MW)
radiation, which essentially provides a system of electric dipoles oriented in
the laboratory frame in the vicinity of few Debye (at full polarization 0.1 D
for LiNa to $\sim$4 D for NaCs, LiCs). Additionally tunability of the dipole
strength and even advanced tailoring of the dipolar potential itself [27, 28,
29] is possible. The only drawback is the extreme complexity and the
difficulty to prepare samples at low enough entropy and therefore a filling
fraction needed to enable percolation [30]. High-lying Rydberg states in atoms
provide yet another example of a relatively young and versatile toolbox toward
engineering of various spin models [31, 32, 33, 34]. The short lifetime of
laser-accessible Rydberg states due to spontaneous decay and their
susceptibility to MW blackbody state transfer have been remedied by utilizing
high-lying circular Rydberg states, cryogenic environment and even spontaneous
emission inhibiting structures [35].

Many proposals exist also with simple alkali atoms where the magnetic
interaction appears as a super-exchange process which scales as $t^{2}/U$ ($t$
is the tunneling rate, $U$ on-site interaction energy). The fact that the
magnetism is generated through motion, demands temperatures in the pK range
[36]. Atoms loaded in a $p$-band utilizing the same super-exchange mechanism
can realize even more demanding models of magnetism, where apart from low
temperatures needed, an additional predicament is the unit filling of the
$p$-band [7].

Atoms with a high magnetic dipole moment offer another path for the same
objective [37]. The simplicity of working with an atom is highly auspicious
although there is an added complexity in order to achieve tuning of the dipole
strength and change the sign of the DDI [38] needed to tune the rates in the
particular spin model. The magnetic moment is also weaker than its electric
counterpart, reaching an equivalent of 0.1 D for the most magnetic atom of Dy.
The above systems are also conceptually different, especially if multiple
Zeeman quantum states are allowed to participate in the DDI. Namely the
induced electric dipole scaling with the applied field compared to its
magnetic counterpart is different, given that the last one is always on. Some
unique to the magnetic moment experiments were performed on dipolar relaxation
[39] and resonant demagnetization in dipolar condensates [40].

Figure 1:  Relevant optical transitions used in the experiment. Two options
for STIRAP to the OPS are shown. The inset shows a zoom into the OPS with a
possibility to engineer a degenerate isospin-1/2 system coupled both with eDDI
and mDDI. The relevant magnetic sublevels of the OPS are shown at no field
(black), Zeeman shifted (blue) and dressed by the linearly polarized MW (red).
The twin dressed state $|9,-9\rangle$ is not shown. The degenerate isospin-1/2
system consists of the unperturbed state $|1\rangle$ and dressed state
$|2\rangle$.

In this article, we describe in detail a new cold-atom experimental apparatus
based on Dy. Our main research goal is to simulate spin models of quantum
magnetism. To achieve these goals we are set up to pursue a familiar strategy,
utilizing the high magnetic moment available in the ground state of the Dy
atom. Additionally we offer an alternative platform, which is attractive for
its simplicity and diversity and offers some further means to approach an even
more exotic spin systems, currently out of reach in the ultra-cold atoms
community or demanding great experimental complexity. The platform is based on
a set of closely-spaced OPS in Dy, that can be efficiently populated by a
Stimulated Raman Adiabatic Passage (STIRAP) technique, and subsequently
manipulated with a MW radiation. The ensuing toolbox, borrows from both
exhaustive magnetic DDI (mDDI) and electric DDI (eDDI), including even the
embedded spin-orbit interaction constituent. This last component allows for
the simulation of the generalized XYZ spin model, with independently tunable
and lattice-dependent rates.

Experimentally, the apparatus contains a few unique and uncommon design
features and engineering choices. A main attribute is a high-resolution QGM,
capable of resolving a quarter micron features, comparable to the site spacing
in short wavelength optical lattices. Another unique feature is the
compactness of the apparatus, containing the laser cooling region and the QGM
within the same glass vacuum vessel.

Generally, the bulk of the article describes prior measurements and
optimization procedures using the 164Dy isotope, as a prerequisite for
pursuing the above goals. The manuscript is organized as follows: First, as a
main motivation, we present two approaches capable of simulating spin models
of quantum magnetism and discuss their respective advantages. The second
approach based on the OPS has been given the major attention in Sec. II due to
its unique features. We then describe in detail the apparatus itself (Sec.
III), focusing on its main constituents: Vacuum system, magnetic field coils,
laser systems and QGM. Section IV describes the steps necessary to achieve
quantum degeneracy and prepare a 2D sample of Dy atoms in the focal plane of
the QGM: Transverse cooling and Zeeman slower, Magneto-optical trap,
Evaporative cooling and transport and Characterization of optical lattices. In
Section V we discuss the first preliminary measurements with the QGM. Finally,
in Sec. VI we discuss perspectives and conclude.

##  II Survey of experimental possibilities

We would like to begin by underlining the flexibility of the current setup. We
are set to pursue a well established approach to simulate quantum spin models
using the ground state magnetic moment of Dy of 10 $\mu_{B}$ [41, 37]. This
approach has both scientific and technical advantages. The long lifetime of
the dipoles and the possibility to study, on the same ground, spin-spin
interaction and tunneling is an asset of this approach. Adversely to generate
significant mDDI one may need lattices with spacing in the UV range, for which
our apparatus is suited. In the ground state of Dy one can isolate a region in
the UV in the range 350-385nm where the dynamic polarizability (DP) is
negative and large (-1000 to -500 a.u.). Furthermore it is free of resonances
and heating should be minimal. This approach may bring new challenges, such as
possible ionization when the atoms are cycled during the imaging process in
such a deep UV lattice. The unknown DP of the upper state, excited by the
imaging photon, in the UV and most importantly the feasibility to directly
resolve UV-lattice spacing with our QGM. The last problem may be remedied
utilizing super-resolution techniques [42, 43], an approach pursued by other
groups [44].

A different, more exotic experimental platform inspired by spectroscopic
findings in [45], can be pursued in parallel with the above scheme based on
ground state mDDI. The proposal capitalizes on the exceptional existence in Dy
electronic structure of nearby OPS with long lifetime and a large reduced
transition electric and magnetic dipole moments of 8 D and 13 $\mu_{B}$
respectively. The states with angular momentum J=10 ($[Xe]4f^{10}6s6p$) and
J=9 ($[Xe]4f^{10}5d6s$) are spaced 35GHz apart and could be mixed by a MW or
DC electric field (Fig. 1). We assume that if two Dy atoms prepared in the OPS
end up in the same lattice site a rapid inelastic loss will occur which will
cause the atoms to leave the trap. Therefore for models utilizing the OPS we
have to assume a hard-core constraint based on the quantum Zeno effect,
meaning no more than one particle per well can reside, similar to chemically
reactive molecules [46].

Figure 2:  View of the main vacuum apparatus, consisting of a Dy atomic-beam
oven, transverse cooling section, ZS and main glass cell. Regarding the
magnetic field coils, only the bottom combination under the glass cell (two
sets of gradient and offset coils for both MOT and QGM regions) is shown.

We envision a scenario where two MW dressed states composed by magnetic
sublevels from the above OPS can be brought to degeneracy and subsequently
coupled by both magnetic and eDDI (Fig. 1 inset). This same scenario was
proposed for symmetric top molecules, where the OPS consists of neighboring
opposite parity rotational levels, where the linear Zeeman effect, available
to us, is substituted with a linear Stark effect [8]. The last feature is
possible provided that such an exotic molecule has a non-zero projection of
the rotational angular momenta on the symmetry axis of the molecule. In Ref.
[8], the DDI interaction was also solely a eDDI. In our scheme, we induce
level crossing between neighboring two m-sublevels for the $J=10$ state
(stretched $m_{J}=-10$ and $m_{J}=-9$ states for example, but not limited to
this pair of states) at some magnetic field, utilizing a linearly polarized MW
and the linear Zeeman shift. In the formed degenerate isospin-1/2 basis the
eDDI coupling is possible due to the MW dressing, handing some opposite parity
portion to one of the states (see for details Appendix A). The fraction of the
opposite parity component can be varied with MW Rabi frequency and detuning,
by borrowing probability amplitude from the J=9 state. One can then write such
a long-range interacting system as an extended XYZ spin model, with tunable
and lattice dependent rates. Similar platforms have been theoretically
proposed only with complex laser-dressing schemes of Rydberg atoms [31],
diatomic molecules with ${}^{2}\Sigma_{1/2}$ electronic ground state [29] or
with symmetric top molecules [47, 8] (such as methyl fluoride CH3F or hydroxyl
radical OH), still to be brought to quantum degeneracy in order to realize
their full scientific and technological potential [48, 49].

In general the XYZ spin model in 2D is very computationally intensive to
simulate for large systems. In the limiting case of 1D the predicted phase
diagram is already extremely rich [7] containing a gapless floating phase non-
existent for the symmetric XXZ spin model. The transitions to this phase are
also intriguing, including a BKT transition to antiferromagnetic (AFM) phase
on one side and a commensurate-incommensurate I-IC [50] transition to a spin-
flip phase on the other. The width of this phase is proportional exactly to
the asymmetry in the X and Y rates [7]. In 2D, a classical Monte Carlo
simulation of few lattice sites of the XYZ model with added Dzyaloshinskii-
Moriya interaction reveals a rich interplay between magnetic orders and spin
spiral orders [51].

Experimentally, populating the OPS can be performed with STIRAP or Raman
pulses. We have a chosen a $\Lambda$-level structure incorporating the excited
state whose $[Xe]4f^{10}5d6s(8,1)^{\circ}$ character and J=8 angular momentum
provides a decent transitional dipole moment of 0.3 a.u. to the J=9 OPS member
(Fig. 1). We can draw conclusions about the DP of the J=10 state of the OPS
from a nearby state with the same character at 15972cm-1 above the ground
state [52]. At 1064nm the DP was calculated to be $\sim$140 a.u., which is
comfortably close to the measured ground state value of 184a.u.[53].
Additionally, the expected large vectorial and tensorial parts of the DP could
be exploited, to achieve ′′magic wavelength′′ conditions for the ground state
and OPS [54]. To investigate the above phases we have developed a sensitive
diagnostic tool, namely a QGM, capable of single atom spin- and site-resolved
in situ detection and therefore measurement of multi-point spatial
correlations [55]. The optical resolution of 0.23$\mu$m and similar depth of
focus of the QGM, makes the apparatus particularly tuned to a single or double
layer 2D structures.

##  III Experimental setup

In this section we give a detailed overview over the main experimental tools.
In section III.1 we discuss the general anatomy of the experiment. We then
describe in great detail our vacuum system and magnetic field coils (Sec.
III.2), laser systems (Sec. III.3), QGM design (Sec. III.4) and optical
lattices implementation (Sec. III.6).

###  III.1 General experimental structure

The main apparatus consists of an effusive oven, immediately followed by a
transverse cooling (TC) section, Zeeman slower (ZS) and a single glass cell,
dedicated to the main cooling and trapping region and containing the QGM
itself. There are two laser cooling systems, two STIRAP laser systems, and
three high power lasers for dipole traps and generation of the optical
lattices. All the lasers that need to be frequency stabilized are referenced
to an ultra-low expansion (ULE) cavity. All the necessary electronics
consisting of digital and analog cards, direct digital synthesizers (DDS),
servo electronics (PIDs) for laser frequency, power and coils current
stabilization are home made and controlled by a digital card (NI 6533 Digital
I/O Card).

Figure 3:  Anatomy of the main glass cell illustrating a) the positioning of
laser cooling region (1), ZS mirror (2) and QGM (3). Two spring loaded (4)
Macor semi-circles (5), provide a stable base for positioning and securing of
components (see text). The connection to the rest of the vacuum chamber is
accomplished via an indium seal (6) and a custom adapter flange (7). b) A
cross section of the QGM, consisting of a beveled front plano-spherical lens
(8) and a second plano-aspheric lens (9). The two lens are held by a Macor
enclosure.

Three cameras (labeled 1 to 3) are used to take images at different Dy cloud
locations in the glass cell. In the central region of the cell, where laser
cooling and trapping takes place initially, we use absorption imaging both
horizontally and vertically with camera 1 (Andor 5.5 Zyla sCMOS). To precisely
position the sample above the QGM we perform both absorption and fluorescence
imaging horizontally with camera 2, identical to camera 1. The fluorescence ce
collected by the QGM, which oriented vertically (Figs. 2 and 3), is imaged on
a camera 3 (Andor-iXon-897-EXF). The software, written on Visual C++ [56],
writes the commands on the NI card (operating at 1MHz) and communicates with
the data acquisition computer. The software for setting the cameras
properties, acquire and present the atomic images and data analysis, is self-
written in Python.

###  III.2 Vacuum system and magnetic field coils

The vacuum system is separated in three sections (Fig. 2). The first section
contains an oven (1WEZ 40-10-22-K-HL-C-0, MBE Komponenten) used generally for
molecular beam epitaxy. It has a motorized shutter, an independent hot lip
temperature control and a water-cooling jacket positioned around a tantalum
crucible, containing pellets of Dy (about 15g). The front of the crucible
(100mm length, $\diameter$12mm) has a long thin tube (40mm length,
$\diameter$2.5mm) to collimate the Dy beam. During operation the oven is held
at 1100∘C and the shutter is opened only during the magneto-optical trap (MOT)
loading stage. At this ratio of the length to diameter of the tube one
theoretically expects a $\pm$4.2∘ atomic cone. The oven is followed by a TC
section formed by a standard vacuum cross, with four anti-reflection coated
(AR) glass ports (Vaqtec). In this section we use a NexTorr D100-5 combined
pump with getter (St-172, 100 l/s for H2) and embedded ion pump (6 l/s for
Ar). Given that the Dy deposited on the walls also serves as an additional
getter the pressure in this section is less than 1$\times$10-11 mbar, as
indicated by the vanishing ion pump current. We don’t incorporate additional
ion gauges to monitor the pressure to decrease complexity and cost. Before
entering the ZS section, the Dy beam crosses the orifice of an all-metal
pneumatic gate valve (VAT GmbH, 48132-CE44-0002). The valve provides necessary
detachment of the oven from the main apparatus during a Dy reloading
procedure, and allows for an emergency shut down if the pressure in that
region exceeds an alarming value.

The next vacuum section is the ZS, which consists of two stainless steel
(alloy 316L) cylindrical pieces with an internal conical surface, formed by
electrical discharge machining. The pieces are welded together in one piece
with total length of 560 mm with small and large diameters of 4 and 14 mm,
respectively. This conical shape matches, but doesn’t restrict, the atomic
beam shape leaving the exit aperture of the effusive oven and arriving at the
trapping MOT position. On the outside, the volume remaining between the
conical surface and an enclosing cylinder serves as a water cooling section. A
simple geometric constraint forces the water flow to travel along the length
of the cylinder twice before exiting, and therefore assures proper cooling
along the full length.

The third vacuum section is a fused-silica glass cell (Precision Glassblowing,
8 horizontal ports $\diameter$50.8mm, top and bottom $\diameter$101.6mm, Fig.
3a) in the shape of an octagon with one side port used as entrance for the
atoms and the rest for laser cooling, dipole traps and optical lattices. All
windows are corrugated with surface relief microstructures providing AR
coating with reflection coefficient $\textless 0.25\%$ in the range 250-1600nm
and at angles of incidence 0-60∘ (produced by Telaztec). The standard glass to
metal transition used in the vacuum industry to bridge between glass vessels
and a ConFlat (CF) vacuum seal standard, for this size cell, would be
impractically long. Therefore, we designed a custom adapter flange, which
contains on one side the CF seal and connects to the glass on the other side
with an indium seal. The indium seal is made out of round cold-bonded indium
wire ($\diameter$ 1mm) pressed between the adapter flange and a flat glass lip
at the entry of the sell (Fig. 3a). Even with the current design the distance
from the end of the ZS and MOT center is 23 cm, substantially longer compared
to standard setups [57, 58]. The vacuum here is provided by a getter-ion pump
NexTorr D500-5. The pump is positioned about 25 cm from the glass cell at a
45∘ angle to the cell entrance, in order to avoid thermally stressing the cell
during the getter activation at 600∘C. Nevertheless due to the relative large
tube (CF63) used, the pumping speed for hydrogen at the MOT center is almost
completely utilized. The pressure in the cell is also $\textless$ $1\times
10^{-11}$ mbar. During the initial bake-out the cell was heated to
$120^{\circ}$C for two weeks by wrapping a heat tape around an aluminum
enclosure concentric with it. A simple thermal simulation assured us that the
cell does not experience large thermal gradients during the NexTorr
activation.

The glass cell, made out of pure glass with no bolting structures, is not
suited for positioning in-vacuum components. We solve this problem by
positioning two semi-circles out of machinable ceramic (macor, Corning Inc.)
with devoted cuts to accommodate the MOT light and the positioning of the
desired in-vacuum elements (Figs. 3 and 4). The two semi-circles were
carefully placed in the cell with a vacuum suction tip attached to a precision
3D linear micrometer stage. Once put down on the bottom glass surface they are
spring-loaded and seize to the side surfaces. The adhesion to the bottom glass
and seizing to the side surfaces creates a stable base and allows positioning
of the QGM and a ZS in-vacuum mirror into a devoted slots.

In order to compensate ambient magnetic fields and to apply small ($\textless
2$G) uniform offsets, a pairs of large compensation coils are symmetrically
installed around the glass cell. The coils have the shape of rectangular
cuboid ($xyz$ dimensions $944\times 1174\times 674$mm, coordinates defined on
Fig. 4 as a reference for the whole manuscript), and are driven by a home-made
bi-polar current source based on high-current paralleled operational
amplifiers. The fields obtainable with these coils are $(0.8,1.5,2.15)$ G for
the $xyz$ directions. We additionally employ a set of offset/gradient coils
(Fig. 2), concentric with the $z$-axis of symmetry of the MOT and QGM regions
respectively. The offset coils for both the MOT and QGM regions are in
Helmholtz configuration. The holding water-cooled structure resembles two
circular loops (with centers 34mm apart as the distance between QGM and MOT
axis), touching internally at a point. Additionally we have an option to apply
a uniform magnetic field in the $y$-direction (Fig. 4) with an independent set
of coils centered around the QGM $y$-symmetry axis. The obtainable fields and
fields gradients of those coils, driven by identical bi-polar supplies as for
the compensation coils, are $(B^{z}_{0},dB^{z}_{gr}/dz)$=(18G, 3 G/cm) and
$B^{y}_{0}$=6G. To prevent induced eddy currents in all metallic structures
forming continuous loops nearby the experiment, such as aluminum structures
holding the coils, they are sliced and the removed material is substituted
with a non-conductive plastic joint to maintain the structural stability.

###  III.3 Laser systems

The laser systems used in the experiment are depicted in Fig. 5. We separate
them in three different groups based on the technology employed. The first
group is based on diode laser technology. We use two home-made, amplified and
frequency-doubled diode laser systems for ZS, TC, imaging and for the first
STIRAP branch. To provide the light for the ZS, TC and imaging we utilize the
421-nm transition $4f^{10}6s^{2}(J=8)\leftrightarrow 4f^{10}6s6p(J=9)$ in Dy
(natural linewidth $\Gamma_{421}$=2$\pi\times$32.2MHz [59], saturation
intensity is $I_{421}=56.3$mW/cm2). The laser system consists of a cat-eye
extended cavity diode laser (ECDL, [60]) operating at 842nm (Eagleyard AR
coated diode, 50mW), tapered amplifier (TA) (Eagleyard, 2-W chip) and a bow-
tie frequency doubling stage based on LBO crystal (Raicol Crystals). The ECDL
delivers 35mW to the TA which amplifies it to 1.4-W useful output before the
frequency doubler. We utilize type-I critical phase-matching and on resonance
attain 600mW of blue light at 421nm. We observe a slight deterioration over
the course of a year, possibly related to the coating of the crystal, although
the doubler is in a sealed box. The doubling cavity is stabilized relative to
the ECDL with a polarization-based Hänsch–Couillaud technique [61]. The laser
system for the first STIRAP branch addresses the
$4f^{10}6s^{2}(J=8)\leftrightarrow 4f^{10}6s6p(J=8)$ transition at 417nm [45]
and is identical to the one described above, except because of the low power
requirement, a low power 1W TA chip (Eagleyard) is employed. We obtain 40mW at
417-nm after the second harmonic generation. Both of the ECDLs of the above
identical systems are frequency locked using a Pound-Drever-Hall (PDH, [62])
method to a home-built optical resonator positioned in a vacuum vessel
($10^{-9}$mbar).

Figure 4:  Cross section of the main cell illustrating the two spring loaded
macor platforms forming a base for the ZS mirror and QGM. The main tweezer
beams performing the trapping, evaporation and transport are shown. Their
crossing point moves from the MOT region (center of the cell) to the point on
the symmetry z-azis of the QGM and 2.6mm above its focal plane. Lattice beams
both at 1064nm (currently 1053nm) and 532nm crossing above the QGM are labeled
as X’Y’ beams. The two green interfering 532-nm beams, propagate in the $x-z$
plane and cross above the QGM, forming a long wavelength lattice (called FA,
see text) of 10$\mu$m.

The resonator, which serves as a reference for all stabilized lasers, is based
on a binocular ULE glass spacer (Hellma, 1.5GHz free spectral range) and
optically contacted partial reflectors (Lens Optics, superpolished) which are
coated (LaserOptik GmbH) in the bands of interest to a finesse of $\sim$30,000
(Fig. 5, binocular ULE). The detuning relative to the ULE, and the sidebands
necessary for the PDH method are generated by a single fibered electro-optic
modulator (f-EOM) preceded by a non-linear transmission line (NLTL). The NLTL
creates a sawtooth wave from a single frequency, which the f-EOM afterwards
converts to a single sideband, bridging the gap between the atomic line and
the ULE resonance. The PDH single frequency (10MHz) signal is added to the
NLTL sawtooth wave by a broadband mixer. Eventually a highly tunable
(300-1700MHz) single sideband, attributed with a PDH modulation is achieved,
allowing for convenient tuning over the full free spectral range of the ULE
cavity [63].

Figure 5:  Diagram of the laser systems used in the experiment. Abbreviations
not defined in the main text: FS- motorized fiber splitter, F- fiber launch,
PhCrFi- photonic crystal fiber, d-aom - double pass AOM, SH- mechanical
shutter, dit-aom- dithering AOM

The second group of laser systems are commercial fiber lasers used as dipole
traps, optical lattices, narrow-line MOT light and the second STIRAP branch.
The central laser system is a 50-W 1053-nm fiber laser. Most of the power
(90$\%$) is devoted to a pair of optical tweezers used for trapping,
evaporation and transport of the atomic cloud (detailed in Section IV) and
additionally for 3D optical lattice beams (Fig. 4). The remaining 5W are
frequency summed with a 5-W, 1544-nm single frequency laser to obtain the
necessary 626-nm light, operating the narrow line MOT (natural linewidth
$\Gamma_{626}=2\pi\times 136$kHz [64]). The 1053-nm (IPG Photonics) and
1544-nm (Keopsys, 10W) amplifiers are both seeded by 5-mW single-frequency
fiber lasers (Koheras Adjustic by NKT Photonics). We use a periodically poled
crystal lithium niobate crystal(PPLN, Covesion), phase matched at 177.4∘C in a
single-pass configuration and derive 1.5W of 626-nm light, which is then
distributed to the MOT vertical and horizontal beams. The 626-nm light is
frequency stabilized to our ULE cavity with PDH technique and the correction
signal is fed to the fast piezo actuator regulating the cavity of the 1544-nm
fiber seeder. The 1544-nm seeder additionally powers another fiber amplifier
at 10-W (Keopsys amplifier, 10-W) which is frequency doubled to 772-nm in PPLN
(Covesion) at 141.8∘C. We obtain 0.7-W useful post-fiber laser power which
then serves as a vertical dipole trap for the atoms at the QGM region, by
propagating along its symmetry axis. The QGM is AR coated in the range
700-900-nm. The last fiber laser is a 40-mW laser at 1572nm (Koheras adjustic,
NKT Photonics), needed for the second STIRAP branch. The laser is inherently
narrow ($\textless 1$kHz) and is simply stabilized with low bandwidth servo
loop to the ULE cavity using the PDH technique.

The last laser group is a single laser system of a solid-state type, based on
a 18-W laser at 532nm (Coherent Verdi), which is needed for our horizontal
short-spacing optical lattice ($x^{\prime}$-$y^{\prime}$ on Fig. 4). It also
powers a vertical large spacing of 10$\mu$m (see Sec. IV.4) lattice, obtained
by interfering two free traveling beams at $\pm$1.5∘ with respect to the
horizontal plane. The interference pattern at the crossing point is coincident
with the QGM symmetry axis and additionally overlapped with the QGM focal
plane.

###  III.4 Quantum gas microscope

Our QGM is an in-vacuum compact design made only out of two lenses, a
Weierstrass sphere serving as a front plano-covex lens [65] and a plano-
aspheric lens (Fig. 3b). The design was inspired by [66], and adapted to the
blue region, specifically for the blue line at 421-nm of Dy. The Weierstrass
sphere enhances the numerical aperture (NA) by a factor of $n^{2}$ (where $n$
is the refraction index of the sphere) therefore reducing the need for extreme
aspheric surface of the second lens. As a result of that the aspheric surface
could be manufactured with magneto-rheological finish [67], achieving the
lowest possible irregularity. The optical performance and tolerances of the
QGM were optimized with optical design software (Zemax 2013). The two lenses
were produced by Sill Optics, with both curved surfaces having a PV maximum
irregularity of 0.15$\mu$m and iRMS $\textless 0.05\mu$m. The enclosure of the
QGM is made out of two cylindrical concentric macor pieces. Each one has a
very fine, 0.15mm pitch tap in order to regulate the distance between the two
lenses. This degree of freedom was necessary given the lens thickness
tolerances and especially the uncertainty of the complex front lens coating (a
30 interchanging layers of Ta2O5 and SiO2, approximated in the simulation by
the total thickness of 2.2 $\mu$m of Ta2O5 and 2.9 µm SiO2). The achieved
parameters are NA of 0.92, working distance of 160$\mu$m (longer working
distances makes the QGM unfitting for our single cell design), field of view
$\pm 40\mu$m and a depth of focus $\pm 125\mu$m. The QGM was tested in air by
shifting the test wavelength by $\sim 1$-nm to shorter wavelengths, where the
performance and distances are the same as for the atomic Dy 421-nm transition
when the QGM is positioned in vacuum. We use shear interferometry [68] on the
re-collimated light that crosses the QGM twice after a retro-reflection from a
silver mirror positioned in the QGM focal plane. We observe parallel
interference fringes with no significant deformation until an aperture of
$\diameter=$ 23mm corresponding to the desired NA. The light was then focused
on a beam-profiler (Thorlabs, BC106N-VIS) with a single lens providing a
magnification of 160. The Strehl ratio was deduced across the full field of
view, confirming a diffraction limited performance.

###  III.5 Optical transportation setup

To be able to reach quantum degeneracy and transport the atoms into the focal
plane of the QGM we developed an optical setup capable of moving in 3D a pair
of two crossed high power optical dipole traps (we refer to them as tweezers)
at 1053-nm crossing at 14∘ (Fig. 4). The setup needs to be able to efficiently
load the Dy cloud from the compressed MOT (CMOT), transport it while
performing evaporative cooling, and eventually position it onto the focal
plane and symmetry axis of the QGM.

We utilize a large dynamic aspheric lens, which is a 20mm wide slice, cut
symmetrically around the diameter from a large commercial asphere (Thorlabs
AL100200-C, $f$=200mm, Fig. 4). This aspheric lens is positioned by an
aluminum frame onto an air-bearing stage (ABS) (Aeroflex,
ABL1000-050-E2-CMS1-PL2-TAS), capable of transporting the two-tweezer
intersection point, over a maximum distance of 50mm. The intersection point
coincides with the asphere focal point during the full transport, due to the
parallelism of the tweezers to the lens symmetry axis, before refracting from
it. The customized lens cut removes a lot of unnecessary weight and size from
the asphere, although we need carefully positioned counter-weights assuring
that the center of mass of the full structure is within the stage
requirements. Such an arrangement allows us to precisely transport the atoms
in the focus of the tweezer pair across the 35mm distance from MOT to QGM
regions along the $x$-direction and additionally along $y$ and $z$ (coordinate
system on Fig. 4). The ABS is slightly magnetic and therefore the holding
structure is designed to keep it far from the atoms.

The tweezer light is transported onto the experimental table with two photonic
crystal fibers (E324-443-500, NKT Photonics), which are water-cooled at the
entrance. We monitor the ratio of the transmitted to input power and a home-
made microprocessor triggers an alarm if this ratio deteriorates under $80\%$.
The tweezer beams are power regulated with two AOMs after the fiber exit,
because we actively steer them horizontally at 100kHz to dynamically broaden
the beams at the focus position. Technically we send an arccosine-shaped
signal from an arbitrary waveform generator to a fast voltage-controlled
oscillator (VCO, AA Optoelectronic, 1$\mu$s full range scanning time).

To set the desired aspect ratio of the tweezers beams, they cross two
expanding telescopes made out of a set of cylindrical lenses in order to
increase the beam size only along the $z$-direction. The ambient aspect ratio,
in the absence of the beam steering is 2.5 ($\omega_{z}=19\mu$m and
$\omega_{y}=50\mu$m). The two telescopes are positioned right before the
dynamic asphere where the tweezers are parallel to each other and 50mm apart.
The front lenses in each telescope is attached to a miniature precision linear
stage equipped with an optical linear encoder (Q-521.130, PI). This allows us
to move the tweezers vertically from their original position during the MOT
loading stage, at 2.6mm above the QGM front surface, and lower them to its
focal plane at 160 $\mu$m above. The final necessary degree of freedom along
the $y$-direction is not automated and therefore optimized once. The ABS rests
on a precisely polished smooth granite block, which is channeled to move along
the $y$-direction with two pairs of ceramic ball bearings pressing on its
$y-z$ opposite walls. The motion along this final degree of freedom is
accomplished by moving the granite block with two micrometers, pressing
against its two opposite $x-z$ walls. By countering the micrometers against
each other we freeze the $y$ degree of freedom and prevent the potential
displacement of the ABS in the $x-y$ plane driven by inertial forces, present
while it is activated.

###  III.6 Optical lattices implementation

Eventually the atoms have to be loaded in a 2D plane coincident with the focal
plane of the QGM and pinned by the lattice geometry of choice in that plane.
This is both for technical reasons, given the tight depth of focus of the QGM,
and fundamental, given the scientific goals of the experiment. As a first step
toward preparing a 2D sample we load the cloud into a single plane of a
vertical lattice with spacing of 10$\mu$m, which we refer to as a fixed
accordion (FA). The FA is formed by the interference of two beams at 532-nm
derived from a 18W Verdi laser (Fig. 5), propagating in the $x-z$ plane and
intersecting above the QGM at an angle of 3∘ (Fig. 4). The two beams are
derived from a single beam incident on a custom coated flat glass substrate
positioned at 45∘ relative to the $z$-axis with a partial reflector
polarization-independent coating on the front surface of 38$\%$ and a high
reflective coating on the back surface. The high parallelism and choice of
reflectivity of the substrate ensures two identical equal-power and highly
parallel beams exiting horizontally (along -$x$) and 5mm apart (defined by the
substrate thickness of 6.35mm). The two beams are derived from the first
reflection and the first transmission of the original beam. About 25$\%$ of
the incoming power is lost in the beam remaining after the second exit from
the substrate. The two beams are then focused onto the focal plane of the QGM
with a f=100mm aspheric lens (Asphericon, AFL25-100-U-U-355-L) and form the
interference pattern along the $z$-direction. The interfence pattern has a
Gaussian envelope with diameter $\diameter 150\mu$m along $y$-direction and
$\diameter 80\mu$m along the interference pattern in the $z$-direction. The
substrate can be moved vertically with sub-micron precision with a slip-stick
actuator (PI, N-470 PiezoMike) to adjust the middle fringe of the interference
pattern onto the QGM focal plane.

Currently the laser is not frequency stabilized and the substrate is not
actively temperature stabilized, nevertheless the interference pattern is
sufficiently stable for the initial characterization of the QGM of this work.
Stability and positioning below the depth of focus of the QGM will only be
achievable once the atomic 2D plane is referenced to the QGM itself (detailed
in Section VI). Furthermore for assuring that the $x-y$ trap frequencies are
not severely elevated when increasing the FA power, we will need to expand the
horizontal diameter to $\sim 1$mm, which demands higher laser power than
currently available. To improve the chances of this method we image the
interference pattern on a 1D charge-coupled device (CCD) camera, and extract
an error signal of the drift in position of the central interference fringe.
In future we will feedback this signal back to an actuator, that corrects the
FA position. This improvement still does not guarantee a long term stability,
and does not cancel vibrations of the interference fringe relative to the QGM.

A better strategy, currently pursued is to avoid vibrations and long term
drifts, by passively locking the position of the atomic 2D cloud to the QGM
focal plane. For this purpose we reflect a 1053-nm vertical lattice beam from
the front face of the QGM ($R>99.5\%$ in the range 1030-1120-nm from
$0-5^{\circ}$ angle of incidence). We discuss in Section VI our future plans
to populate a single plane of such a lattice.

The horizontal $x^{\prime}$$y^{\prime}$ lattices are rotated at 23∘ relative
to the $x-y$ coordinate system, due to the available space, and consist of two
(for both $x^{\prime}$ and $y^{\prime}$ directions) super-lattice beams of co-
propagating 532-nm and 1053-nm beams (Fig. 4). Eventually the 1053-nm beams,
currently used for testing will be substituted with 1064-nm beams. The retro-
reflective optics for each of the super-lattice beams consists of two
polarizing beamsplitters with a motorized half-waveplate in between, followed
by a mirror. Each of the polarization elements, the mirrors and lenses for
shaping the lattice beams are chosen to perform equivalently at both 532-nm
and 1064-nm wavelengths. With this arrangement by rotating the waveplate the
reflection could be extinguished and the lattice beams become regular dipole
traps. This construction simplifies traps alignment procedures and also could
be used during the experimental cycle to utilize the lattice beams as traps
during the evaporation process and later converting them to lattices (the
minimum time for the switch, limited by our servo motors is 100ms).

##  IV Experimental procedures and system characterization

###  IV.1 Transverse cooling and Zeeman slower

We operate the Dy oven with the crucible and the hot lip temperature at 1000∘C
and 1100∘C, respectively (Dy melting point is 1407∘C), to produce a beam with
a most probable longitudinal velocity of about 450m/s [69, 70, 71, 57].
Immediately following the oven, before enetering the Zeeman slower (Fig. 6),
we perform TC (via the four glass ports following the oven in Fig. 2) to
decrease the angular spread of the beam [72]. We apply cooling in 2D, by
utilizing a orthogonal retro-reflected beam configuration with 30mW in each
dimension (elliptical shape with $\diameter$ 26$\times$5mm with long axis
along the atomic beam). We experimentally optimize polarization of the
individual beams and find the optimum detuning to be $0.5\Gamma_{421}$, as
expected for low saturation. The increase in atom number in the 3D MOT, due to
the TC is shown on Fig. 7a. It is clear that the atom number does not plateau
out with laser power, given the available laser intensity. We achieve a factor
of 7 increase in atom number in the MOT (described below) at the maximum
available power.

Figure 6:  ZS coils and main set of coils. Each set consists of gradient and
offset coils in Helmholtz configuration, concentric with the MOT and QGM
$z$-axis of symmetry, respectively but sharing a common water-cooled sink.
Presented are also the measured individual fields of each ZS coil, total on-
axis field and the desired theoretical field (dashed line).

Next the atoms enter the ZS region. Here the atoms experience a resonant
421-nm slowing beam, focused on the oven exit aperture in order to match the
diverging atomic beam. We operate at large detuning of $\sim 20\Gamma_{421}$
and send about 150mW of 421-nm light, which is reflected from the in-vacuum
aluminum coated mirror (custom made with pure aluminum deposited on glass
without protective layer, Figs. 3 and 4). We observe a vague spot on the
mirror due to the deposited Dy and assume that about 20$\%$ of the reflected
light is lost, based on experience of other laboratories utilizing a in-vacuum
mirror for Dy ZS. The ZS is designed with a safety factor of
$\eta=a_{zs}/a_{max}\approx 0.4$ (here $a_{zs}$ is the true acceleration and
$a_{max}=5.8\times 10^{5}$m/s2 is the max acceleration possible). The length
is chosen to achieve a targeted final velocity of $v_{f}=7$m/s to match the
MOT capture velocity. Given the large distance from the end of the ZS to the
MOT center, we may in future adapt a better strategy, letting a higher final
velocity to reduce the transverse expansion and then slow the atoms to the MOT
trapping velocity right before the MOT [73]. We first tested the ZS
performance before assembly, by mapping the magnetic field of each individual
coil ($B_{i}(z)$, $i$ is the coil index and $z$ is the longitudinal
coordinate) first for a current value of 1A. Subsequently a minimization
procedure over this basis is used to find the optimal individual currents
$I_{i}$, realizing a total experimentally optimized magnetic field
$B_{ZS}(z)=\sum_{i}I_{i}B_{i}(z)$, matching the ideal theoretical field of
$B_{th}=B_{b}+B_{0}\sqrt{1-z/z_{0}}$. Here $B_{b}$ and $B_{0}$ are the bias
and overall height of the field profile and $z_{0}$ is the ZS length (Fig. 6).
Further fine tuning of the coils currents was done experimentally by directly
maximizing the number of atoms in the MOT.

###  IV.2 Magneto-optical trap

Exiting the ZS the atoms are captured in a 626-nm narrow-line six-beam MOT
[70, 71, 57]. We increase the MOT capture velocity by creating a comb
structure of sidebands spaced by 110 kHz. We use a resonant EOM (Qubig
PM6-VIS) to generate an effective linewidth of 7MHz. During the MOT loading
process (Fig. 7b), which takes 2s, the laser detuning is $38\Gamma_{626}$. We
gain a factor of 2 in MOT loading rate ($2.85\times 10^{7}$s-1) utilizing the
above spectral broadening. Following the loading we enter the CMOT stage,
where we reduce the temperature of the sample by extinguishing first the
spectral broadening in 2ms and successively ramp down the magnetic field
gradient $1.5\rightarrow 1$G/cm and the total laser intensity from
$625\rightarrow 0.02I_{s}$ (saturation intensity $I_{s}=72\mu$W/cm2, MOT beams
$\diameter$45mm) in 50ms. In parallel we linearly ramp down the laser detuning
toward the resonance $\Delta_{626}=-38\rightarrow-10\Gamma_{626}$. This is not
to be confused with the local detuning $\Delta_{\rm loc}$ relative to the
$m_{J}=-8\rightarrow m_{J}=-9$ which remains constant at
$-\Gamma_{626}/2(\sqrt{(\eta-2)s-1})$, where $\eta=\hbar
k\Gamma_{626}/2m_{Dy}g$, $m_{Dy}$ is the mass of Dy, $g$ is the gravitational
acceleration and $k$ is the wavenumber for the 626-nm transition [74]. At
higher final laser intensities we achieve higher atom number in the CMOT of
$2\times 10^{8}$ but at higher temperature. We further hold the sample for
another 300ms to reach a temperature of $5.6\mu$K which is above the limiting
Doppler cooling temperature of
$T_{min}=\eta\hbar\Gamma_{626}/(2k_{B}(\eta-2))\simeq 3.4\mu$K. The 300ms hold
time exceeds the time ($\sim$50ms) for the sample temperature to reach a
plateau but it is necessary for establishing local density equilibrium and
therefore is needed for optimum dipole trap loading which follows.

Figure 7: MOT characterization. a) Increase of the atom number in the CMOT as
a function of total laser power of the TC. b) MOT loading vs time. The atom
number is measured after the CMOT stage at $s=0.02$. c) Atom number vs time in
a CMOT for (blue) $s$=0.5 and (red) $s$=0.02.

To characterize the atom losses in the MOT we take two decay curves at a fixed
detuning $\Delta_{626}=-10\Gamma_{626}$ and saturation parameter $s=I/I_{s}$
($I$ is the laser intensity) for two different final values of $s$=0.02 and
$s$=0.5 (Fig. 7c). We make a leap forward and mention, that we achieve the
best phase-space density (PSD) in the dipole trap loading, following the CMOT
stage, at $s$=0.02$I_{s}$. The PSD is calculated as
PSD=$N(\hbar\bar{\omega}/k_{B}T)^{3}$, where $N$ is the atom number,
$\bar{\omega}$ is the geometric average of the trap frequencies along
orthogonal directions and $T$ is the temperature. Only for these extremely low
$s$ parameter values we observe a steep initial decay, until a plateau with a
very slow decay ($\textgreater 20$s) is reached (Fig. 7c, $s=0.02$). This
initial decay is caused most probably by diffusion and loss of atoms from the
trap, unable to hold the complete cloud, but nevertheless in the next stage,
when supplemented with a dipole trap performs best. The background pressure is
$\simeq 1\times 10^{-11}$mbar and therefore we disregard the slow one-body
decay due to collisions with background atoms and attribute this decay to one-
body scattering processes due to the 626-nm light. For larger saturation value
of $s$=0.5 the observed initial loss can be attributed to two-body loss due to
light-assisted collisions [74] (Fig. 7c, blue trace). We extract a two-body
loss rate from the initial slope of $\beta=(1/N\bar{n})dN/dt=4\times
10^{-11}$cm3/s, where $\bar{n}=N/(8\pi^{3/2}\sigma_{x}^{2}\sigma_{z})$ is the
average density and $\sigma_{x,z}$ are the cloud size along $x$ and $z$
assuming $\sigma_{x}=\sigma_{y}$. The obtained loss rate is close to than the
predicted one from a theoretical model of light-induced collisions described
in [74]. We vary the two most important parameters to achieve the best loading
conditions for the dipole trap, namely detuning $\Delta_{626}$ and saturation
parameter $s$. For the temperature dependence on the saturation parameter we
observe a linear slope of $T/\sqrt{s}=28\mu K$ for $s\in(0.5,10)$. We do not
observe any temperature dependence on $\Delta_{626}$ for red detuned values
$\textgreater 2\pi\times 0.3$MHz but a large dependence of the spin
polarization.

Figure 8: Tweezer traps loading vs time.

To quantify the degree of spin polarization we perform a Stern-Gerlach
experiment after the MOT light is switched off, where we briefly turn on a
gradient field before imaging. Given the size and the temperature of the MOT
we cannot resolve the individual spin components but can use the vertical
cloud size $\sigma_{z}^{\rm sg}$, normalized $\sigma_{z}^{n}=\sigma_{z}^{\rm
sg}/\sigma_{z}^{0}$ to the one without gradient pulse $\sigma_{z}^{0}$, as a
merit for the polarization purity. At detunings $\Delta_{626}\geq 2\pi\times
1.4$MHz the normalized size is $\sigma_{z}^{n}\rightarrow 1$ . This is
consistent with the behavior observed in other experiments [74, 71, 70],
explained by the sagging of the cloud under the quadrupole center in order to
provide equilibrium between gravity and the radiative forces, subsequently
leading to optical pumping due to the predominant $\sigma^{-}$ transition. We
choose the limiting value of $\Delta_{626}=2\pi\times 1.4$MHz as a compromise
between spin purity and cloud size, given that the horizontal size
$\sigma_{x}$ grows linearly with the detuning and compromises the dipole trap
loading efficiency later on. The spin polarization is crucial for the
subsequent evaporative cooling in the dipole trap.

Here in passing we comment on the importance of spin polarization on the
evaporative cooling efficiency, described in Sec. IV.3. Out of scientific
curiosity, we performed eveporative cooling starting with unpolarized sample
(using detuning $\Delta_{626}=2\pi\times 0.5$MHz), which was possible only in
a very narrow $\textless 10$mG magnetic field region around zero magnetic
field. Apart from the technical difficulty, eventually we barely achieve the
onset of a Bose-Einstein condensate (BEC) with a tenfold compromised atom
number. Eventually the sample becomes polarized during the evaporation ramp
but in that process dipolar relaxation heats the sample and impairs the
evaporative cooling efficiency.

###  IV.3 Tweezer loading, evaporative cooling and transport

Figure 9: Horizontal and vertical transport with time. The accompanying MOT,
CMOT and tweezers loading regions together with the three evaporation ramps
are bounded by the vertical dashed lines (the state of the cloud on the
pictures refers to the end of each period). Top row pictures are absorption
images of Dy sample after a) 2.5s MOT $+$ 300ms CMOT, b) tweezers 100ms after
CMOT at aspect ratio 2.5 and $P$=4W c) tweezers after horizontal transport and
first evaporation down to $P$=2W, d) tweezers after vertical transport and
evaporation 2 and 3 down to $P$=0.07W. Onset of a BEC appears after
evaporation stage 2. Images a) and b) are taken with Camera 1 along $x$ at the
MOT region, and images c) and d) with camera 2 at the QGM region along
$y^{\prime}$(see text).

In order to load the tweezers, they are already turned on during the MOT stage
with a power per beam of 11W. We increase the aspect ratio of the tweezer
beams by a factor of 10 during the loading from the CMOT. This dynamic mode-
matching to the post laser-cooled cloud size improves our loading efficiency
from the CMOT by a factor of 2.5 to a rate of $3.7\times 10^{7}$s-1 and an
absolute number of trapped atoms of $1.3\times 10^{7}$ (Fig. 8).

After the tweezers loading, we extinguish the modulation and linearly ramp the
powers of the two tweezers to 2W each in 500ms. At this point we have a
PSD=0.007 and $2.5\times 10^{6}$ atoms at $9\mu$K. Next we initiate the first,
out of three evaporation ramps, and simultaneously the horizontal transport.
As shown in Fig. 9 (magenta solid trace) in 1s we transverse the horizontal
gap between the MOT and QGM regions and exponentially lower the power of the
tweezers to $P$=0.5W (atom number $9\times 10^{5}$, $T$=$2\mu$K, PSD=0.03).
Until this point we evaporate at the same magnetic field of $B_{0}=0.8$G as
the one set during the CMOT stage after extinguishing the CMOT gradient field.
We set this field with our large offset coils assuring a good spatial
uniformity during the transport. Once the cloud is transported above the QGM
we engage also the local offset coils, concentric with the QGM (Fig. 4), which
allows us to adjust the $z$-field in the foothills of the Feshbach resonance
at 2.75G (Fig. 10). The field is switched to the new value of 2.4G in 5ms and
we initiate the vertical transport (Fig. 9, blue dashed trace). The same
Feshbach region is mapped with the magnetic field pointing along
$y$-direction. Rotating the the magnetic field in a precise manner, while
maintaining a partuclar contact scattering length is important for future
plans to achieve a 2D sample by effectively canceling the DDI and the contact
interaction (see VI). During the vertical transport, which takes 2.5s, we
execute the second evaporation ramp ending at $P$=0.12W. We see the onset of a
BEC at the end of evaporation 2 at $T$=$200$nK (Fig. 11a) and b)). The last
ramp is executed in 1s and delivers a BEC of a condensate fraction 70$\%$
(Fig. 11c) and d)).

Figure 10:  Atom-loss spectrum taken at an initial temperature of 200nK in the
low magnetic field range of interest. The arrow point at the region where the
main evaporation and measurements in the manuscript are performed. The hold
time at every point is 500ms. Normalization is done relative to the atom
number at zero holding time.

During the last ramp we have the option to reshape the cloud by including in
the evaporation either a vertical 772-nm beam ($\diameter$ 150$\mu$m), or two
orthogonal horizontal 1053-nm dipole traps ($\diameter$100$\mu$m each) that
coincide with the X′Y′ coordinate system (Fig. 4). The horizontal traps can be
turned in real time into lattice beams later in the experimental sequence
(detailed below). The automatic tuning of the aspect ratio of the tweezers
completes the full control over all the trap frequencies. The 772-nm dipole
trap goes in the positive $z$-direction through the QGM, instead of the more
natural choice to propagate the beam in the negative $z$-direction. This is
due to an undesired lattice formation from the non-perfect AR coating of the
front face of the QGM prevents, which prevents proper evaporation.

Figure 11:  Phase transition to a BEC. Optical density profile a) and c) and
1D atomic densities b) and d) revealing bi-modal structure. Both bi-quadratic
and thermal Gaussian fits are displayed in b) and d) to describe the BEC
fraction and thermal component respectively. Atom number, temperature and BEC
fraction are a), b) 4.5$\times 10^{5}$ atoms, 200nK, 15$\%$ and c), d)
1.5$\times 10^{5}$ atoms, 40nK, 70$\%$. The effective pixel size in the object
plane is 4$\mu$m. The time-of-flight is 25ms. The imaging is performed in
absorption with Camera 2 along $y^{\prime}$-axis.

###  IV.4 Optical lattices characterization

The inset of Fig. 12 displays the interference pattern of the FA with 10$\mu$m
spacing, imaged by a CDD. We load the atomic cloud in a single fringe by
simultaneously raising the FA power and the 772-nm vertical beam power in
500ms, so we can barely hold the cloud against gravity. Meanwhile we linearly
ramp down the tweezers power to zero. Figure 12 shows an exponential decay of
the atom number with time constant of 2.6s in a FA with $\omega_{z}=2\pi\times
1$kHz trap frequency along the $z$-direction. The atom number is deduced by
utilizing fluorescence on the 421-nm atomic transition for 1$\mu$s by the QGM.
The polarization of each of the FA beams is in the $x\mbox{-}z$ plane. The
lifetime is reasonable for future experiments, and we don’t observe a
detectable shift from the 421-nm resonance, while holding the atoms in the FA
during imaging. The expansion after releasing from the FA is anisotropic and
in the vertical waist follows the expected linear time dependence of
$R(t)=\sqrt{3.5\hbar\omega_{0}/m_{Dy}}t$, where $\omega_{0}$ is the trap
frequency along the tight vertical $z$-direction and $t$ is the time of flight
[75].

Figure 12:  Lifetime of the Dy cloud loaded in the 532-nm FA with a trap
frequency $\omega_{z}=2\pi\times 1$kHz. The inset shows the FA interference
pattern.

To calibrate the short lattices at 1053nm and 532nm, as described in Sec.
III.6, we use a standard method, where we pulse the lattice power ($\textless
0.5\mu$s rise, fall times) over a short pulse and vary its time duration [76].
The BEC plane wave is then projected onto Bloch states, which evolve during
the time of the pulse, and subsequently are projected back onto plane waves.
The actual momentum peaks of this matter wave interference pattern, for both
horizontal 532nm and vertical 1053-nm lattices is shown as an example in Fig.
13a,b. We detect oscillations between the population in the $0$ and $\pm
2\hbar k_{1053}$ momentum states ($k$ is the wave-vector for the 1053-nm
lattice), with a frequency corresponding to the energy difference between the
zeroth and second energy bands. An example of such oscillation in the vertical
1053 lattice at $\sim 30E_{R}$ ($E_{R}=h^{2}/(2m_{Dy}\lambda_{1053}^{2})$, is
the photon recoil energy, $h$ is the Plank constant and $\lambda_{1053}$ is
the wavelength at 1053nm) is shown on (Fig. 13c). We have calibrated similarly
our 532-nm lattices. The decay of the oscillation is possibly due to the
inhomogeneity of our lattice beams and the present both contact interaction
with scattering length of about $100a_{0}$ and DDI. The lifetime of a sample
adiabatically loaded into the vertical lattice, at powers barely holding the
atoms against gravity, reveals a dual exponential decay with the longer
lifetime $\textgreater 20$s (Fig. 13d).

Figure 13:  Characterization of optical lattices. Population in the $0\hbar k$
and $\pm 2\hbar k$ momentum states for both vertical 1053-nm lattice a) with
10ms time-of-flight, and a horizontal $x^{\prime}$ lattice beam at 532nm b)
with 4ms time-of-flight. The boundary visible on panel b) represents the QGM
front surface. c) A lattice depth measurement showing oscillations between
$0\hbar k$ and $\pm 2\hbar k$ momentum states after sudden loading in a
lattice. The inset shows the 0-2 band gap at at ER. d) Lifetime of the full
cloud (BEC and thermal fraction) loaded in the vertical retro-reflected from
the QGM lattice at 1053-nm.

##  V Fluorescence imaging with the QGM

Typically QGMs with alkali atoms [55] are supplemented with a cooling
mechanism that keeps the atoms pinned in the lattice as they fluoresce.
Currently we are attempting another approach given the large mass of Dy and
the broad 421-nm imaging transition. Our detection efficiency is approximately
20$\%$. This includes the QGM solid angle of 30$\%$, the total transmission of
the QGM ($R\textless 0.3\%$ per surface) and two narrow transmission filters
centered at 420-nm (Semrock, $T\textgreater 95\%$) placed in front of Camera
3. Furthermore the fluorescence is guided by two dichroic mirrors (Semrock,
$R\textgreater 97\%$) in reflection to the camera, which has quantum
efficiency of $83\%$. Given this significant collection efficiency we are
currently pursuing a fast illumination of 1-2$\mu$s during which we detect
20-40 photons/atom, or $\sim$ 2-4 photons/pixel/atom given our current
magnification of 160 [77]. Given the large mass of Dy for this short time the
atom will barely diffuse across a single lattice site and therefore one can
even turn off the lattices. For this preliminary work lattices and traps are
always kept on during the fluorescence detection through the QGM.

For the above strategy to succeed we first need to eliminate the linear net
radiative force on the atoms by the excitation beam. This beam is resonant
with the 421-nm Dy transition, with an intensity $\textgreater 100I_{421}$,
and its focus at the atom position is $\diameter 100\mu$m. The tight focus
avoids clipping from the front face of the QGM. This beam is practically co-
propagating with the $y^{\prime}$ lattice, making a $3^{\circ}$ angle with it,
and will therefore tilt the lattice potential along this direction. As an
example, the needed lattice depth for 532-nm lattice to contain the atoms
against this tilt, if retro-reflection was not used, is $V_{min}=\hbar
k_{421}\Gamma_{421}/2k_{532}\sim 1.9$mK. Here $k_{421}$ and $k_{532}$ are the
wave-vectors of the excitation and lattice light at 421nm and 532nm
respectively. This is rather substantial given the power available for our
lattices. The small angle of $3^{\circ}$ allows us to deviate the excitation
beam from the lattice light after the cloud and retro-reflected it back onto
it with an orthogonal polarization and an identical beam parameters.

To assure a good overlap with the original illuminating beams, we utilize
fluorescence imaging transversely to the QGM using Camera 2. We first block
the retro-reflected beam and provide a single excitation pulse of $50\mu$s.
The fluorescence image resembles a cone aligned in the direction of the
excitation beam, formed by atoms being accelerated along its $k_{421}$ wave-
vector (Fig. 14a). We then carefully align the retro-reflected beam until we
see no offset in the original position of the cloud (Fig. 14b). The leftover
heating during the excitation is due to diffusion. The expected heating rate
due to momentum kicks of absorption and emission is
$dT/dt=\Gamma_{421}\hbar^{2}k_{421}^{2}/2k_{B}m_{\rm Dy}=67\mu$K/$\mu$s.

Once the addressing 421-nm beam is balanced we adjust the sample with the
tweezers at a specific height above the QGM, in the vicinity of its focal
plane and extinguish tweezer 1, while keeping tweezer 2. Simultaneously we
raise the 1053-nm lattice beam along $x^{\prime}$ in a trap mode (Fig. 4). The
two beams are derived from the same laser but diffracted trough AOMs driven at
different frequency to avoid interference. The purpose of this first
positioning procedure is to create a lattice with a crude spacing, in order to
be imaged by the QCM handily. Therefore we implemented an option to drive the
AOMs at the same frequency, derived from a single DDS and therefore create
interference. The switching is automated and can be triggered at any time
during the sequence. The horizontal lattice formed this way has a spacing of
2$\mu$m and allows for a rough positioning of the cloud above the QGM. A
fluorescence image of the crude lattice through the QGM is shown on Fig. 15a
after $1\mu$s illumination time.

Figure 14:  Compensation of excitation beam radiative force effects. a) Side
fluorescence imaging of Dy cloud showing an accelerated Dy cloud due to
unbalanced excitation beam. b) The same as a) with balanced excitation beam by
counter-propagating it with orthogonal polarization. The black line in a) and
b) shows the surface of the QGM. Underneath the cloud mirror image from the
top QGM surface is visible.

As another diagnostics on the QGM and the overall system, we evaporatively
cool the Dy cloud into a droplet state by evaporating down to a trap
configuration with anisotropic frequencies ($f_{x}$, $f_{y}$, $f_{z}$)=(11,
76, 160)Hz at scattering length $\sim 90a_{0}$ (at 1.9G) with a relatively
high atom number of 1.5-2$\times 10^{5}$. The magnetic field is oriented along
the $z$-axis. At these parameters one expects a condensation into a droplet-
array ground state as supported by a simulation shown in Fig. 15b, which is
based on a extended Gross-Pitaevskii equation (eGPE) [78, 79, 80, 81, 82, 83].
A in situ 1$\mu$s fluorescence image through the QGM reveals the expected
droplet formation (Fig. 15c), which remains robust at magnetic fields range of
$1.7-2.1$G [84].

These patterns imaged with the QGM, prove that the resolution is within
1$\mu$m. The collected photons during the short exposure time of 1$\mu$s
validate our estimation of optical losses in the imaging system and the
numerical aperture of the QGM and assure single atom sensitivity. For
demonstrating a resolution down to 1/4$\mu$m, one must assure a stability of
the optical lattices relative to the QGM within a region of several hundred nm
from its focal plane. Leaving this region will blur the image and smear the
individual atomic images. The oscillator length the 2D sample should be also
within the QGM depth of focus.

##  VI Conclusions and Perspectives

We presented a potential experimental platform capable of simulating spin
models of quantum magnetism based on highly-magnetic Dy atoms pinned on a
optical lattice. Additionally Dy atoms prepared in a specific set of
degenerate magnetic sublevels, members of a highly electrically coupled
opposite parity doublet, cast a peculiar pseudospin-1/2 system, that permits
both eDDI and mDDI to operate within. Due to the degeneracy, the intrinsic to
the DDI spin-orbit coupling term is activated additionally to the conventional
Ising and spin-exchange (state swapping) DDI terms primarily considered.
Unlike those terms the spin-orbit coupling changes the spin angular momentum
by $\pm 2$ and therefore imprints a phase factor of $\exp(\pm 2i\phi_{ij})$
associated with a change of the orbital angular momentum among a atom pair.

Once the DDI is projected onto the above pseudospin-1/2 basis and rewritten in
terms of a conventional spin-1/2 operator set $\hat{S}_{x,y,x}$ one arrives at
a generalized XYZ spin model where the asymmetry of the rates governing the
$\hat{S}_{x}\hat{S}_{x}$ and $\hat{S}_{y}\hat{S}_{y}$ interactions is assured
by the spin-orbit DDI. Furthermore these rates depend on the lattice geometry
though the azimutal phase $\phi_{ij}$. Quantum simulators, such as this one,
present a irreplaceable tool for exploring tunable low-symmetry models, that
could not be approached analytically or numerically.

Figure 15:  Fluorescence imaging with the QGM. a) A 2$\mu$m optical lattice
for initial QGM alignment imprinted on the atoms. b) eGPE simulation of a Dy
cloud with the experimental parameters (see text) c) in situ image of a Dy
cloud condensed in a droplet state taken with the QGM.

Furthermore we described a new apparatus and its basic operation, tailored to
achieve the above goals. The apparatus consists of many atypical, or out of
the mainstream alternatives to conventional cold atom experimental approaches,
which we hope this work validates. Specifically utilizing a large glass cell
with a indium seal eliminates the necessity of a long glass to metal
transition. Having a single cell serving as a main laser cooling vessel and
containing a QGM facilitates the atomic transport. The glass cell nano-coating
provides lossless access for any laser wavelength from the mid-UVC region to
the NIR even at large angle of incidence. The QGM simplistic miniature design,
allows its positioning in-vacuum, and therefore possesses a large NA, field of
view and reasonable working distance, while eliminating the need to include
glass vacuum ports into the optical design. The last approach suffers from the
glass warping due to the atmospheric pressure and the viewport manufacturing
process itself.

In near future we plan to complement the vertical 1053-nm lattice, currently
retro-reflected from the QGM front face with a secondary retro-reflected beam
at 1095-nm. The formed beat-note lattice [85] should form the same long
wavelength potential envelope as we currently have with the 532-nm FA (with
step 13$\mu$m), with the difference that this potential will be referenced to
the QGM. Preliminary simulations show that one can load a single plane of the
short wavelength lattices by allowing a careful adiabatic increase of the
beat-note potential and additionally entering a regime where the contact
interaction and the DDI compensate each other [86]. The beat-note lattice
could be further used to load two nearby 2D layers allowing the engineering of
bilayer dipolar systems [87, 88, 89].

###### Acknowledgements.

We are highly indebted to R.N. Bisset for providing us with a eGPE Matlab
simulation of the droplet formation and beat-note lattice loading. We thank M.
Fattori for discussion regarding the beat-note lattice and its implementation
and M. Lepers for providing us with details on the OPS. We thank C.
Ravensbergen for providing the ZS design. We thank M. Kreyer, A. Canali and C.
Baroni for useful suggestions on this script. We acknowledge a generous
financial support by a ESQ discovery grant (306532) and by the Julian
Schwinger foundation (JSF-22-05-0010).

##  Appendix A Detailed preparation of a degenerate isospin-1/2 system with
mDDI and eDDI

As shown on the inset of Fig. 1, we depict the rightmost magnetic sublevels of
the OPS manifold, as $|1\rangle=|J=10,m=-10\rangle$ (we drop the J and m
notation from here on), $|\alpha\rangle=|10,-9\rangle$ and
$|\beta\rangle=|9,-9\rangle$. We restrict ourselves to Dy atoms in the $x-y$
plane, with applied magnetic field $\vec{B}=B\hat{z}$ and a MW
$\vec{E_{m}}=E_{m}e^{i\omega t}\hat{z}$ with linear polarization directed
along the $\hat{z}$ direction. The MW ′′dresses′′ the bare states
$|\alpha\rangle$ and $|\beta\rangle$ [90, 91].

For this geometry and choice of states, the state $|1\rangle$ has no
′′partner′′ in the $J=9$ to be coupled by the MW. Moreover the g-factors of
both $J=9$ and $J=10$ states are almost identical ($g_{10}=1.3$, $g_{9}=1.32$)
therefore we can consider the MW detuning $\delta$ as unaffected by the Zeeman
shift. Then for certain magnetic field $B$, and MW detuning $\delta$ and Rabi
frequency $\Omega$ we can induce degeneracy between the bare state $|1\rangle$
and the MW dressed state
$|2\rangle=\sin{\theta}|\alpha\rangle+\cos{\theta}\exp(i\omega
t)|\beta\rangle$ (where $\cos{2\theta}=-\delta/\sqrt{\delta^{2}+\Omega^{2}}$).
The crossing will occur at magnetic field
$g\mu_{B}B=\hbar/2(-\delta+\sqrt{\delta^{2}+\Omega^{2}})$ with the induced
electric dipole moment in the $|2\rangle$ state of $\langle
2|d|2\rangle=(1/\sqrt{210})\langle
10||d||9\rangle(1/\sqrt{1+(\delta/\Omega)^{2}})$.

We now focus on the degenerate two level system ($|1\rangle$, $|2\rangle$) in
the limit of small $\theta$, coupled by both mDDI and eDDI. In the geometry
discussed the relevant parts of the electric and magnetic DDI are
$\hat{H}^{2}_{0}=(1/R^{3}_{ij})((\hat{d}^{i}_{1}\hat{d}^{j}_{-1}+\hat{d}^{i}_{-1}\hat{d}^{j}_{1})/2+\hat{d}^{i}_{0}\hat{d}^{j}_{0})$
and
$\hat{H}^{2}_{+2,-2}=(-3/2R^{3}_{ij})(\hat{d}^{i}_{1}\hat{d}^{j}_{1}e^{-2i\phi_{ij}}+h.c.)$.
Here $\phi_{ij}$ is the azimuthal angle of the vector connecting the atoms,
positioned at lattice sites $i$,$j$, $R_{ij}$ is the distance between them,
and the polar angle is automatically substituted with $\pi/2$; superscripts
refer to the rank of the spherical tensor and the subscripts to its
components. Like in proposals based on magnetic atoms [41] or polar molecules
[28, 92] both DDI are projected in the $|1\rangle$,$|2\rangle$ basis one
generates a spin model of the type
$\hat{H}_{spin}=\Sigma_{i,j}(A_{i,j}\hat{S}^{i}_{x}\hat{S}^{j}_{x}+B_{i,j}\hat{S}^{i}_{y}\hat{S}^{j}_{y}+C_{i,j}\hat{S}^{i}_{z}\hat{S}^{j}_{z}+D_{i,j}\\{\hat{S}^{i}_{x},\hat{S}^{j}_{y}\\})+\Sigma_{i}H_{i}\hat{S}^{i}_{z}$
($\\{,\\}$ is a anti-commutator). Here spin operators are defined in the
standard way: $\hat{S}^{i}_{z}=1/2(|1\rangle_{i}\langle
1|_{i}-|2\rangle)_{i}\langle 2|_{i})$,
$\hat{S}^{i}_{x}=1/2(|1\rangle_{i}\langle 2|_{i}+|2\rangle)_{i}\langle
1|_{i})$ and $\hat{S}^{i}_{y}=1/2i(|1\rangle_{i}\langle
2|_{i}-|2\rangle)_{i}\langle 1|_{i})$. We have omitted terms proportional to
$\hat{n}_{i}\hat{n}_{j}$, which are constant for pinned dipoles
($\hat{n}_{i}$, the molecular density is a substitute for the identity
operator and is present in $H_{i}$). One unique feature of the current system
is the asymmetry between the $A_{i,j}$ and $B_{i,j}$ exchange rates coming
from the added/subtracted contribution respectively of the spin-orbit part of
the DDI $\propto\cos(2\phi_{ij})$ to the otherwise symmetric $A_{i,j}$ and
$B_{i,j}$ rates. The spin-orbit coupling adds also the anti-commutator term
with a lattice index dependent rate $D_{i,j}\propto\sin(2\phi_{ij})$, which
vanishes in 1D or on 2D square lattice. Since we envision a regime where both
magnetic and electric DDI are of the same order
$(|d_{e}|\tan(\theta)c^{2}/g_{L}\mu_{B}\sqrt{J(J+1)(2J+1)})^{2}\propto 1$
(neglecting Wigner 3-j coefficients ratios which are very similar in magnitude
among the states of interest) one needs only a small admixture
($\theta_{0}\sim\pi/180$ rad). In this limit the corresponding rates can be
expressed
$(A_{i,j};B_{i,j};C_{i,j};D_{i,j})=1/r^{3}_{i,j}(D_{m}+D_{e}\theta^{2}+3D_{m}\cos(2\phi_{i,j});D_{m}+D_{e}\theta^{2}-3D_{m}\cos(2\phi_{i,j});P_{m}+Q_{e}\theta^{2};D_{m}\sin(2\phi_{i,j}))$
and the effective magnetic field
$H_{i}=\Sigma_{j}(R_{m}+S_{e}\theta^{2})(1/r^{3}_{i,j})\hat{n}_{j}$, where we
use the indexes $e,m$ to refer to terms generated by the magnetic and electric
DDI respectively and
$\hat{n}_{j}=\Sigma_{\alpha=|1\rangle,|2\rangle}\hat{a}^{{\dagger}}_{j\alpha}\hat{a}_{j\alpha}$
is the molecular density operator.

One can vary the above rates by changing the mixing angle $\theta$ around
$\theta_{0}$ which depends only on the ratio $\Omega/\delta$ and then
adjusting the B-field to reach again degeneracy. On a typical optical lattice
at 532-nm the above rates can be tuned in the vicinity of 50Hz (the static
mDDI rate for two atoms prepared in $|1\rangle$ is 150Hz). Preparing
neighboring degenerate states with lower angular momentum projection provides
solely mDDI rates in the vicinity of 300Hz. Moreover for such choice of
states, unlike the example discussed above, there will be also a spin-orbit
eDDI. Therefore overall rates in the vicinity of 700Hz are achievable with
mixing angles of $\theta\sim 3\theta_{0}$. We expect a maximally mixed
eigenvector in the degenerate basis, with ($\theta\sim\theta_{0})$ to have
lifetime exceeding $250$ms limited by the theoretically estimated lifetime of
the $|J=9\rangle$ state.

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