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arXiv:cond-mat/0310130 · Physical Review A

Control of an atom laser using feedback

Simon A. Haine, Andrew J. Ferris, J. D. Close, J. J. Hope

Published Jan 26, 2004• 26 citations
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Abstract

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.

DOI
10.1103/physreva.69.013605

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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.
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We present a quantum control scheme in which two different feedback methods are combined to produce a stable single mode atom laser. A difficulty of producing an atom laser comes from the nonlinear effect of Bose-Einstein Condensates which is described by Gross-Pitaevskii type of equations. One feedback method is used to eliminate the nonlinear effect of atom-atom interactions. Another difficulty comes from nonlinear interactions with an optical field which is introduced to detect the BEC state for feedback. The other feedback method is used to suppress fluctuations due to this interaction and keep the coherent properties of the atom laser.
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.
The spatial structure of a Bose–Einstein condensate (BEC) loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.
The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. A 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.
Abstract We consider the problem of decoherence in a Bose – Einstein condensate (BEC) of noninteracting atoms during interferometric probing with a classical monochromatic external field. The condensate is located in one of the arms of the Mach – Zehnder interferometer, while part of the radiation from the interferometer output is fed back to the input, thereby closing the coherent feedback loop. A more general setting of the problem is also considered, in which the condensate is located in a system of interferometers ‘nested’ into each other, while part of the output radiation of each of them is also fed back to its input, closing the so-called multiloop feedback. The possibility of effective control of decoherence rates of various matrix elements is shown. The application of feedback of the proposed type to BEC in a double-well potential is investigated. It is found that this feedback allows efficient control of the distribution of atoms between the wells.