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Journal of Experimental and Theoretical Physics Letters

Quantum Limits of Feedback Cooling in Optical Lattices

T. Yu. Ivanova

Published Jan 1, 2005• 9 citations
Publisher

Abstract

A quantum-mechanical analysis of feedback cooling [see Phys. Rev. Lett. 94 , 153002 (2005)] of atoms trapped in a far-off-resonant optical lattice is presented. The model considered is valid for ultralow energies of atoms, thus, allowing for the study of an ultimate cooling limit. The influence of the measurement-induced noise and feedback-induced atom-atom correlations on the cooling efficiency is discussed. It is shown that there are regimes where the quantum noise can be effectively compensated for.

DOI
10.1134/1.2150866

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A quantum-mechanical analysis of feedback cooling [see Phys. Rev. Lett. 94 , 153002 (2005)] of atoms trapped in a far-off-resonant optical lattice is presented. The model considered is valid for ultralow energies of atoms, thus, allowing for the study of an ultimate cooling limit. The influence of the measurement-induced noise and feedback-induced atom-atom correlations on the cooling efficiency is discussed. It is shown that there are regimes where the quantum noise can be effectively compensated for.
We consider the problem of suppression of noise acting on atomic ensembles trapped in optical lattices in the low-energy limit. Noise affecting external degrees of freedom of each atom independently and noise influencing only the center-of-mass (c.m.) mode of the ensemble are addressed. Taking into account the quantum character of the atomic motion, we show that negative feedback loop acting on the c.m. coordinate of the atomic ensemble is able to partially compensate both noise sources mentioned above.
We discuss the influence of atom-atom correlations on the collective feedback of atoms trapped in an 1D optical lattice. Analytically deriving the dynamics of these correlations we consider a series of feedback steps and analyze the average energy change as a measure of the feedback efficiency. It is demonstrated that the correlations strongly affect the feedback process, so that without destroying them the energy of the system can not be effectively reduced. The situations when a correlation-destroying mechanism operates are discussed as well.
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.
We derive an equation for the cooling dynamics of the quantum motion of an atom trapped by an external potential inside an optical resonator. This equation has broad validity and allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. Our result shows that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
Summary form only given. Atoms in an optical lattice, though very slow, perform a slight random motion that reflects the non-zero temperature of the trapped atoms. We are proposing a way of reducing such random motion using real-time feedback. The method is related to the stochastic cooling used to transversely cool particle beams. Another stochastic cooling method for laser-cooled atoms has been proposed in "Stochastic cooling of atoms using lasers," see Phys. Rev. A, vol. 58, p. 4757 (1998). Our scheme involves a measurement of the coherent redistribution of photons between different laser beams of the optical lattice.
We investigate the fundamental viability of cooling ultracold atomic gases with quantum feedback control. Our Letter shows that the trade-off between the resolution and destructiveness of optical imaging techniques imposes constraints on the efficacy of feedback cooling, and that rapid rethermalization is necessary for cooling thermal gases. We construct a simple model to determine the limits to feedback cooling set by the visibility of density fluctuations, measurement-induced heating, and three-body atomic recombination. We demonstrate that feedback control can rapidly cool high-temperature thermal clouds in quasi-2D geometries to degenerate temperatures with minimal atom loss compared to traditional evaporation. Our analysis confirms the feasibility of feedback cooling ultracold atomic gases, providing a pathway to new regimes of cooling not achievable with current approaches.