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arXiv:quant-ph/0501101 · Physical Review A

Stabilizing an atom laser using spatially selective pumping and feedback

Mattias Johnsson, Simon A. Haine, J. J. Hope

Published Nov 3, 2005• 10 citations
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Abstract

We perform a comprehensive study of stability of a pumped atom laser in the presence of pumping, damping, and outcoupling. We also introduce a realistic feedback scheme to improve stability by extracting energy from the condensate and determine its effectiveness. We find that while the feedback scheme is highly efficient in reducing condensate fluctuations, it usually does not alter the stability class of a particular set of pumping, damping, and outcoupling parameters.

DOI
10.1103/physreva.72.053603

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We perform a comprehensive study of stability of a pumped atom laser in the presence of pumping, damping, and outcoupling. We also introduce a realistic feedback scheme to improve stability by extracting energy from the condensate and determine its effectiveness. We find that while the feedback scheme is highly efficient in reducing condensate fluctuations, it usually does not alter the stability class of a particular set of pumping, damping, and outcoupling parameters.
A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum nondemolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.
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.
The feasibility of using feedback for stabilization of atoms in an off-resonance optical lattice is demonstrated. In the proposed scheme, the collective coordinate of atoms is measured and instantaneously compensated for via a spatial shift of the potential of the optical lattice. An external action that provides for heating of atoms with subsequent decrease in their lifetime in the lattice is simulated by a set of independent reservoirs, each interacting only with one atom. A quantum-mechanical analysis of the problem shows that the use of the feedback within the proposed scheme makes it possible to stabilize the energy of atoms at a level below the equilibrium energy.
A generalized method of using feedback to control multimode behavior in Bose-Einstein condensates is introduced. We show that for any available control, there is an associated moment of the atomic density and a feedback scheme that will remove energy from the system while there are oscillations in that moment. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of nonlinear controls. If the nonlinear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency.