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Nonlinearities can have a profound influence on the dynamics and equilibrium properties of discrete lattice systems. The simple case of two coupled modes with self-nonlinearities gives rise to the rich bosonic Josephson effects. In many-site arrays, nonlinearities yield a wealth of rich phenomena, including a variety of solitonic excitations, the emergence of vortex lattices in the presence of gauge fields, and the general support of chaotic dynamics. Here, we experimentally explore a three-site mechanical ring with tunable gauge fields and nonlinearities. We observe a macroscopic self-trapping transition that is tunable by the magnetic flux, consistent with the equilibrium response. We further observe novel behavior that appears only out of equilibrium, the emergence of interaction-stabilized chiral solitary waves. These results provide a starting point to explore nonlinear phenomena arising in larger mechanical arrays coupled to static and dynamical gauge fields., Comment: 6 pages, 3 figures

Coherent dynamics of interacting quantum particles plays a central role in the study of strongly correlated quantum matter and the pursuit of quantum information processors. Here, we present the state-space of interacting Rydberg atoms as a synthetic landscape on which to control and observe coherent and correlated dynamics. With full control of the coupling strengths and energy offsets between the pairs of sites in a nine-site synthetic lattice, we realize quantum walks, Bloch oscillations, and dynamics in an Escher-type "continuous staircase". In the interacting regime, we observe correlated quantum walks, Bloch oscillations, and confinement of particle pairs. Additionally, we simultaneously tilt our lattice both up and down to achieve coherent pair oscillations. When combined with a few straightforward upgrades, this work establishes synthetic Rydberg lattices of interacting atom arrays as a promising platform for programmable quantum many-body dynamics with access to features that are difficult to realize in real-space lattices., Comment: 5 pages, 4 figures

Flat bands play a central role in hosting emergent states of matter in many condensed matter systems, from the nascent insulating states of twisted bilayer graphene to the fractionalized excitations found in frustrated magnets and quantum Hall materials. Here, we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. Using the approach of synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries, and through nonequilibrium dynamics we explore the control of Aharonov--Bohm (AB) caging via a tunable $U(1)$ gauge field. Through microscopic measurements of Rydberg pairs, we explore the interaction-driven breakdown of AB caging in the limit of strong dipolar interactions that mix the lattice bands. In the limit of weak interactions, where caging remains intact, we observe an effective magnetism that arises due to the interaction-driven mixing of degenerate flat-band states. These observations of strongly correlated flat-band dynamics open the door to explorations of new emergent phenomena in synthetic quantum materials., Comment: 7 pages, 4 figures

Inspired by recent advances in observational astrophysics and continued explorations in the field of analog gravity, we discuss the prospect of simulating models of cosmology within the context of synthetic mechanical lattice experiments. We focus on the physics of expanding Universe scenarios described by the Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric. Specifically, quantizing scalar fluctuations in a background FLRW spacetime leads to a quadratic bosonic Hamiltonian with temporally varying pair production terms. Here we present a mapping that provides a one-to-one correspondence between these classes of cosmology models and physical mechanical oscillator systems. As proof-of-principle, we then perform experiments on an actual synthetic lattice system composed of such oscillators. We simulate two different FLRW expansion scenarios driven by inflationary dark energy- and matter-dominated Universes and discuss our experimental results., Comment: 7 pages, 3 figures

Molecules have vibrational, rotational, spin-orbit and hyperfine degrees of freedom or quantum states, each of which responds in a unique fashion to external electromagnetic radiation. The control over superpositions of these quantum states is key to coherent manipulation of molecules. For example, the better the coherence time the longer quantum simulations can last. The important quantity for controlling an ultracold molecule with laser light is its complex-valued molecular dynamic polarizability. Its real part determines the tweezer or trapping potential as felt by the molecule, while its imaginary part limits the coherence time. Here, our study shows that efficient trapping of a molecule in its vibrational ground state can be achieved by selecting a laser frequency with a detuning on the order of tens of GHz relative to an electric-dipole-forbidden molecular transition. Close proximity to this nearly forbidden transition allows to create a sufficiently deep trapping potential for multiple rotational states without sacrificing coherence times among these states from Raman and Rayleigh scattering. In fact, we demonstrate that magic trapping conditions for multiple rotational states of the ultracold $^{23}$Na$^{87}$Rb polar molecule can be created., Comment: 9 pages, 6 figures

We introduce feedback-measurement technologies to achieve flexible control of Weyl points and conduct the first experimental demonstration of Weyl type I-II transition in mechanical systems. We demonstrate that non-Hermiticity can expand the Fermi arc surface states from connecting Weyl points to Weyl rings, and lead to a localization transition of edge states influenced by the interplay between band topology and the non-Hermitian skin effect. Our findings offer valuable insights into the design and manipulation of Weyl points in mechanical systems, providing a promising avenue for manipulating topological modes in non-Hermitian systems.

Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases - two are localized in the synthetic dimension, predicted as zero-temperature ground states in Refs. [Sci. Rep., 8, 1 (2018) and Phys. Rev. A 99, 013624 (2019)], and a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength, for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tri-critical point on the phase boundary. By examining the dependence of the tri-critical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension., Comment: 9 pages, 3 figures

Novel geometries can be created by coupling internal states of atoms or molecules to mimic movement in real-space, Comment: An early draft of Physics Today 76(4), 62 (2023). Please refer to the published paper for a significantly improved (edited and formatted) version. A free pdf is available at https://kaden.rice.edu/p2023-2.pdf

Synthetic dimensions, wherein dynamics occurs in a set of internal states, have found great success in recent years in exploring topological effects in cold atoms and photonics. However, the phenomena thus far explored have largely been restricted to the non-interacting or weakly interacting regimes. Here, we extend the synthetic dimensions playbook to strongly interacting systems of Rydberg atoms prepared in optical tweezer arrays. We use precise control over driving microwave fields to introduce a tunable $U(1)$ flux in a four-site lattice of coupled Rydberg levels. We find highly coherent dynamics, in good agreement with theory. Single atoms show oscillatory dynamics controllable by the gauge field. Small arrays of interacting atoms exhibit behavior suggestive of the emergence of ergodic and arrested dynamics in the regimes of intermediate and strong interactions, respectively. These demonstrations pave the way for future explorations of strongly interacting dynamics and many-body phases in Rydberg synthetic lattices., Comment: 6 pages, 4 figures; 6 pages and 5 figures of Supplementary Material

Building on the development of momentum state lattices (MSLs) over the past decade, we introduce a simple extension of this technique to higher dimensions. Based on the selective addressing of unique Bragg resonances in matter-wave systems, MSLs have enabled the realization of tight-binding models with tunable disorder, gauge fields, non-Hermiticity, and other features. Here, we examine and outline an experimental approach to building scalable and tunable tight-binding models in two dimensions describing the laser-driven dynamics of atoms in momentum space. Using numerical simulations, we highlight some of the simplest models and types of phenomena this system is well-suited to address, including flat-band models with kinetic frustration and flux lattices supporting topological boundary states. Finally, we discuss many of the direct extensions to this model, including the introduction of disorder and non-Hermiticity, which will enable the exploration of new transport and localization phenomena in higher dimensions., Comment: 12 pages, 5 figures

We explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique and observe qualitative agreement between the measured and simulated energy spectra for small two- and three-site lattices as well as a uniform many-site lattice. Finally, through simulations, we show that this technique should allow for the exploration of the topological bands and the fractal energy spectrum of the Hofstadter model as realized in synthetic lattices., Comment: 9 pages, 5 figures

Non-Hermitian two-site ``dimers'' serve as minimal models in which to explore the interplay of gain and loss in dynamical systems. In this paper, we experimentally and theoretically investigate the dynamics of non-Hermitian dimer models with non-reciprocal hoppings between the two sites. We investigate two types of non-Hermitian couplings; one is when asymmetric hoppings are externally introduced, and the other is when the non-reciprocal hoppings depend on the population imbalance between the two sites, thus introducing the non-Hermiticity in a dynamical manner. We engineer the models in our synthetic mechanical set-up comprised of two classical harmonic oscillators coupled by measurement-based feedback. For fixed non-reciprocal hoppings, we observe that, when the strength of these hoppings is increased, there is an expected transition from a $\mathcal{PT}$-symmetric regime, where oscillations in the population are stable and bounded, to a $\mathcal{PT}$-broken regime, where the oscillations are unstable and the population grows/decays exponentially. However, when the non-Hermiticity is dynamically introduced, we also find a third intermediate regime in which these two behaviors coexist, meaning that we can tune from stable to unstable population dynamics by simply changing the initial phase difference between the two sites. As we explain, this behavior can be understood by theoretically exploring the emergent fixed points of a related dimer model in which the non-reciprocal hoppings depends on the normalized population imbalance. Our study opens the way for the future exploration of non-Hermitian dynamics and exotic lattice models in synthetic mechanical networks., Comment: 16 pages, 9 figures -- added references

The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site $\mathcal{PT}$-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for non-cyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov--Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken $\mathcal{PT}$ symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards the further studies of non-Hermitian and topological physics in synthetic metamaterials., Comment: 7 pages, 4 figures; supplemental materials with two SM figures

The non-Hermitian skin effect (NHSE), the accumulation of eigen wavefunctions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum many-body setting remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain -- a non-Hermitian topological model with NHSE -- in the momentum space of a two-component Bose-Einstein condensate. We identify unique signatures of NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our work sets the stage for further investigation on the interplay of many-body statistics and interactions with NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics., Comment: 13 pages, 11 figures

Robust cooling and nondestructive imaging are prerequisites for many emerging applications of neutral atoms trapped in optical tweezers, such as their use in quantum information science and analog quantum simulation. The tasks of cooling and imaging can be challenged, however, by the presence of large trap-induced shifts of their respective optical transitions. Here, we explore a system of $^{39}$K atoms trapped in a near-detuned ($780$ nm) optical tweezer, which leads to relatively minor differential (ground vs. excited state) Stark shifts. We demonstrate that simple and robust loading, cooling, and imaging can be achieved through a combined addressing of the D$_\textrm{1}$ and D$_\textrm{2}$ transitions. While imaging on the D$_\textrm{2}$ transition, we can simultaneously apply $\Lambda$-enhanced gray molasses (GM) on the D$_\textrm{1}$ transition, preserving low backgrounds for single-atom imaging through spectral filtering. Using D$_\textrm{1}$ cooling during and after trap loading, we demonstrate enhanced loading efficiencies as well as cooling to low temperatures. These results suggest a simple and robust path for loading and cooling large arrays of potassium atoms in optical tweezers through the use of resource-efficient near-detuned optical tweezers and GM cooling., Comment: 8 pages, 4 figures, and 2-page Supplementary Materials

Metamaterials based on mechanical elements have been developed over the past decade as a powerful platform for exploring analogs of electron transport in exotic regimes that are hard to produce in real materials. In addition to enabling new physics explorations, such developments promise to advance the control over acoustic and mechanical metamaterials, and consequently to enable new capabilities for controlling the transport of sound and energy. Here, we demonstrate the building blocks of highly tunable mechanical metamaterials based on real-time measurement and feedback of modular mechanical elements. We experimentally engineer synthetic lattice Hamiltonians describing the transport of mechanical energy (phonons) in our mechanical system, with control over local site energies and loss and gain as well as control over the complex hopping between oscillators, including a natural extension to non-reciprocal hopping. Beyond linear terms, we experimentally demonstrate how this measurement-based feedback approach opens the window to independently introducing nonlinear interaction terms. Looking forward, synthetic mechanical lattices open the door to exploring phenomena related to topology, non-Hermiticity, and nonlinear dynamics in non-standard geometries, higher dimensions, and with novel multi-body interactions., Comment: 14 pages, 8 figures

A topological $\theta$-term in gauge theories, including quantum chromodynamics in 3+1 dimensions, gives rise to a sign problem that makes classical Monte Carlo simulations impractical. Quantum simulations are not subject to such sign problems and are a promising approach to studying these theories in the future. In the near term, it is interesting to study simpler models that retain some of the physical phenomena of interest and their implementation on quantum hardware. For example, dimensionally-reducing gauge theories on small spatial tori produces quantum mechanical models which, despite being relatively simple to solve, retain interesting vacuum and symmetry structures from the parent gauge theories. Here we consider quantum mechanical particle-on-a-circle models, related by dimensional reduction to the 1+1d Schwinger model, that possess a $\theta$-term and realize an 't Hooft anomaly or global inconsistency at $\theta = \pi$. These models also exhibit the related phenomena of spontaneous symmetry breaking and instanton-anti-instanton interference in real time. We propose an experimental scheme for the real-time simulation of a particle on a circle with a $\theta$-term and a $\mathbb{Z}_n$ potential using a synthetic dimension encoded in a Rydberg atom. Simulating the Rydberg atom with realistic experimental parameters, we demonstrate that the essential physics can be well-captured by the experiment, with expected behavior in the tunneling rate as a function of $\theta$. Similar phenomena and observables can also arise in more complex quantum mechanical models connected to higher-dimensional nonabelian gauge theories by dimensional reduction., Comment: 25 pages, 11 figures; minor changes and refs added, version accepted for publication in PRD

The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, the idea of synthetic dimensions -- in which transport occurs in a space spanned by internal or motional states coupled by field-driven transitions -- has played a key role in this expansion. While approaches based on synthetic dimensions have led to rapid advances in single-particle Hamiltonian engineering, strong interaction effects have been conspicuously absent from most synthetic dimensions platforms. Here, in a lattice of coupled atomic momentum states, we show that atomic interactions result in large and qualitative changes to dynamics in the synthetic dimension. We explore how the interplay of nonlinear interactions and coherent tunneling enriches the dynamics of a one-band tight-binding model, giving rise to macroscopic self-trapping and phase-driven Josephson dynamics with a nonsinusoidal current-phase relationship, which can be viewed as stemming from a nonlinear band structure arising from interactions., Comment: 6 pages, 3 figures, 3 pages of supplementary material

Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle interactions are slow and can be parallelized to efficiently create a cluster state. However, understanding how two-qubit errors impact algorithm accuracy and developing experimentally viable approaches to characterize cluster-state fidelity are outstanding challenges. Here, we consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of these errors on the cluster state. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To enable construction of larger cluster states, we design lowest-order refocusing pulses for correcting these slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.

We report a theoretical description of the synthetic momentum-state lattices with a 3D Gross-Pitaevskii equation (GPE), where both the external trap potential and the mean-field spatial-density-dependent many-body interactions are naturally included and exactly treated. The GPE models exhibit better performance than the tight-binding model to depict the experimental observations. Since the trap modifies the dispersion relation for free particles and shapes the spatial density distribution that leads to inhomogeneous interactions, decoherences (damping oscillation) appear even for a short-time evolution. Our parametric calculations for the two-state oscillation suggest that we should work with a relatively shallow trap in the weakly interacting regime, especially when the long-term dynamics are concerned. The impact of the mean-field interaction, i.e., the self-trapping behavior, on the transport dynamics and the topological phase transition in a finite multiple-state lattice chain is also specifically investigated. Such an accurate treatment of the inhomogeneous interactions allows for further investigations on the interplay with disorder, the pair correlation dynamics, and the thermalization process in momentum space., Comment: 8 pages, 7 figures

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-Andr\'{e} (AA) model, with an energy-dependent self duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing the lowest and highest energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of the highest energy state due to screening. This study paves the way for quantitative studies of interaction effects on self duality induced mobility edges., Comment: 6 pages, 3 figures, and ancillary Supplementary Materials file

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using \narb and \rbcs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules., Comment: 15 pages, 8 figures, version 2

Quantum state transformations that are robust to experimental imperfections are important for applications in quantum information science and quantum sensing. Counterdiabatic (CD) approaches, which use knowledge of the underlying system Hamiltonian to actively correct for diabatic effects, are powerful tools for achieving simultaneously fast and stable state transformations. Protocols for CD driving have thus far been limited in their experimental implementation to discrete systems with just two or three levels, as well as bulk systems with scaling symmetries. Here, we extend the tool of CD control to a discrete synthetic lattice system composed of as many as nine sites. Although this system has a vanishing gap and thus no adiabatic support in the thermodynamic limit, we show that CD approaches can still give a substantial, several order-of-magnitude, improvement in fidelity over naive, fast adiabatic protocols., Comment: 10 pages (+2 supplementary), 4 figures

We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of degrees of freedom and discrete values. We construct the effective Hamiltonian of a system of dipolar molecules with electric dipole-dipole interactions, where we use the tunable parameters of the system to match it to the target Hamiltonian describing a U(1) quantum link model in 1+1 dimensions., Comment: Proceedings of the 37th International Symposium on Lattice Field Theory - Lattice 2019, Wuhan (China)

We report the experimental observation of tunable, non-reciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parameters. We demonstrate that the non-reciprocity originates from the interplay of the synthetic magnetic flux and the laser-induced loss, which simultaneously breaks the inversion and the time-reversal symmetries. Our results open up the avenue for investigating non-reciprocal dynamics in cold atoms, and highlight the dissipative AB ring as a flexible building element for applications in quantum simulation and quantum information., Comment: 6 pages, 4 figures

Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itinerant degrees of freedom. Each molecule represents either a site or gauge degree of freedom, and Gauss law is preserved by a direct and programmatic tuning of positions and internal state energies. This approach can be regarded as a form of analog systems programming and charts a path forward for near-term quantum simulation. As a first step, we numerically validate this scheme in a small-system study of U(1) quantum link models in (1+1) dimensions with link spin S = 1/2 and S = 1 and illustrate how dynamical phenomena such as string inversion and string breaking could be observed in near-term experiments. Our work brings together methods from atomic and molecular physics, condensed matter physics, high-energy physics, and quantum information science for the study of nonperturbative processes in gauge theories.

The Su-Schrieffer-Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higher-dimensional extension of the mean chiral displacement measurement, however this has not yet been verified in experiment. Here we report the realization of this model with ultracold atoms in a momentum lattice. We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary., Comment: 15 pages, 6 figures

We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system's ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e, one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments., Comment: 8 pages main text + 3 pages Appendix + references; 7 figures

Dissipation can serve as a powerful resource for controlling the behavior of open quantum systems.Recently there has been a surge of interest in the influence of dissipative coupling on large quantum systems and, more specifically, how these processes can influence band topology and phenomena like many-body localization. Here, we explore the engineering of local, tunable dissipation in so-called synthetic lattices, arrays of quantum states that are parametrically coupled in a fashion analogous to quantum tunneling. Considering the specific case of momentum-state lattices, we investigate two distinct mechanisms for engineering controlled loss: one relying on an explicit form of dissipation by spontaneous emission, and another relying on reversible coupling to a large reservoir of unoccupied states. We experimentally implement the latter and demonstrate the ability to tune the local loss rate over a large range. The introduction of controlled loss to the synthetic lattice toolbox promises to pave the way for studying the interplay of dissipation with topology, disorder, and interactions., Comment: 8 pages, 3 figures

Topology and disorder have deep connections and a rich combined influence on quantum transport. In order to probe these connections, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. We characterize the system's topology through measurement of the mean chiral displacement of the bulk density extracted from quench dynamics. We find evidence for the topological Anderson insulator phase, in which the band structure of an otherwise trivial wire is driven topological by the presence of added disorder. In addition, we observed the robustness of topological wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform will enable future realizations of strongly interacting topological fluids., Comment: 6 pages, 3 figures; 9 pages of supplementary materials

In this work we perform polarization spectroscopy of erbium atoms in a hollow cathode lamp (HCL) for the stabilization of a diode laser to the 401-nm transition. We review the theory behind Doppler-free polarization spectroscopy, theoretically model the expected erbium polarization spectra, and compare the numerically calculated spectra to our experimental data. We further analyze the dependence of the measured spectra on the HCL current and the peak intensities of our pump and probe lasers to determine conditions for optimal laser stabilization., Comment: 11 pages, 7 figures

Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using measurements of rotational state populations., Comment: 5-page article + 4 figures + references; 7 pages + 4 figures in Supplement

We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the added exchange energy between atoms in distinguishable momentum states leads to an effectively attractive, finite-ranged interaction in momentum space. In this work, we observe the onset of self-trapping driven by such interactions in a momentum-space double well, paving the way for more complex many-body studies in tailored MSLs. We consider the types of phenomena that may result from these interactions, including the formation of chiral solitons in topological zigzag lattices., Comment: 6 pages, 3 figures; 3 pages of supplementary materials; This submission supersedes arXiv:1702.07315 with updated experimental results

There has been great interest in realizing quantum simulators of charged particles in artificial gauge fields. Here, we perform the first quantum simulation explorations of the combination of artificial gauge fields and disorder. Using synthetic lattice techniques based on parametrically-coupled atomic momentum states, we engineer zigzag chains with a tunable homogeneous flux. The breaking of time-reversal symmetry by the applied flux leads to analogs of spin-orbit coupling and spin-momentum locking, which we observe directly through the chiral dynamics of atoms initialized to single lattice sites. We additionally introduce precisely controlled disorder in the site energy landscape, allowing us to explore the interplay of disorder and large effective magnetic fields. The combination of correlated disorder and controlled intra- and inter-row tunneling in this system naturally supports energy-dependent localization, relating to a single-particle mobility edge. We measure the localization properties of the extremal eigenstates of this system, the ground state and the most-excited state, and demonstrate clear evidence for a flux-dependent mobility edge. These measurements constitute the first direct evidence for energy-dependent localization in a lower-dimensional system, as well as the first explorations of the combined influence of artificial gauge fields and engineered disorder. Moreover, we provide direct evidence for interaction shifts of the localization transitions for both low- and high-energy eigenstates in correlated disorder, relating to the presence of a many-body mobility edge. The unique combination of strong interactions, controlled disorder, and tunable artificial gauge fields present in this synthetic lattice system should enable myriad explorations into intriguing correlated transport phenomena., Comment: 10 pages, 5 figures, 5 pages of supplementary materials; updated version has additional data

Ergodicity and chaos play an integral role in the dynamical behavior of many-particle systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how randomness and chaos emerge in the dynamical evolution of closed quantum systems remains elusive. Here, we develop an experimental platform for the realization of canonical quantum chaotic Hamiltonians based on quantum simulation with synthetic lattices. We map the angular momentum projection states of an effective quantum spin onto the linear momentum states of a $^{87}$Rb Bose-Einstein condensate, which can alternatively be viewed as lattice sites in a synthetic dimension. This synthetic lattice, with local and dynamical control of tight-binding lattice parameters, enables new capabilities related to the experimental study of quantum chaos. In particular, the capabilities of our system let us tune the effective size of our spin, allowing us to illustrate how classical chaos can emerge from a discrete quantum system. Moreover, spectroscopic control over our synthetic lattice allows us to explore unique aspects of our spin's dynamics by measuring the out-of-time-ordered correlation function, and enables future investigations into entirely new classes of chaotic systems., Comment: 9 pages, 6 figures

We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven atomic transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the distinguishability of the discrete momentum states coupled in MSLs gives rise to an added exchange energy between condensate atoms in different momentum orders, relating to an effectively attractive, finite-ranged interaction in momentum space. We explore the types of phenomena that can result from this interaction, including the formation of chiral self-bound states in topological MSLs. We also discuss the prospects for creating squeezed states in momentum-space double wells., Comment: 6 pages, 3 figures; This submission is superseded by arXiv:1708.01237 with updated experimental results

Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of optical lattice experiments, a more general control over site-energy and off-diagonal tunneling disorder has been lacking. The use of atomic quantum states as "synthetic dimensions" has introduced the spectroscopic, site-resolved control necessary to engineer new, more tailored realizations of disorder. Here, by controlling laser-driven dynamics of atomic population in a momentum-space lattice, we extend the range of synthetic-dimension-based quantum simulation and present the first explorations of dynamical disorder and tunneling disorder in an atomic system. By applying static tunneling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading as in the case of uniform tunneling. When the applied disorder fluctuates on timescales comparable to intersite tunneling, we instead observe diffusive atomic transport, signaling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localization in the momentum-space lattice., Comment: 6 pages, 3 figures

The prospect of studying topological matter with the precision and control of atomic physics has driven the development of many techniques for engineering artificial magnetic fields and spin-orbit interactions. Recently, the idea of introducing nontrivial topology through the use of internal (or external) atomic states as effective "synthetic dimensions" has garnered attraction for its versatility and possible immunity from heating. Here, we directly engineer tunable artificial gauge fields through the local control of tunneling phases in an effectively two-dimensional manifold of discrete atomic momentum states. We demonstrate the ability to create homogeneous gauge fields of arbitrary value, directly imaging the site-resolved dynamics of induced chiral currents. We furthermore engineer the first inhomogeneous artificial gauge fields for cold atoms, observing the magnetic reflection of atoms incident upon a step-like variation of an artificial vector potential. These results open up new possibilities for the study of topological phases and localization phenomena in atomic gases., Comment: 5 pages, 3 figures; 3 pages of supplementary materials

This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole-dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime. We discuss in detail the recent experimental progress in realizing and studying strongly interacting systems of polar molecules trapped in optical lattices, with particular emphasis on the study of interacting spin systems and non-equilibrium quantum magnetism. Finally, we conclude with a brief discussion of the future prospects for studies of strongly interacting dipolar molecules., Comment: 14 figures, 2 tables

The Su-Schrieffer-Heeger (SSH) model, which captures the most striking transport properties of the conductive organic polymer $trans$-polyacetylene, provides perhaps the most basic model system supporting topological excitations. The alternating bond pattern of polyacetylene chains is captured by the bipartite sublattice structure of the SSH model, emblematic of one-dimensional chiral symmetric topological insulators. This structure supports two distinct nontrivial topological phases, which, when interfaced with one another or with a topologically trivial phase, give rise to topologically-protected, dispersionless boundary states. Using $^{87}$Rb atoms in a momentum-space lattice, we realize fully-tunable condensed matter Hamiltonians, allowing us to probe the dynamics and equilibrium properties of the SSH model. We report on the experimental quantum simulation of this model and observation of the localized topological soliton state through quench dynamics, phase-sensitive injection, and adiabatic preparation., Comment: 6 pages, 4 figures

We present a simple experimental scheme, based on standard atom optics techniques, to design highly versatile model systems for the study of single particle quantum transport phenomena. The scheme is based on a discrete set of free-particle momentum states that are coupled via momentum-changing two-photon Bragg transitions, driven by pairs of interfering laser beams. In the effective lattice models that are accessible, this scheme allows for single-site detection, as well as site-resolved and dynamical control over all system parameters. We discuss two possible implementations, based on state-preserving Bragg transitions and on state-changing Raman transitions, which respectively allow for the study of nearly arbitrary single particle Abelian U(1) and non-Abelian U(2) lattice models., Comment: 10 pages, 4 figures

We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate that this technique allows for a local and time-dependent control over all system parameters, and additionally allows for single-site resolved detection of atomic populations. We demonstrate full control over site-to-site off-diagonal tunneling elements (amplitude and phase) and diagonal site-energies, through the observation of continuous-time quantum walks, Bloch oscillations, and negative tunneling. These capabilities open up new prospects in the experimental study of disordered and topological systems., Comment: 5 pages, 3 figures; 3 pages of supplemental materials

Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena such as quantum magnetism. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle has been an outstanding experimental challenge. In this paper, we report the synthesis of a low entropy molecular quantum gas by creating molecules at individual sites of a three-dimensional optical lattice that is initially loaded from a low entropy mixture of K and Rb quantum gases. We make use of the quantum statistics and interactions of the initial atom gases to load into the optical lattice, simultaneously and with good spatial overlap, a Mott insulator of bosonic Rb atoms and a single-band insulator of fermionic K atoms. Then, using magneto-association and optical state transfer, we efficiently produce ground-state molecules in the lattice at those sites that contained one Rb and one K atom. The achieved filling fraction of 25% indicates an entropy as low as $2.2\,k_B$ per molecule. This low-entropy molecular quantum gas opens the door to novel studies of transport and entanglement propagation in a many-body system with long-range dipolar interactions.

We investigate the interplay of disorder and interactions in the accelerated transport of a Bose-Einstein condensate through an incommensurate optical lattice. We show that interactions can effectively cancel the damping of Bloch oscillations due to the disordered potential and we provide a simple model to qualitatively capture this screening effect. We find that the characteristic interaction energy, above which interactions and disorder cooperate to enhance, rather than reduce, the damping of Bloch oscillations, coincides with the average disorder depth. This is consistent with results of a mean-field simulation., Comment: 9 pages, 3 figures

Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics.

We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations., Comment: 4+ pages main text, 4 figures. 3 pages supplementary material, 2 figures

With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for exploring quantum magnetism. In atomic systems, where interactions require wave function overlap, effective spin interactions on a lattice can be realized via superexchange; however, the coupling is weak and limited to nearest-neighbor interactions. In contrast, dipolar interactions exist in the absence of tunneling and extend beyond nearest neighbors. This allows coherent spin dynamics to persist even at high entropy and low lattice filling. Effects of dipolar interactions in ultracold molecular gases have so far been limited to the modification of chemical reactions. We now report the observation of dipolar interactions of polar molecules pinned in a 3D optical lattice. We realize a lattice spin model with spin encoded in rotational states, prepared and probed by microwaves. This spin-exchange interaction arises from the resonant exchange of rotational angular momentum between two molecules. We observe clear oscillations in the evolution of the spin coherence in addition to an overall decay. The frequency of these oscillations, the strong dependence of the spin coherence time on the lattice filling, and the effect of a multi-pulse sequence designed to reverse dynamics due to two-body exchange interactions all provide evidence of dipolar interactions. We also demonstrate suppression of loss in weak lattices due to a quantum Zeno mechanism. Measurements of these tunneling-induced losses allow us to independently determine the lattice filling factor. These results comprise an initial exploration of the behavior of many-body spin models with direct, long-range spin interactions and lay the groundwork for future studies of many-body dynamics in spin lattices., Comment: 18 pages, 6 figures