Synthetic Dimensions
Novel geometries can be created by coupling internal states of atoms or molecules to mimic movement in real-space
physics.pop-ph↗
arXiv subjects
Bryce Gadway
Publications and source records attributed to Bryce Gadway.
Strongly interacting Rydberg atoms in synthetic dimensions with a magnetic flux
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.
cond-mat.quant-gas↗
Two dimensional momentum state lattices
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.
cond-mat.quant-gas↗
Spectroscopy of momentum state lattices
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.
cond-mat.quant-gas↗
Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
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.
cond-mat.quant-gas↗
Simulating Quantum Mechanics with a $θ$-term and an 't Hooft Anomaly on a Synthetic Dimension
A topological $θ$-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 $θ$-term and realize an 't Hooft anomaly or global inconsistency at $θ= π$. 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 $θ$-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 $θ$. Similar phenomena and observables can also arise in more complex quantum mechanical models connected to higher-dimensional nonabelian gauge theories by dimensional reduction.
quant-ph↗
Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators
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.
cond-mat.mes-hall↗
A Gross-Pitaevskii-equation description of the momentum-state lattice: roles of the trap and many-body 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.
cond-mat.quant-gas↗
Quantifying Entanglement in Cluster States Built with Error-Prone Interactions
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.
quant-ph↗
Gray molasses cooling of $^{39}$K atoms in optical tweezers
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 $Λ$-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.
physics.atom-ph↗
Synthetic Mechanical Lattices with Synthetic Interactions
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.
cond-mat.mes-hall↗
Nonlinear dynamics in a synthetic momentum state lattice
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.
cond-mat.quant-gas↗
Framework for simulating gauge theories with dipolar spin systems
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.
quant-ph↗
Observation of tunable mobility edges in generalized Aubry-André lattices
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-André (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.
cond-mat.quant-gas↗
Nondestructive dispersive imaging of rotationally excited ultracold molecules
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.
physics.atom-ph↗
Counterdiabatic control of transport in a synthetic tight-binding lattice
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.
cond-mat.quant-gas↗
(1+1)-d U(1) Quantum link models from effective Hamiltonians of dipolar molecules
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.
hep-lat↗
Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
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.
cond-mat.quant-gas↗