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Physical Review Letters

Phase Standard for Bose-Einstein Condensates

Jacob Dunningham, Keith R. Burnett

Published May 10, 1999• 39 citations
Publisher

Abstract

We discuss how a consistent phase standard for Bose-Einstein condensates may be defined. We show that it has the properties we would wish for in a phase standard: it is not corrupted by subsequent comparisons. A quantum jump technique is employed to study the time evolution of a three mode condensate system on which we make measurements, which entangle the modes and so establish relative phases between them. By establishing, in turn, the phases of two condensates relative to a reference condensate, we show that the relative phase between them can be predicted accurately. The existence of such a phase standard gives a precise definition to the phase of a condensate.

DOI
10.1103/physrevlett.82.3729

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We discuss how a consistent phase standard for Bose-Einstein condensates may be defined. We show that it has the properties we would wish for in a phase standard: it is not corrupted by subsequent comparisons. A quantum jump technique is employed to study the time evolution of a three mode condensate system on which we make measurements, which entangle the modes and so establish relative phases between them. By establishing, in turn, the phases of two condensates relative to a reference condensate, we show that the relative phase between them can be predicted accurately. The existence of such a phase standard gives a precise definition to the phase of a condensate.
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We study how phase information is developed and transferred between Bose-Einstein condensates. First, we investigate how the phase of an output pulse of an idealized atom laser can be controlled. We then use quantum simulations to show how a relative phase between coupled systems is established by dissipation and atomic interactions. Our simulations show that each realization settles to the same relative phase between modes: for uncoupled systems the phase varies from realization to realization. We use this to demonstrate how condensates may `naturally' possess a relative phase, and to explain the phase-locking mechanism in a recent experimental demonstration of a mode-locked atom laser.
We have measured the relative phase of two Bose-Einstein condensates using a time-domain, separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double-condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have separated spatially and their relative center-of-mass motion has damped.