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arXiv:cond-mat/0208319 · Physical Review Letters

Decoherence due to Three-Body Loss and its Effect on the State of a Bose-Einstein Condensate

Michael W. Jack

Published Sep 11, 2002• 60 citations
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Abstract

A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large-number limit only coherent states remain pure for times longer than the decoherence time: the time it takes for just three atoms to be lost from the trap. For large numbers of atoms (N>10(4)) the decoherence time is found to be much faster than the phase-collapse time caused by intratrap atomic collisions.

DOI
10.1103/physrevlett.89.140402

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A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large-number limit only coherent states remain pure for times longer than the decoherence time: the time it takes for just three atoms to be lost from the trap. For large numbers of atoms (N>10(4)) the decoherence time is found to be much faster than the phase-collapse time caused by intratrap atomic collisions.
In this review we discuss the dynamics of the phase of trapped Bose–Einstein condensates. In particular we consider the phenomena of phase decoherence (termed also as phase collapse, or diffusion), and phase revival in systems of interacting atoms. We analyse the dependence of the collapse and revival times on the trap potential, dimensionality of the gas, atom number fluctuations, and on the coherent dynamics of the condensate. We show that in a class of experimentally relevant systems, the collapse time is relatively short, and in some cases vanishes in the limit of a large number of atoms, implying that the trapped Bose gas cannot sustain a well-defined quantum phase, and that the phase memory is lost on a relatively short time scale. Furthermore, we calculate the relative atom number fluctuations or a model of two interacting condensates, and show that the fluctuations are generically sub-Poissonian.
In view of the coherent properties of a large number of atoms, Bose-Einstein condensates (BECs) have a high potential for sensing applications. Several proposals have been put forward to use collective excitations such as phonons in BECs for quantum-enhanced sensing in quantum metrology. However, the associated highly nonclassical states tend to be very vulnerable to decoherence. In this article, we investigate the effect of decoherence due to the omnipresent process of three-body loss in BECs. We find strong restrictions for a wide range of parameters, and we discuss possibilities to limit these restrictions.
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We experimentally and theoretically study phase coherence in two-component Bose-Einstein condensates of ^{87}Rb atoms on an atom chip. Using Ramsey interferometry we determine the temporal decay of coherence between the |F=1,m_{F}=-1⟩ and |F=2,m_{F}=+1⟩ hyperfine ground states. We observe that the coherence is limited by random collisional phase shifts due to the stochastic nature of atom loss. The mechanism is confirmed quantitatively by a quantum trajectory method based on a master equation which takes into account collisional interactions, atom number fluctuations, and losses in the system. This decoherence process can be slowed down by reducing the density of the condensate. Our findings are relevant for experiments on quantum metrology and many-particle entanglement with Bose-Einstein condensates and the development of chip-based atomic clocks.
Bose-Einstein condensates (BEC) serve as a model system for the study of decoherence and dephasing processes. We denote ‘dephasing’ as the loss of overall common phase due to the coherent evo lution of the macroscopic wavefunction of the BEC. In contrast, ‘decoherence’ in this case is the coupling of the macroscopic wavefunction state to a continuum of initially unoccupied momentum excitations via collisions. Decoherence is driven by the fluctuations in th ese momentum modes and is irreversible on the timescales larger than the so -called ‘memory time’ of the continuum [1].