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arXiv:quant-ph/0303028 · Physical Review A

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

Gilberto Aparecido Prataviera

Published Apr 22, 2003• 2 citations
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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.

DOI
10.1103/physreva.67.045602

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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.
The recoil momentum and energy of ultracold atoms is studied for situations where collective scattering or emission of photons is important. Effects due to the dipole-dipole interaction are emphasized. For two and many atoms confined in optical traps, calculations of the energy and momentum with respect to atomic separation are performed. When the atomic separation is comparable to or larger than the transition wavelength, the ultracold atoms' recoil energy depends mainly on collective spontaneous decay rather than forces from the cooperative frequency shift. Calculations for a laser pulse reflecting from an atomic array suggest that the recoil energy of atoms can be substantially larger than might be expected from an independent atom picture.
The interaction between Bose Einstein condensates (BECs) and coherent light fields is treated within the framework of nonlinear wave mixing and studied using techniques developed in the fields of nonlinear and quantum optics. We focus in particular on two situations involving a BEC driven by a strong off-resonant 'pump' laser. First, we consider the case where the laser light is scattered into a single mode of an optical ring cavity. We then consider the case where the light is scattered into the continuum of vacuum modes of the electric field. The first problem is an extension of recent theoretical and experimental work on the so-called collective atomic recoil laser (CARL), whereas the second corresponds to a recent condensate-superradiance experiment performed at MIT. In the cavity situation, we develop a CARL model in which both the atomic and optical fields are treated fully quantum mechanically. We first show that the previous CARL model, which treats the atomic motion classically, breaks down at the recoil temperature due to the effects of matter-wave diffraction. We then show that when combined with a BEC the CARL can be viewed as a device which parametrically amplifies atomic and optical fields. The existence of entanglement and non-classical intensity correlations between the amplified atomic and optical fields is demonstrated, as well as the ability to manipulate the quantum statistical properties of the matter and light waves by injecting a weak laser field into the optical cavity to trigger the device. By replacing the cavity mode with a continuum of modes, we are able to formulate a quantum theory of condensate superradiance in which the scattered light field is eliminated in the Markov approximation. This model shows that condensate depletion leads to mode competition which prevents light scattering in all but the preferred direction(s). The outcome of the mode-competition is highly sensitive to the quantum fluctuations which trigger the phenomenon, resulting in large run-to-run variations in the angular pattern of the superradiant light pulse, an effect which is observed experimentally.
We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as \ensuremath{\beta}, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for \ensuremath{\beta} are $0.01<\ensuremath{\beta}<1.0.$ We find that for large enough \ensuremath{\beta}, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as \ensuremath{\beta} is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with \ensuremath{\beta} values in the range considered here. As \ensuremath{\beta} is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.