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Quantum Electronics

Bose condensates from the point of view of laser physics

Anatolii N Oraevsky

Published Dec 31, 2001• 14 citations
Publisher

Abstract

The dynamic analogy between the Bose condensate of photons (laser), Bose condensate of atoms, and Bose condensate of Cooper pairs in a superconductor is discussed. It is pointed out that the coherent state of Bose condensates of different types can appear only due to stimulated transitions.The equations are discussed that combine into a unified dynamic system the order parameter of the Bose condensate and the concentration of atoms beyond the condensate for an ensemble of atoms captured by a trap, as well as the order parameter of Cooper pairs, the concentration of free quasi-particles, and the densities of phonons and photons in a semiconductor.

DOI
10.1070/qe2001v031n12abeh002099

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The dynamic analogy between the Bose condensate of photons (laser), Bose condensate of atoms, and Bose condensate of Cooper pairs in a superconductor is discussed. It is pointed out that the coherent state of Bose condensates of different types can appear only due to stimulated transitions.The equations are discussed that combine into a unified dynamic system the order parameter of the Bose condensate and the concentration of atoms beyond the condensate for an ensemble of atoms captured by a trap, as well as the order parameter of Cooper pairs, the concentration of free quasi-particles, and the densities of phonons and photons in a semiconductor.
An analysis is made of the condition for stimulated precipitation of Bose particles to form a coherent Bose condensate. Experimental observations of the interference of Bose condensates are described. A system of equations is proposed for the dynamics of a generator of coherent atomic beams, i.e. an 'atom laser'. This system of equations takes account of the interaction of a Bose condensate with incoherent particle subsystems. A description is given of experimental observations of stimulated amplification of an exciton bunch. The possibility of generation of a coherent state of excitons by direct binding of free carriers in semiconductors and insulators is considered.
A nonequilibrium approach to the dynamics and statistics of the condensate of an ideal N-atom Bose gas cooling via interaction with a thermal reservoir using the canonical ensemble is developed. We derive simple analytical expressions for the canonical partition function and equilibrium distribution of the number of atoms in the ground state of a trap under different approximations, and compare them with exact numerical results. The N-particle constraint associated with the canonical ensemble is usually a burden. In the words of Kittel, ``in the investigation of the Bose-Einstein\dots{}laws it is very inconvenient to impose the restriction that the number of particles in the subsystem shall be held constant.'' But in the present approach, based on the analogy between a second-order phase transition and laser threshold behavior, the N-particle constraint makes the problem easier. We emphasize that the present work provides another example of a case in which equilibrium (detailed balance) solutions to nonequilibrium equations of motion provide a useful supplementary approach to conventional statistical mechanics. We also discuss some dynamical and mesoscopic aspects of Bose-Einstein condensation. The conclusion is that the present analytical (but approximate) results, based on a nonequilibrium approach, are in excellent agreement with exact (but numerical) results. The present analysis has much in common with the quantum theory of the laser.
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.
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