Effects of Measurement back-action in the stabilization of a Bose-Einstein condensate through feedback

Abstract

We apply quantum filtering and control to a particle in a harmonic trap under continuous position measurement, and show that a simple static feedback law can be used to cool the system. The final steady state is Gaussian and dependent on the feedback strength and coupling between the system and probe. In the limit of weak coupling this final state becomes the ground state. An earlier model by Haine et. al. (PRA 69, 2004) without measurement back-action showed dark states: states that did not display error signals, thus remaining unaffected by the control. This paper shows that for a realistic measurement process this is not true, which indicates that a Bose-Einstein condensate may be driven towards the ground state from any arbitrary initial state.

1 Tex, 4 PS pictures, 1 bbl file

References in corpus (3)

• Feedback control of quantum state reduction
• Stochastic pure state representation for open quantum systems
• Feedback cooling of atomic motion in cavity QED

Cited by in corpus (8)

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• Feedback control in quantum optics: an overview of experimental breakthroughs and areas of application
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• Cavity driven by a single photon: conditional dynamics and non-linear phase shift
• Robustness of System-Filter Separation for the Feedback Control of a Quantum Harmonic Oscillator Undergoing Continuous Position Measurement
• Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator
• Temporal and spatio-temporal correlation functions for trapped Bose gases
• Fundamental Limits of Feedback Cooling Ultracold Atomic Gases