Abstract Exploring Bloch oscillations in a Fock-state synthetic dimension is of considerable interest because of the favorable scalability and modest experimental resource requirements of this approach. Previously， Bloch oscillations in a nearly uniform Fock-state lattice have been demonstrated in a cold-atom ensemble, but the nonuniform case still remains to be explored. Here, we realize this physics in the radial motional mode of a single trapped 40 Ca + ion and observe high-fidelity Bloch-like dynamics in the Fock-state synthetic dimension. The trapped-ion implementation provides deterministic preparation of coherent and Fock motional states, long-time coherent evolution with high contrast, and direct state-resolved readout of both phonon-number statistics and phase-space probability distributions. We observe clear signatures of Bloch-like oscillations in both the synthetic Fock-state dimension and motional phase space and show that the oscillation period and the mean phonon number oscillation amplitude are independent of the initial Fock state. A systematic study of the oscillation amplitude and period as functions of the driving parameters shows excellent agreement with theoretical predictions. This work establishes a versatile trapped-ion Fock-state platform for exploring richer Bloch dynamics, such as Floquet-Bloch behavior and noise-assisted transport, and provides a practical route to simulating more complex lattice models within the Fock-state framework.
Abstract Exploring Bloch oscillations in a Fock-state synthetic dimension is of considerable interest because of the favorable scalability and modest experimental resource requirements of this approach. Previously， Bloch oscillations in a nearly uniform Fock-state lattice have been demonstrated in a cold-atom ensemble, but the nonuniform case still remains to be explored. Here, we realize this physics in the radial motional mode of a single trapped 40 Ca + ion and observe high-fidelity Bloch-like dynamics in the Fock-state synthetic dimension. The trapped-ion implementation provides deterministic preparation of coherent and Fock motional states, long-time coherent evolution with high contrast, and direct state-resolved readout of both phonon-number statistics and phase-space probability distributions. We observe clear signatures of Bloch-like oscillations in both the synthetic Fock-state dimension and motional phase space and show that the oscillation period and the mean phonon number oscillation amplitude are independent of the initial Fock state. A systematic study of the oscillation amplitude and period as functions of the driving parameters shows excellent agreement with theoretical predictions. This work establishes a versatile trapped-ion Fock-state platform for exploring richer Bloch dynamics, such as Floquet-Bloch behavior and noise-assisted transport, and provides a practical route to simulating more complex lattice models within the Fock-state framework.
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.
We identify a type of periodic evolution that appears in driven quantum systems. Provided that the instantaneous (adiabatic) energies are equidistant we show how such systems can be mapped to (time-dependent) tilted single-band lattice models. Having established this mapping, the dynamics can be understood in terms of Bloch oscillations in the instantaneous energy basis. In our lattice model the site-localized states are the adiabatic ones, and the Bloch oscillations manifest as a periodic repopulation among these states, or equivalently a periodic change in the system's instantaneous energy. Our predictions are confirmed by considering two different models: a driven harmonic oscillator and a Landau-Zener grid model. To strengthen the link between our energy Bloch oscillations and the original spatial Bloch oscillations we add a random disorder that breaks the translational invariance of the spectrum. This verifies that the oscillating evolution breaks down and instead turns into a diffusive spreading. Finally, we consider a trapped ion setup and demonstrate how the mechanism can be utilized to prepare motional cat state of the ion.
Aharonov-Bohm (AB) caging is a complete localization phenomenon in two-dimensional lattices due to destructive interference induced by the background gauge fields. However, current investigations of AB caging are mostly restricted to the Abelian gauge field case, and the observation of AB caging under non-Abelian gauge fields in a quantum system still remains elusive. Here, we report experimental realization of tunable synthetic non-Abelian SU(2) gauge fields in a rhombic lattice, engineered within the synthetic dimensions of a vibrating trapped ion with multiple levels. We realize AB caging under both Abelian and non-Abelian gauge fields and systematically investigate the distinctive transport properties of the non-Abelian case. In particular, we observe typical emergent quantum dynamics unique to non-Abelian AB caging, including initial-state-dependent dynamics, second-order effects, and asymmetric caging behavior. These observations demonstrate the trapped ion system as a powerful platform for simulating emergent phenomena in high-dimensional quantum systems with exotic synthetic gauge fields.
Synthetic dimension approach has emerged as a versatile and powerful technique in cold-atom toolbox for quantum simulation, serving as a complementary alternative to conventional optical lattice platforms. By mapping internal or external atomic states into discrete lattice sites, this method provides precise control over local tunneling amplitudes, phases, and on-site potentials, enabling flexible engineering of tight-binding Hamiltonians. Such capabilities have facilitated the experimental exploration of topology, synthetic gauge fields, disorder-induced phenomena, and exotic time-dependent dynamics across a range of platforms, including hyperfine and Rydberg states, momentum lattices, and harmonic-trap modes. In this review, we summarize the underlying principles of the key experimental synthetic dimension platforms, and their recent advances in quantum simulation. We also discuss the advantages and current limitations of the synthetic method, and provide a perspective on future directions, including hybrid-dimensional architectures and the study of high-dimensional many-body physics.
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.
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being pi becomes half of that for two bosons. However, these statisticdependent Bloch oscillations have never been observed in experiments up to now. Here, we report the first experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping eigenstates of two anyons to modes of designed circuit simulators, the Bloch oscillation of two bosons and two pseudofermions are verified by measuring the voltage dynamics. It is found that the oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, which is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics, and could have potential applications in the field of the novelty signal control.