Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap

Abstract

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 realisation 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.

19 pages, 14 figures. Extended format version

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Topological Photonics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Dynamical control of matter-wave tunneling in periodic potentials
• Topological properties of linear circuit lattices
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Single Particle Tunneling in Strongly Driven Double Well Potentials
• Observation of Quantized Conductance in Neutral Matter
• Periodically-driven quantum matter: the case of resonant modulations
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Scattering Theory for Floquet-Bloch States
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
• Transverse collisional instabilities of a Bose-Einstein condensate in a driven one-dimensional lattice
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice
• Introduction to the physics of artificial gauge fields
• Integrals of products of Hermite functions

Cited by in corpus (71)

• Topological Photonics
• Atomic quantum gases in periodically driven optical lattices
• Topological Bands for Ultracold Atoms
• Synthetic Dimension in Photonics
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Topological quantum matter in synthetic dimensions
• Photonic Topological Insulator in Synthetic Dimensions
• Topological quantum matter with cold atoms
• Artificial gauge fields in materials and engineered systems
• Direct observation of chiral currents and magnetic reflection in atomic flux lattices
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Atomtronic circuits: from many-body physics to quantum technologies
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• The 6D quantum Hall effect and 3D topological pumps
• Correlated dynamics in a synthetic lattice of momentum states
• Interacting atomic quantum fluids on momentum-space lattices
• Coherent control of quantum topological states of light in Fock-state lattices
• Laughlin-like states in bosonic and fermionic atomic synthetic ladders
• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions
• Parametric Instability Rates in Periodically-Driven Band Systems
• Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• A comprehensive review on developments of synthetic dimensions
• Parametric instabilities in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime
• Floquet engineering to exotic topological phases in systems of cold atoms
• Realization of all-band-flat photonic lattices
• Nonlinear dynamics in a synthetic momentum state lattice
• Ballistic, diffusive, and arrested transport in disordered momentum-space lattices
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
• Topology and entanglement in quench dynamics
• Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
• Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals
• Pretopological fractional excitations in the two-leg flux ladder
• The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
• Coupled Atomic Wires in a Synthetic Magnetic Field
• Many-body chiral edge currents and sliding phases of atomic spinwaves in momentum-space lattice
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Four-dimensional topological lattices through connectivity
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Perspective on new implementations of atomtronic circuits
• Measuring Chern numbers in Hofstadter strips
• Electric fields for light: Propagation of microwave photons along a synthetic dimension
• Six-dimensional time-space crystalline structures
• Different models of gravitating Dirac fermions in optical lattices
• Multi-Photon Synthetic Lattices in Multi-Port Waveguide Arrays: Synthetic Atoms and Fock Graphs
• Tunable Flux through a Synthetic Hall Tube of Neutral Fermions
• Colloquium: Synthetic quantum matter in non-standard geometries
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Quantum Membrane Phases in Synthetic Lattices of Cold Molecules or Rydberg Atoms
• Superfluid Vortices in Four Spatial Dimensions
• Beyond effective Hamiltonians: micromotion of Bose Einstein condensates in periodically driven optical lattices
• Synthetic dimensions and topological chiral currents in mesoscopic rings
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Flat-band-induced superconductivity in synthetic bilayer optical lattices
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields
• Meissner effect in Fock space
• Non-Hermitian synthetic lattices with light-matter coupling
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Simulating a Chern Insulator with C = $\pm$2 on Synthetic Floquet Lattice
• Topological Chiral Edge States in a Synthetic Dimension of Atomic Trap States
• Homogeneous Magnetic Flux in Rydberg Lattices
• Quantum Signatures of Topological Phase in Bosonic Quadratic System
• Decoding the drive-bath interplay: A guideline to enhance superconductivity
• Two-particle topological Thouless spin pump
• Liouville Fock state lattices and potential simulators
• Advances in Synthetic Gauge Fields for Light Through Dynamic Modulation
• Extended degenerate perturbation theory for the Floquet-Hilbert space
• Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates