Trap environment effects over quantum statistics and atom-photon correlations in the collective atomic-recoil laser

Abstract

We consider the effects of the trap environment on atomic and optical quantum statistical properties and on atom-photon correlations in the collective atomic-recoil laser. Atomic and optical statistical properties, as well as atom-photon correlations are dependent on the optical-field intensity and phase. In particular, depending on the values of the optical-field intensity and phase, the field statistics vary from coherent to superchaotic.Realization of Bose-Einstein condensation in trapped atomic gases ͓1͔ has produced new advances in atom optics. Particularly, the interaction of condensates with single-mode quantized light fields has been a challenging topic ͓2-5͔, allowing for instance light and matter-wave amplification ͓3-5͔ and optical control of atomic statistical properties ͓3,5͔.It is known that the trap environment can modify the properties of ultracold atoms, such as its critical temperature ͓6͔. In Ref. ͓7͔, the trap environment effect on the condensate collective atomic-recoil laser ͑CARL͒ ͓8͔ was included by expanding the matter-wave field in the trap matter-wave modes. Such a situation was called cavity atom optics ͑CAO͒, in analogy with the cavity quantum electrodynamics where the spontaneous emission is modified by the presence of the cavity. The dynamics of this model was compared with its counterpart free space model ͓5͔, where the matterwave field was expanded in plane waves. It was found that in the CAO regime, the atomic and optical-field intensities present two regimes of exponential instability. However, the trap effect over the quantum statistical properties and the atom-photon correlations was not considered. These properties are important to characterize the role of trap environments on the control of atomic and optical statistical properties, which can be useful for quantum information processing.This Brief Report concerns with the effects of trap environment over the quantum statistical properties and the atom-photon correlations in the CARL. By analyzing the second order correlation functions and intensity cross correlations, we verify that the statistical properties of the atomic and optical fields as well as the atom-photon correlations are dependent on the optical-field initial intensity and phase. Furthermore, by setting the optical-field intensity and phase, the fields statistics can be varied from coherent to superchaotic.Following Ref. ͓7͔, we consider a Schrödinger field of noninteracting bosonic two-level atoms interacting with two single-mode running wave optical fields of frequencies 1 and 2 , both being far off resonant from any electronic transition. By two-photon virtual transitions, in which the atoms internal state remains unchanged, the center-of-mass motion may change due to the recoil. In the far-off resonant regime, the excited-state population and spontaneous emission may be neglected, and the ground-state atomic field evolves coherently under the effective Hamiltonianwhere m is the atomic mass, V(r) is the trap potential, g 1 and g 2 are the probe and pump coup...

Stability and entanglement in optical-atomic amplification of trapped atoms: The role of atomic collisions

“…This paper deals with the extension of the model of atom-optical parametric amplifier considered in Refs. [20,23] by including collisions between atoms. A study of the changes due collisions on the thresholds of exponential instability as well as in growth rate of the fields amplitudes is presented.…”

“…Such a situation was called Cavity Atom Optics (CAO), in analogy with the Cavity Quantum Electrodynamics (CQE) where the spontaneous emission is modified by the presence of the cavity. The model obtained presents interesting properties such as two regimes of exponential instability [20] and statistical properties that depend on intensity and phase of the optical field [23]. However, neither atomic collisions was taken into account nor a detailed study of the degree of entanglement between atomic and optical fields was done.…”