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Journal of Experimental and Theoretical Physics

Quantum dynamics and statistics of a Bose condensate generated by an atomic laser

A. V. Kozlovskiĭ

Published Jun 1, 2003• 1 citation
Publisher

Abstract

A self-consistent quantum theory is developed for an atomic laser utilizing cooling of atoms in a trap by the method of stimulated evaporation. The model describes the pumping and extraction of the atomic field from a trap upon its interaction with independent atomic reservoirs. The stimulated collisions between atoms in the trap, which produce a Bose condensate in the lower state of the trap, are considered. The interaction of atoms with a phonon field causes spontaneous transitions between the discrete states of the trap. Calculations performed for the three-and four-level models of the trap showed the possibility of generation of a strongly squeezed sub-Poisson Bose condensate.

DOI
10.1134/1.1591212

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A self-consistent quantum theory is developed for an atomic laser utilizing cooling of atoms in a trap by the method of stimulated evaporation. The model describes the pumping and extraction of the atomic field from a trap upon its interaction with independent atomic reservoirs. The stimulated collisions between atoms in the trap, which produce a Bose condensate in the lower state of the trap, are considered. The interaction of atoms with a phonon field causes spontaneous transitions between the discrete states of the trap. Calculations performed for the three-and four-level models of the trap showed the possibility of generation of a strongly squeezed sub-Poisson Bose condensate.
The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ∼10 6 , the Fano factor may be as high as ≅0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.
Summary form only given. We report the first successful use of direct quantum dynamical calculations of the cooling and formation of Bose-Einstein condensates of trapped atoms. The calculations utilize phase-space methods that have already proved successful in laser theory. Some of the computational results are very similar to those already observed experimentally. In particular, we find quantum evaporative cooling, followed by a clear transition to a condensate; this is strongly influenced by non-classical features of the quantum dynamics. The calculations indicate additional structure, which we interpret as spontaneous formation of vortices in small condensates. These originate in the residual orbital angular momentum of the trapped atoms, which was neglected in previous studies - and would provide a significant test of the present theory.
The first-order coherence dynamics of a Bose condensate generated by a cw atomic laser with evaporative cooling is analyzed. For the atomic-laser multimode model, the coherence functions and atomic field spectra are calculated by the master equation technique. Elastic collisions in the trapped atomic gas lead to significant broadening of the atomic laser line, a shift of its center, and a multi peak structure of the spectra. The oscillatory time dynamics of the atomic-field coherence function is studied. For the atomic laser, the free phase diffusion of the field typical of optical lasers, and characterized by monotonically decreasing mean field with a constant mean phase, is absent due to elastic collisions.
Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.
A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the nonclassical properties, such as sub-Poisson distribution and quadrature squeezing effect, mutually oscillate between the quantum states of the applied optical field and the resulting atom laser beam with time. In particular, it is shown that an initially squeezed optical field will lead to squeezing in the outcoupled atomic beam at later times.
We present a many-body theory of a driven and damped trapped gas of interacting bosons, and demonstrate that one of the trap levels can become coherently populated, thereby leading to a coherent atomic-beam generator, or ``laser for atoms.'' The specific system we consider consists of a sample of bosonic atoms interacting via the near-resonant dipole-dipole interaction. The transverse center-of-mass motion of the atoms is confined by a two-dimensional potential well created by an array of cooling laser beams, while their longitudinal motion is quantized by a Fabry-P\'erot for atoms. Under appropriate conditions, the dipole-dipole selection rules lead to the simplification that only two quantized levels of atomic motion need to be considered explicitly, the other levels being treated as reservoirs. One of the two levels is the ``pump level,'' while the other is the one where atomic coherence builds up (the ``lasing'' level). The master equation describing the dynamics of these levels can be solved numerically, and its solution exhibits a ``threshold behavior'' with a transition from super-Poissonian to Poissonian atom statistics in the ``lasing mode.'' \textcopyright{} 1996 The American Physical Society.