Cavity QED with Quantum Gases: New Paradigms in Many-Body Physics

Abstract

We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose-Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and nonequilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunablerange atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.

Optomechanical Response of a Strongly Interacting Fermi Gas

“…We consider the coupling of a Fermi gas to light in an optical cavity in the dispersive limit, where the light-matter coupling is given as equation (1) in the main text. In the presence of such a coupling, the Heisenberg-Langevin (input-output) equation for the photon field in the frame rotating at a driving frequency is given by [22,23]…”

“…The connection between many-body physics in the gas and the optomechanical nonlinearity originates from the structure of the dispersive light-matter coupling Hamiltonian [22,23]…”

Self-ordering Supersolid Phase beyond Dicke Superradiance in a Ring Cavity

“…Meanwhile, ultracold quantum gases coupled to optical cavities provide a new platform for exploring periodic order of crystals in controlled environments [26][27][28]. In particular, an additional collective-emission-induced cooling mechanism could facilitate the experimental investigations of crystal properties in cavity quantum electrodynamics (QED) [29,30].…”

“…In the far dispersive regime,|∆ c | ≫ {Ω, Ω m }, the cavity field â can be adiabatically eliminated and replaced by steady-state solution since its dynamic evolution is much faster than external atomic motion [26,27]. By introduce the parameter Ξ = ψ ↓ | cos(k L y)e −ikLx |ψ ↑ , the intra-cavity amplitude can be expressed α = â = ΩΞ/(− ∆c + iκ) with ∆c = (∆ c + U 0 N a ) being N a depended effective dispersive shift of cavity.…”

“…Particularly, it has shown that the observed supersolid CB phase with a large periodic density modulation possesses an undamped gapless Goldstone mode even in the presence of cavity dissipation, which is essential different from superradiant Dicke lattice-supersolid with a gapped excitation [37][38][39][40]. Our scheme could provide a versatile platform for creating and detecting intriguing quantum phases in cavity QED and introduce new capabilities into quantum simulations [26][27][28]. Interesting, the controlled strongly cavity-mediated long-range spin-exchange interaction for atomic fields can be derived by integrating out the cavity field [54], which could facilitate the study of complex phenomena of quantum matters [43][44][45][46][47][48].…”