Steering Matter Wave Superradiance with an Ultranarrow-Band Optical Cavity

Abstract

A superfluid atomic gas is prepared inside an optical resonator with an ultranarrow bandwidth on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.

Nonequilibrium Phase Transition of Interacting Bosons in an Intra-Cavity Optical Lattice

“…Depending on initial thermal or quantum fluctuations the SO density wave can arise with two spatial phases shifted with respect to each other by λ p /2 along the xaxis, i.e., the system faces a symmetry breaking when crossing V crit p . The SO phase transition also occurs for a vanishing depth of the external lattice, in which case it represents the well-known Dicke phase transition [2,26] that has been observed in recent experiments [6,7]. A related result for Φ vs V p was obtained by a static meanfield approach [15], but we cannot quantitatively compare it with our results since in BDMFT the interactions are not fixed a priori, but are calculated dynamically and self-consistently.…”

“…An early insightful theoretical proposal [4] and a subsequent experiment [5] have shown that in a thermal atom ensemble in a highfinesse optical cavity, two different phases can emerge depending on the strength of an external pump laser field: a normal phase, characterized by a homogeneous density distribution and a vanishing intra-cavity field, and a self-organized (SO) phase, where the atoms form a matter grating trapped by a stationary intra-cavity optical standing wave. Only recently, similar experiments were realized with Bose-Einstein condensates (BECs) [6][7][8]. It was realized that in the limit of zero temperature and moderate external pumping this scenario represents an experimental implementation of the open Dicke model [9].…”

“…We set the scattering length to a s = 5.77 nm and the pump laser wave length to λ p = 803 nm according to the setup in Refs. [7,21]. In what follows, we focus on the homogeneous system and set the external trap potential to zero, i.e., V trap i = 0.…”

“…[6] but not for those of Refs. [7,21], where the photons remain much longer inside the cavity before they are lost, such that an explicitly dynamical treatment of the light field is required. The first line in Eq.…”

Dynamical phase transition in the open Dicke model

“…A second interesting consequence is the observation of an instability boundary for positive detuning δ eff > 0. The physics of this instability, which is also predicted by the Dicke model but not much discussed in the literature, resembles cavity-assisted matter wave superradiance (41), recently observed to prevail at any value of δ eff for single-sided pumping (42). The system is excited by a cascade of successive superradiant pulses to form coherent superpositions of discrete momentum states with the zero momentum condensate mode practically depleted.…”