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Atom laser coherence and its control using feedback

L. K. Thomsen, Howard M. Wiseman

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.

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We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.
We present a quantun-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.
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.
An atom laser is a device which would ideally produce a coherent excitation of a single mode of the Bose-atom field. That is to say, an atom laser field would have a well defined number of atoms, and a slow rate of phase diffusion. Here we consider an atom laser model recently proposed by Holland et al, based on evaporative cooling of atoms. We extend their model, and give approximate analytical results for the time-dependent intensity and phase statistics of the atom laser in different regimes. Although the intensity fluctuations may be relatively small, the laser linewidth is always in excess of the bare linewidth of the laser mode. Nevertheless, in one regime (weak collisions), the laser linewidth may be less than the output flux of atoms, which is a minimum requirement for considering the output to be coherent.
Coherence control is the key to success in the applications of atom-laser beams. A multiloop measurement feedback control scheme is proposed to improve atom-laser coherence. The first loop aims to cancel the decohering effects of the nonlinear atom-atom interactions via direct measurement feedback. However, there are nonlinear interactions with the optical probe field used in the measurement scheme which may also contribute to a degradation in atom-laser performance. Accordingly, a second feedback loop is used to reduce these effects based on linear quadratic Gaussian control. The multiloop design achieves improved atom-laser coherence.
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.
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.