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arXiv:cond-mat/0103597 · Physical Review A

Atom-laser dynamics

Nicholas P. Robins, Craig M. Savage, Elena A. Ostrovskaya

Published Sep 13, 2001• 22 citations
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Abstract

An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice, the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive one-dimensional, mean-field numerical model. We fully model the output beam and experimentally important physics such as three-body recombination. We find that at high-pump rates, the latter plays a role in suppressing the high-frequency dynamics, which would otherwise limit the stability of the output beam.

DOI
10.1103/physreva.64.043605

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An ideal atom laser would produce an atomic beam with highly stable flux and energy. In practice, the stability is likely to be limited by technical noise and nonlinear dynamical effects. We investigate the dynamics of an atom laser using a comprehensive one-dimensional, mean-field numerical model. We fully model the output beam and experimentally important physics such as three-body recombination. We find that at high-pump rates, the latter plays a role in suppressing the high-frequency dynamics, which would otherwise limit the stability of the output beam.
We present a steady-state analysis of a quantum-mechanical model of an atom laser. A single-mode atomic trap coupled to a continuum of external modes is driven by a saturable pumping mechanism. In the dilute flux regime, where atom-atom interactions are negligible in the output, we find an analytic form for the linewidth and frequency shift of the laser. This result does not make the Born-Markov approximation, but is based on the far less restrictive ``self-consistent Markov approximation.'' The more exact treatment has a different effective damping rate and occupation of the lasing mode, as well as a shifted frequency and linewidth of the output. We examine gravitational damping numerically, finding linewidths and frequency shifts for a range of pumping rates. We treat mean-field damping analytically, finding a memory function for the Thomas-Fermi regime. The occupation and linewidth are found to have a nonlinear scaling behavior which has implications for the stability of atom lasers.
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We review experimental progress on atom lasers out-coupled from Bose-Einstein condensates, and consider the prop-erties of such beams in the context of precision inertial sensing. The atom laser is the matter-wave analog of the optical laser. Both devices rely on Bose-enhanced scattering to produce a macroscopically populated trapped mode that is output-coupled to produce an intense beam. In both cases, the beams often display highly desirable properties such as low divergence, high spectral flux and a simple spatial mode that make them useful in practical applications, as well as the potential to perform measurements at or below the quantum projection noise limit. Both devices display similar second-order correlations that differ from thermal sources. Because of these properties, atom lasers are a promising source for application to precision inertial measurements.
We discuss the influence of injected atomic coherence on laser dynamics. The nonlinear equations of motion for the intensity and phase give the dependence on external parameters (inversion, amplitude of the atomic coherence, and cavity-field detuning). Depending on the inversion, there can be one or three steady-state solutions corresponding to a given value of the injected coherence. The situation is analogous to optical bistability, the atomic coherence playing the role of the injected field. For zero detuning the upper, laser-like branch starts at zero value of the injected coherence and a numerical stability analysis indicates that it is the only stable solution, the lower branch being everywhere unstable. For finite detuning the upper branch starts at a finite threshold value of the injected coherence. For coherences smaller than this threshold the system exhibits oscillatory behavior that corresponds to a stable limit cycle in the phase plane of the laser quadrature variables. The intensity fluctuations of the laser exhibit antibunching for sub-Poissonian pumping statistics.