Artificial gauge fields with ultracold atoms
Victor Galitski, Gediminas Juzeliūnas, and Ian B. Spielman
Citation: Physics Today 72, 1, 38 (2019); doi: 10.1063/PT.3.4111
View online: https://doi.org/10.1063/PT.3.4111
View Table of Contents: http://physicstoday.scitation.org/toc/pto/72/1
Published by the American Institute of Physics

ARTIFICIALGAUGE FIELDS

with ultracold atoms

COURTESY OF INDU SATIJAVictor Galitski and Ian Spielman are both fellows at the
Joint Quantum Institute, in College Park, Maryland; theresearch partnership is between NIST, where Spielman is a
NIST fellow, and the University of Maryland, where he andGalitski are professors. Gediminas Juzeliūnas is a researchprofessor at the Institute of Theoretical Physics andAstronomy at Vilnius University in Lithuania.

Victor Galitski,
Gediminas Juzeliūnas,and Ian B. Spielman
Suitable combinations of laser
beams can make neutral atoms
behave like electrons in amagnetic field.

Gauge fields are ubiquitous in nature. In thecontext of quantum electrodynamics, you may bemost familiar with the photon, which represents
the gauge field mediating electromagnetic forces.
But there are also gluons, which mediate strong
forces, and the W and Z particles, which mediate the weak forces.
According to the standard model, those few gauge bosons, in fact,
mediate all elementary interactions.

In materials physics, applied gauge
ﬁelds in the form of laboratory magnetic
ﬁelds are essential for realizing exotic quantum phenomena, such as the quantum Halleﬀect (see the article by Joseph Avron,Daniel Osadchy, and Ruedi Seiler, PHYSICSTODAY, August 2003, page 38). In a twodimensional lattice, for instance, electrons
that move through a periodic potential
and a strong magnetic ﬁeld are expected
to exhibit a recursive, fractal energy spectrum known as Hofstadter’s butterﬂy, pictured here.
Furthermore, strongly correlated systems can host new gauge ﬁelds or particles known as anyons, which obey unusual

quantum statistics—not those of everyday
fermions or bosons. This article explains
how to create artiﬁcial gauge ﬁelds—madeon demand in a controlled laboratory setting—by using ultracold atomic gases. The
engineered gauge ﬁelds can lead to phenomena that naturally occur in other systems and to new phenomena that occur
nowhere else in nature.
To understand the concept of a gauge
ﬁeld, one must confront a diﬃcult andperplexing aspect of physics, in which theequations describing physical reality involve variables that are not measurable.
Such equations occur even in elementary classical electrodynamics, where the
JANUARY 2019 | PHYSICS TODAY 39

ARTIFICIAL GAUGE FIELDS
magnetic vector potential A, satisfying B = ∇×A, is used in placeof the magnetic ﬁeld B to describe the familiar Lorentz force
that curves charged particles around magnetic ﬁeld lines. A static
vector potential is not measurable by itself—only its curl, the actual magnetic ﬁeld, is. Hence A is deﬁned only up to an arbitrarycurl-free function—allowing the so-called gauge choice—that
keeps the observable electromagnetic forces intact. That reality
cannot depend on an arbitrary function is an example of gauge
invariance, a fundamental physical principle that requires all
physical observables to be independent of the choice of a gauge.
The concept of gauge ﬁeld is merely auxiliary in classicalphysics. Maxwell’s equations and Newton’s force law can optionally be reframed in the Hamiltonian or Lagrangian formalisms
that replace physical ﬁelds with gauge potentials. Although thegauge potentials provide a convenient mathematical frameworkfor solving some problems, a complete understanding of classical physics does not require the reframing.
In contrast, the gauge-ﬁeld formulation is the only consistent mathematical description of quantum particles interactingwith electromagnetic ﬁelds. Indeed, the central object in quantum mechanics, the wavefunction ψ(r)—often represented as aposition-dependent complex function having both real andimaginary components—is not directly observable. The wavefunction’s overall complex phase factor eiϕ can be changed withno physical consequence. For charged particles, that ambiguityin the deﬁnition of a wavefunction is tied one-to-one to the ambiguity in the choice of a gauge for the electromagnetic ﬁeld.
Gauge ambiguity is not a mathematical curiosity. It’s an intrinsic property of quantum mechanics and a source of many
important and peculiar quantum eﬀects, such as the Aharonov–Bohm eﬀect (see the article by Herman Batelaan and Akira
Tonomura, PHYSICS TODAY, September 2009, page 38) and topological phases of matter, the focus of the 2016 Nobel Prize inPhysics (see PHYSICS TODAY, December 2016, page 14).

Ultracold atoms
Although gauge ﬁelds and their associated forces abound inphysics, their properties cannot be fully controlled. For example, the charge of an electron is a fundamental constant, andthe Lorentz force is a law of nature; both are nonnegotiable.
And yet gauge-ﬁeld physics can be simulated in tabletop experiments by using ultracold atoms.
A cloud of ultracold atoms, held at temperatures typicallybetween hundreds of picokelvins to tens of microkelvins, is
up to a million times thinner than air. The atoms live in ultrahigh vacuum, isolated from their environment and trapped by
optical or magnetic forces. Each aspect of their physical description must be assembled from quantum mechanical building blocks.
The energy of the atoms’ interactions with each other is feeble, typically on the order of 10−31 joules. Yet the gases can still
form strongly interacting quantum systems. For example, neutral atoms trapped in an optical lattice—the standing waves
formed by mutually interfering laser beams—tunnel from onesite to another, just as electrons do in a crystalline solid, andrepel each other whenever they share the same lattice site.
The energy balance between the atoms’ tunneling and theirinteractions can be adjusted by changing the intensity of the interfering lasers. The change can drive the transition between
an itinerant phase, in which atoms hop freely between latticesites, and a crystalline phase, in which they are immobile,pinned to their sites. The change in intensity also provides away to realize the Hubbard model in strongly correlated electronic materials (see the article by Gabriel Kotliar and Dieter
Vollhardt, PHYSICS TODAY, March 2004, page 53). The Hubbard
model and other standard theoretical models rarely occur intheir pristine form in materials. To give such iconic and idealized models life in the laboratory, one can use cold atoms toforge a link between quantitative, precise atomic-physics experiments and many-body theory.
The response of a material to electromagnetic ﬁelds is perhaps the most versatile and informative way to probe its electronic phases. As simulators, though, cold atoms lack a crucial
ingredient that makes such probing possible: electric charge.
Because of their charge neutrality, individual atoms do not experience Lorentz forces in a magnetic ﬁeld. It would therefore
seem that a wide range of phenomena would be forever out ofreach of cold-atom experiments. Fortunately, that’s not so.

FIGURE 1. THE APPEARANCE OF QUANTIZED VORTICES in a rotating superfluid is a smoking gun for the presence of an artificial magnetic
field. The density of vortices is in direct proportion to the artificial field’s magnitude. (a) Quantized vortex arrays in superfluids were firstimaged in liquid helium in 1979 at the University of California, Berkeley.1 (b)They were later seen, in 2000, in a slowly rotating Bose–Einsteincondensate (BEC) of rubidium.2 (c) This 2003 image of a quickly rotating BEC of Rb captures a large array of vortices created at JILA.4
40 PHYSICS TODAY | JANUARY 2019

FIGURE 2. STIMULATED RAMAN TRANSITIONS. Two counterpropagating laser beams (pink and blue) incident on a Bose–Einsteincondensate (BEC) can create artificial magnetic fields. (a) The beams drive stimulated Raman transitions in the atoms; each transition absorbs
a photon from one beam and emits one into the other beam while imparting a momentum kick to the atom. As an atom is moving upward,say, it also moves right from the recoil. The reverse happens for atoms moving downward. The kicks simulate a transverse, velocity-dependent
Lorentz force. (b) An atomic BEC with an artificial gauge field turned off (left) and turned on (right). The appearance of quantized vortices
mark the presence of the artificial gauge field. (Adapted from ref. 5.)

Rotation as simulation
The ﬁrst artiﬁcial magnetic ﬁeld experiments using cold atoms
exploited the equivalence between the Lorentz force in a uniform magnetic ﬁeld and the Coriolis force in a spatially rotating
frame. The equivalence may be most familiar in the context of
the Foucault pendulum, whose axis of oscillation slowly rotates at an angular velocity ω. The reason for the rotation is simple: A particle traveling linearly with velocity v in a stationary
frame undergoes curved motion in a rotating frame from the
Coriolis force FC ∝ v × ω, just as a charged particle follows a circular cyclotron orbit in a uniform magnetic ﬁeld from theLorentz force FL ∝ v × B.
One of the most beautiful and direct manifestations of superconductivity is the formation of vortices—sharply localized
quanta of circulation of magnetic ﬂux or angular momentum.
Quantized vortices were predicted for superﬂuid helium by Lars
Onsager in 1947 and by Richard Feynman in 1955. Russian theorist Alexei Abrikosov extended the prediction to superconductors in 1957 and showed that interactions between the vortices
ordered them into a regular array, the so-called Abrikosov latBatice. The achievement earned him a Nobel Prize in Physics almost 50 years later (see PHYSICS TODAY, December 2003, page 21).
Vortices can be induced in a superﬂuid by the eﬀective magnetic ﬁeld present in rotating systems. In 1979 Richard Packard
and colleagues ﬁrst imaged a vortex array, as shown in ﬁgure 1,
in helium by using a rotating cryostat.1 Two decades later, Jean
Dalibard and colleagues found much the same thing—a small
cluster of three uniformly spaced vortices—in atomic Bose–
Einstein condensates (BECs) of rubidium-87 stirred by a focusedlaser beam.2 The observation provided strong evidence for superﬂuidity in BECs.
The groups of Wolfgang Ketterle at MIT and Eric Cornell at
JILA made technical improvements that led to observations oflarge vortex arrays—a qualitative leap beyond the earlier results
found in liquid He and the atomic BECs.3,4 Those large Abrikosov
lattices set the stage for studying the dynamics of vortex crystals during melting and in other nonequilibrium settings.
As exciting as the experiments on rotating superﬂuids havebeen, though, they only probed phenomena observable inweak gauge ﬁelds. An important ﬁgure of merit in many-body

b

Φ
φ3

φ2

φ4
φ2

φ1

φ2 − φ1
2π

=

∫

q
Φ
= ⊙ A · dℓ
h/q h

φ1
Φ
= (φ1 + φ2 + φ3 + φ4)/2π
h/q

FIGURE 3. PHASE ENGINEERING. Quantum mechanical particles experience magnetic fields by acquiring Aharonov–Bohm (AB) phases.
(a) In an AB interferometer, a magnetic field B is confined to the interior of a solenoid and is zero outside it. Nevertheless, a particle thattravels on opposite sides of the solenoid will acquire a phase difference proportional to the enclosed magnetic flux Φ. That flux equals theline integral of the vector potential A around the solenoid. The charge is specified by q. (b) Particles that tunnel in a lattice experience anapplied magnetic field in much the same way as in the AB effect. Their tunneling motion from one site to another acquires a so-called Peierls
phase, such that the sum of the phases around a closed loop equals the enclosed flux.
JANUARY 2019 | PHYSICS TODAY 41

ARTIFICIAL GAUGE FIELDS
systems is the ratio of the radius of theminimum cyclotron orbit to the averageinterparticle separation. The smaller theratio, the stronger the magnetic ﬁeld
effects and the closer one gets to probing the diﬃcult and exciting physics ofstrongly correlated topological phases ofmatter. Those phases include the fractional quantum Hall states, collective
states of matter that occur in ultrastrong
ﬁelds and in which electrons behave as if
their elementary charge is a fraction of
their actual charge. (See the article byJainendra Jain, PHYSICS TODAY, April 2000,
page 39.) Unfortunately, the range of rotation-induced artiﬁcial magnetic ﬁelds
are far from that interesting territory.
New approaches were required to reachlarger artiﬁcial ﬁelds.

Laser-induced gauge fields

FIGURE 4. LASER-ASSISTED TUNNELING. The native tunneling in an optical lattice does
not produce the phase differences required to emulate a gauge field. But the phases can becreated in a two-step process. (a) When a potential gradient of energy Δ is applied to alattice, the energy states in adjacent sites go out of resonance with each other, which blocks
a localized atomic wavepacket (pink) from tunneling. (b) Additional laser fields illuminating
the lattice can provide the required energy to reestablish tunneling (yellow arrow). The
applied fields also imprint a local optical phase on the atom’s wavefunction as it moves
between lattice sites.

The ﬁrst new approach in the laboratory
used an atomic BEC illuminated by a pair of counterpropagating laser beams, each having a distinct wavelength λ(ﬁgure 2a). Most atoms, including those in a BEC, have several
spin states that are distinguished by a combination of orbital,
electron, and nuclear spin degrees of freedom. When the laser
beams strike the BEC, they become quantum mechanicallycoupled to the spin states of individual atoms. During eachinteraction, an atom’s spin ﬂips, a process accompanied by
the exchange of a photon from one beam to the other. The exchange imparts to the atom a momentum kick of 2h/λ, whichchanges the atomic velocity by about 1 cm/s. The BEC atoms
are so cold that even that tiny change exceeds the thermal velocity of the system.
The recoil of the atoms depends on their vertical motion andslight diﬀerences in the beam wavelengths. As an atom moves
upward, for instance, it is stimulated to emit a photon into theleftward-moving beam (blue) in ﬁgure 2 and, as a result, acquiresa kick to the right. The change in momentum emulates thetransverse response of a Lorentz force, which moves the atom
in circles, to use the classical analogy. An artiﬁcial magnetic
ﬁeld is created.
Although that intuitive picture alludes to forces, the quantum system is mathematically better described by the appearance of an electromagnetic vector potential—a gauge ﬁeld.5–7 In2009, a team including one of us (Spielman) demonstrated thetechnique at NIST.5 The artiﬁcial magnetic ﬁeld was marked by
the presence of vortices, as shown in ﬁgure 2b, but in the laboratory frame rather than in a rotating frame.
In the ﬁnal analysis, the experimental scheme in ﬁgure 2
turned out to be well suited for creating elongated trappedatom geometries but not for creating extended systems withlarge ﬁelds. Even so, the pioneering work opened the door forexperiments that now do operate at large ﬁelds.

The Aharonov–Bohm effect
In quantum mechanical systems, gauge ﬁelds are inseparablyintertwined with the wavefunction’s phase. The connection isdramatically evident in the Aharonov–Bohm (AB) eﬀect,
42 PHYSICS TODAY | JANUARY 2019shown in ﬁgure 3a, for charged quantum particles moving
about an inﬁnite solenoid. The magnetic ﬁeld is zero outside
the rings of the solenoid, where the particles actually move.
But even though they never experience a magnetic ﬁeld, theparticles still respond to the electromagnetic vector potential,
which, unlike the magnetic ﬁeld, necessarily extends outside
the solenoid.
Upon completing a closed loop, each particle’s wavefunction acquires an additional phase—the AB phase—which is
proportional to the magnetic ﬂux enclosed by the solenoid. By
Stokes’s theorem, that ﬂux is equal to the line integral of thevector potential around the loop traversed by the particle.
Hence the acquired phase is a direct consequence of the vector
potential, not the magnetic ﬁeld itself.
One can see that connection in a lattice in which atoms tunnel between adjacent sites. The AB phase acquired by an atom
as it encircles a square plaquette in the lattice, as shown infigure 3b, is just the sum of the four phases gained on the associated links.

Gauge fields in optical lattices
Extending that one plaquette to a larger array would produce
a 2D square lattice with a constant magnetic ﬂux in each unit
cell. But how can the tunneling phases be created in the laboratory without the real magnetic ﬁeld of a solenoid? The ﬁrst
theoretical proposal was to make an artiﬁcial gauge ﬁeld thatuses “laser-induced tunneling” of atoms between sites in an
optical lattice.8 In the proposal, the atoms don’t tunnel throughthe barrier on their own volition; rather, they are pushed
through it with additional laser ﬁelds.
The concept is illustrated in ﬁgure 4, using just two latticesites: Imagine a conventional optical lattice that is tilted—with
one site higher in energy than the other. The tilting takes theatoms in the two sites out of resonance with each other andprevents tunneling. Two light ﬁelds whose photon energies
diﬀer by the tilt energy then provide just the right amount ofenergy to link the states together.
In addition to reestablishing tunneling between sites, thelaser-induced tunneling also imprints a position-dependent
optical phase onto the wavefunction of the atoms. The phases
emulate the quantum mechanical phases picked up by electrons tunneling between the lattice sites of a crystal in a realmagnetic ﬁeld.7 The optical phases that accumulate around eachsquare plaquette in the lattice are equal and emerge from a uniform artiﬁcial magnetic ﬁeld.
Unlike in naturally occurring solids, where the magnetic
ﬂux through a plaquette is much smaller than the ﬂux quantum h/q, where q is the magnitude of the relevant charge, verylarge laser-induced ﬂuxes can be produced in an optical lattice.
Figure 5a shows one experimental demonstration,9 in which an
atomic wavepacket prepared in a single site of an optical latticeundergoes cyclotron-like motion around a square plaquette; its
center-of-mass motion, from dark green to light green, is plotted over 2 ms. A similar scheme was experimentally implemented by Ketterle’s group around the same time.10 Nontrivial
phases have also been imprinted by literally shaking the opticallattices,11 but in a way that does not correspond to a uniform
magnetic ﬁeld.

Synthetic dimensions
An essential step in creating gauge ﬁelds with laser-assisted
tunneling is to suppress the native tunneling of atoms between
lattice sites. In the preceding section, we took the natural approach of using a tilted lattice to do the job. But that’s not the
only solution. Five years ago, a group of researchers, including
two of us (Spielman and Juzeliūnas), proposed a scheme usingtransitions between diﬀerent spin states of the BEC atomic
ground state to create “synthetic dimensions.”12
Lattice sites, according to that approach, need not be in different places in space. Dimension can also refer to the connectivity, or number of independent states, into which the atoms
can tunnel. In addition to a real dimension, along which motion
corresponds to a displacement in space, there’s a synthetic dimension that corresponds to the internal spin states of ultracold atoms. When lasers couple the spin states together, the resulting “motion” between the spin states is accompanied by an
optical phase that gives rise to a uniform ﬂux.

In addition to reestablishingtunneling between sites, thelaser-induced tunneling also
imprints a position-dependent
optical phase onto the wavefunction of the atoms.
The concept, which Spielman and others subsequently implemented in 2015, oﬀers new opportunities for control andmeasurement.13 For one thing, it’s easy to detect individual synthetic lattice sites using standard spin-selective detection techniques. Also in 2015 Leonardo Fallani’s group concurrently
demonstrated the utility of synthetic dimensions in a degenerate Fermi gas of ytterbium.14
Figure 5b presents the experimental trajectories followed by
BEC atoms on a long, thin virtual strip, whose real dimension
is space, plotted horizontally, and whose synthetic dimension
is the atoms’ magnetic quantum numbers m = 1, 0, and −1, plotted vertically.13 By preparing the atoms on the strip’s edges andthen allowing them to move in the artiﬁcial magnetic ﬁeld, theresearchers observed them following “skipping orbits” along
the top and bottom edges. Each time an atom struck the hardwall potential along an edge, it reﬂected and began following
yet another cyclotron orbit.

To be non-abelian
As we’ve seen, artiﬁcial gauge ﬁelds make charge-neutral particles curve as if they were under the inﬂuence of a Lorentz
force. But in quantum systems, the rabbit hole is deeper: As wehave noted, quantum particles have internal degrees of freedom, like the spin-up and spin-down of an electron.
That simple addition opens the door for new kinds of socalled non-abelian gauge ﬁelds, in which the eﬀective Lorentz
force can depend on the magnitude and sign of the spin oreven drive changes to the spin state as the particle moves. (Sucha non-abelian gauge ﬁeld is distinct from the non-abelian

FIGURE 5. DYNAMICS IN AN ARTIFICIAL GAUGE FIELD. Atoms that move from one optical lattice site to another under laser-assisted
tunneling circle through the sites, as in figure 3b. (a) One experiment measured the center-of-mass positions of atoms (dots) <x> and <y>,scaled to the lattice constants dx and dy , as the atoms move among the four sites (inset) over 2.1 ms. (Adapted from ref. 9.) (b) In anotherexperiment, the positions (dots) of BEC atoms are mapped along the edges of a long, thin virtual strip. The horizontal dimension, scaled to
the lattice constants, is real, and the narrow dimension is synthetic, formed by the atoms’ spin states 1, 0, and −1. The edge currents to theleft (pink) and right (blue) evolve in time with opposite velocities and are the result of the “skipping orbits,” in which the atoms mimic
cyclotron motion and periodically reflect from the strip’s edges. (Adapted from ref. 13.)JANUARY 2019 | PHYSICS TODAY 43

ARTIFICIAL GAUGE FIELDS
quasiparticles that are potentially relevant for quantum computation. See the article by Nick Read, PHYSICS TODAY, July 2012,page 38.) In essence, the Aharonov–Bohm phases φ of ﬁgure 3awould each be replaced by a matrix that can give diﬀerent phases
for the diﬀerent spin states or that can even change the spinstate entirely.
Spin–orbit coupling in a material is an interaction between
the electron’s momentum and its spin. In many cases, the interaction is equivalent to a non-abelian gauge ﬁeld. Spin–orbit
coupling is responsible for various interesting physical phenomena—from the spin Hall eﬀect to Majorana fermions andtopological insulators (see the box on this page and PHYSICSTODAY, March 2011, page 20). By extending the ideas discussed
above, certain types of non-abelian gauge ﬁelds have also seen
the light of day in cold-atom experiments.7

Applications
The experiments described in this article serve as quantum
simulations to better understand the toy models that approximately describe real materials. Vortex physics is an ideal target
for quantum simulation. Because the motion of vortices is aleading source of dissipation in superconductors, understanding them has wide-ranging real-world impact, from high-ﬁeld
superconducting magnets used in medical magnetic resonanceimaging to magnetic levitating trains.
Much is still unknown about quantum vortices: How dolarge collections of them interact and evolve? (See, for example,
PHYSICS TODAY, January 2017, page 19.) When do their positions
become pinned to the disorder potential? How do we understand the ﬂow of angular momentum in a material with vortices, in analogy to the ﬂow of electrons in a metal? Cold-atomsuperﬂuids in the presence of an artiﬁcial magnetic ﬁeld serve
as a medium for exploring those questions.
Artiﬁcial gauge ﬁelds provide new techniques for realizing
topological states of matter (see the Quick Study by Mohammad
Hafezi and Jake Taylor, PHYSICS TODAY, May 2014, page 68).
Topological insulators and the integer and fractional quantum
Hall eﬀects were discovered and understood in conventional
material systems, but the practical limitations of material systems hinder the ability to create new types of topologicalmatter. For example, although many 2D models host anyon excitations, their only known physical manifestation is the fractional quantum Hall eﬀect. Three-dimensional counterparts—
interacting topological insulators—are beyond the reach ofcurrent experiment and theory. Cold atoms with artiﬁcial magnetic ﬁelds provide a realistic system experimentalists can use
to engineer and observe their exotic states.
Artiﬁcial gauge ﬁelds can also host completely new physics
that have no analogues elsewhere in nature. One example isspin-½ bosons made with spin–orbit coupling. Recall that bosons
normally have integer spin and fermions have half-integer
spin. As in quantum Hall systems, spin-½ bosons would boast
a massively degenerate ground state and be ideally suited for
creating strongly correlated topological matter.16
The gauge ﬁelds present in high-energy physics are, like thephoton, dynamical gauge ﬁelds. Aspects of those dynamical
gauge ﬁelds may be modeled with time-dependent artiﬁcial
gauge ﬁelds. A dynamical gauge ﬁeld samples all possible conﬁgurations of the associated classical ﬁeld. In certain cases,
quantum ﬂuctuations in a dynamical gauge ﬁeld have average
44 PHYSICS TODAY | JANUARY 2019

TOPOLOGICAL MATTER
Band insulators are crystalline materials with an energy gap
between the materials’ occupied valence bands and unoccupied conduction bands. A single excitation produces a mobile
electron free to move in the crystal lattice. The charge andquantum statistics of that excitation are the same as those of
the material’s constituent electrons.
Topological insulators (TIs) are a broad class of band insulators, distinguished by different windings of the phase of theatom’s eigenstates for different crystal momenta in the lattice.
Although excitations deep inside TIs separate, much like conventional insulators, into valance and conduction bands, TIs
form new conducting states at crystal boundaries. (See the article by Xiao-Liang Qi and Shou-Cheng Zhang, PHYSICS TODAY,
January 2010, page 33.)
Strongly correlated materials give new excitations calledanyons. As Frank Wilczek put it, “The statistics of these objects,
like their spin, interpolates continuously between the usualboson and fermion cases.”15 Often referred to as fractionalized
quasiparticles, anyons occur in strongly correlated topologically ordered states.
Such strongly correlated states are theoretically present invarious quantum spin models. But laboratory realizations of
TIs are few: They have been seen experimentally only in fractional quantum Hall systems, which require highly restrictive
experimental conditions, such as ultralow temperatures, highmagnetic fields, and ultraclean samples. Strongly interacting
ultracold atoms subject to artificial gauge fields are one promising avenue for realizing those fractional states of matter.
properties similar to that of noise added to a classical gaugeﬁeld. Sampling those ﬂuctuations can be experimentally modeled using atoms in optical lattices coupled to a synthetic gauge
ﬁeld to which laboratory-controlled noise has been added.
That would be a good ﬁrst step to simulating lattice gauge theories in the low-temperature limit.
For financial support, we thank NIST, the US Army Research Office,the US Air Force Office of Scientific Research, NSF through its Physics
Frontier Center at the Joint Quantum Institute at the University of
Maryland, and the Lithuanian Research Council. Victor Galitski and Ian
Spielman also appreciate the support of Paul Baker and Peter Reynolds.

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