Cavity QED with a Bose–Einstein condensate

Abstract

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.

Controllability of optical bistability, cooling and entanglement in hybrid cavity optomechanical systems by nonlinear atom–atom interaction

“…On the other hand an effective optomechanical coupling can be simulated by a Bose-Einstein condensate (BEC) trapped inside a high finesse optical cavity [8][9][10]. In the dispersive regime where the laser pump is far detuned from the atomic resonance the excited electronic state of the atoms can be adiabatically eliminated and consequently the only degrees of freedom of atoms will be their mechanical motions [11,12].…”

Topological superradiant state in Fermi gases with cavity induced spin–orbit coupling

“…Furthermore, if the cavityatom coupling is in the strong-coupling regime, the cavity field can reach a dynamical steady state within a short period of time in comparison to 1/κ. Moreover, the atoms typically respond to the photon variation on an even longer time scale such that the photon dynamics can be treated adiabatically [24,25]. In this case, the steady-state solution of the system can be approximated by the stationary condition ∂α/∂t = 0 [31][32][33], which leads to…”

“…(4) by considering an effective attractive interaction in one dimension with g 1D > 0. Notice that here we consider the strong-coupling regime where the response of cavity photons to the atomic fields can be treated adiabatically [24,25,[31][32][33]. By performing the gauge transformationψ ↓ (x) → −i exp(ik 0 x)ψ ↓ (x) and adopting the mean-field formalism, we obtain the effective Hamiltonian…”

“…3(a), we plot the steady-state phase diagram under the single-band tight-binding model, Eq. (24). Whereas the SR transition boundary (red) is determined self-consistently from Eq.…”

“…Another exciting example of quantum control over atom-light interaction is the combination of ultracold atoms and cavity quantum electrodynamics in the strongcoupling regime, where the quantum effects of both the atoms and the cavity photons become dominant [24][25][26]. In these cavity-atom hybrid systems, an outstanding feature is the interplay between the atoms and the cavity field: As the cavity field couples the internal states of atoms and affects the collective properties of the ensemble, the ensuing dynamics of the atomic gas feeds back to the cavity photons.…”