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.
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 introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.
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.
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.
A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably that of “synthetic dimensions” in which internal states are coupled together and reinterpreted as sites along an artificial spatial dimension. However, previous atomic synthetic dimension implementations have been limited to relatively small system sizes with inflexible boundaries. In this paper, we propose instead how to use a synthetic dimension of atomic trap states to observe chiral edge states in a large quantum Hall system with a tunable edge. We present numerical simulations for relevant experimental parameters, showing how this scheme may be used to probe the properties and robustness of the edge states to defects. Our work opens the way for future experiments in topological physics with synthetic dimensions, while also providing new ways to manipulate and control highly excited trap states.
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).
Engineering the on-site frequencies of a photonic lattice provides a powerful route to endow emitted photons with non-trivial dynamical and topological properties, reshaping the way a coupled qubit decays. This thesis investigates the emission dynamics of a qubit weakly coupled to photonic lattices hosting such synthetic potentials, showing how the resulting band structure dictates qualitatively distinct regimes of light-matter interaction.In the first part, we study a qubit coupled to a one-dimensional coupled-cavity array with a linear gradient in the cavity frequencies, which acts on photons as a synthetic force F. For strong F, emission becomes reversible and is captured by an effective Jaynes--Cummings model, producing a chiral, time-periodic excitation of an extended region of the array, either to the right or to the left of the qubit depending on its frequency. For weak F, the decay is non-Markovian and exhibits revivals reminiscent of atoms between mirrors, even though no mirrors are present: the finite bandwidth confines the emitted photon, and the dynamics is well described by a delay differential equation in which the amplitude and period of Bloch oscillations play the role of cavity length and round-trip time.In the second part, we move to two dimensions and couple a giant atom, a qubit with multiple, spatially separated coupling points, non-locally to a honeycomb lattice of resonators with detuned sublattice frequencies. By suitably arranging the coupling points, the giant atom selectively addresses a single valley, a capability unattainable with a local emitter. This valley-selective coupling endows the emitted photons with an effective valley-polarized Berry curvature, giving rise to valley-polarized edge modes at domain walls between regions of opposite sublattice detuning. As a consequence, a giant atom placed near such a domain wall exhibits chiral emission of valley-polarized photons without breaking time-reversal symmetry, suggesting a natural implementation in circuit QED.Together, these results establish synthetic potentials in photonic lattices as a versatile tool for controlling qubit emission, linking waveguide QED to Bloch-oscillation physics and to valleytronics.