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arXiv:cond-mat/9912252 · Physical Review A

Phase-resolution limit in the macroscopic interference between Bose-Einstein condensates

Sigmund Kohler, Fernando Sols

Published Apr 17, 2001• 13 citations
arXivHTMLPDF

Abstract

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.

DOI
10.1103/physreva.63.053605

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We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.
We study the interference of two Bose-Einstein condensates within an elementary model. The detection of the atoms is modeled by adapting the standard theory of photon detection. Even though the condensates are taken to be in number states with no phases whatsoever, our stochastic simulations of atom detection produce interference patterns as would also be predicted on the basis of the phases of the macroscopic wave functions describing the condensates. In statistical mechanics terms, we have devised a method to analyze spontaneous symmetry breaking for an arbitrary (not necessarily larger) number of particles.
Interference of an array of independent Bose-Einstein condensates, whose experiment has been performed recently, is theoretically studied in detail. Even if the number of the atoms in each gas is kept finite and the phases of the gases are not well-defined, interference fringes are observed on each snapshot. The statistics of the snapshot interference patterns, i.e. the average fringe amplitudes and their fluctuations (covariance), are computed analytically, and concise formulas for their asymptotic values for long time of flight are derived. Processes contributing to these quantities are clarified and the relationship with the description on the basis of the symmetry-breaking scenario is revealed.