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.
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.
Synthetic gauge fields have recently emerged, arising in the context of quantum simulations, topological matter, and the protected transportation of excitations against defects. For example, an ultracold atom experiences a light-induced effective magnetic field when tunneling in an optical lattice, and offering a platform to simulate the quantum Hall effect and topological insulators. Similarly, the magnetic field associated with photon transport between sites has been demonstrated in a coupled resonator array. Here, we report the first experimental demonstration of a synthetic gauge field in the virtual lattices of bosonic modes in a single optomechanical resonator. By employing degenerate clockwise and counterclockwise optical modes and a mechanical mode, a controllable synthetic gauge field is realized by tuning the phase of the driving lasers. The nonreciprocal conversion between the three modes is realized for different synthetic magnetic fluxes. As a proof-of-principle demonstration, we also show the dynamics of the system under a fast-varying synthetic gauge field, and demonstrate synthetic electric field. Our demonstration not only provides a versatile and controllable platform for studying synthetic gauge fields in high dimensions but also enables an exploration of ultrafast gauge field tuning with a large dynamic range, which is restricted for a magnetic field.
Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter.On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize.Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian-a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics.Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade.Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs.We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations.We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.
Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and reinterpreted as lattice sites along an artificial spatial dimension. However, atomic experimental realizations have been limited so far by the number of artificial lattice sites that can be feasibly coupled along the synthetic dimension. Here, we experimentally realize for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behavior in the real-space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. The Bloch oscillations thus act as a smoking-gun signature of the synthetic dimension, and allow us to characterize the effective band structure. Our methods provide an efficient approach for the manipulation and control of highly excited trap states, and set the stage for the future exploration of topological physics in higher dimensions through the use of a tunable artificial gauge field and finite-range interactions.
Topology can imbue lattice systems with special properties, notably the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated quantum pumping phenomena.
Synthetic dimensions are powerful tools for quantum simulation and computation. They are realized by harnessing internal or external degrees of freedom of an atom or molecule, which can mimic the motion of an electron in a real-space lattice potential. Such degrees of freedom are highly tunable and can be engineered to create configurations difficult to access or realize in real space. Some of the exciting possibilities include realizing higher dimensions systems[1, 2, 3], nontrivial real space[4, 5] and band structure[6, 7] topologies and artificial gauge fields[8, 9]. Experiments have utilized various degrees of freedom to create synthetic dimensions, such as motional[10, 11], spin[8, 12, 13, 14] and rotational[15] levels of atoms and molecules, and frequency modes, spatial modes, and arrival times in photonic systems[16]. Atomic synthetic dimensions have demonstrated artificial gauge fields, spin-orbit coupling, chiral edge states using Raman-coupled ground magnetic sublevels[8, 12, 17] of atoms, and phenomena such as Anderson localization using two-photon Bragg transitions by coupling free-particle momentum states[18]. Here, we harness the Rydberg levels of 84Sr to realize a synthetic lattice for studying quantum matter. Resonant millimeter-wave (mm-wave) radiation coupling Rydberg levels |i⟩ and |j⟩ with amplitude Ωij (Rabi frequency) are described by the same Hamiltonian as a particle tunneling between lattice sites |i⟩ and |j⟩ with tunneling amplitude Jij = Ωij /2. The mathematical equivalence to particles moving in a real-space lattice enables Rydberg levels to function as a synthetic spatial dimension. Rydberg-atom synthetic dimensions offer control over connectivity, tunneling rates and on-site potentials, which allows for the creation of a broad range of synthetic dimensional system. The capabilities of such a system are demonstrated by realizing the famous Su-Schrieffer-Heeger (SSH) model[19] and studying its topologically protected edge states(TPS).
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. We engineer tunable gauge fields through the local control of tunneling phases in an effective 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. Furthermore, we 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 new possibilities for the study of topological phases and localization phenomena in atomic gases.