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Physical Review A

Interference of two condensates

William Hoston, Li You

Published Jun 1, 1996• 46 citations
Publisher

Abstract

We propose an experimental scheme to probe the relative global phase of two condensates and thus demonstrate the spontaneous symmetry breaking of global gauge invariance in Bose-Einstein condensation. A positive measurement would justify the standard view of the condensate wave function as a coherent state when there are interparticle interactions. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.4254

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We propose an experimental scheme to probe the relative global phase of two condensates and thus demonstrate the spontaneous symmetry breaking of global gauge invariance in Bose-Einstein condensation. A positive measurement would justify the standard view of the condensate wave function as a coherent state when there are interparticle interactions. \textcopyright{} 1996 The American Physical Society.
We show that, when two Bose-Einstein condensates are combined, a spatial interference pattern ensues even if the condensates are in number states with no spontaneously broken gauge symmetry. In our measurement-theoretical approach the interference pattern arises from correlations between the detected positions of the atoms. We also simulate numerically experiments intended to distinguish number-state condensates and spontaneous symmetry breaking, the latter being modelled by coherent-state condensates. To detect the difference in the pair correlation functions, the experiment has to be repeated about a thousand times even for condensates with as few as five atoms each.
We analyze theoretically an optical scheme to detect the phase of a Bose-Einstein condensate associated with spontaneously broken gauge symmetry. Two condensates in different Zeeman states are confined to the same trap, and two phase-coherent laser beams are used to drive Raman transitions between the condensates. Amplification of one of the Raman beams immediately following the turn-on of light is an unambiguous sign of the presence of phase coherence in the atoms. \textcopyright{} 1996 The American Physical Society.
We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a condensate wave function with a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state for which the particle number is uncertain, but the phase is known. How such a state would be prepared before an experiment is not obvious. We show that a phase can also arise from experiments using condensates with known particle numbers. The analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of spontaneously broken gauge symmetry and to hidden variables is discussed.
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.
We investigate the prospects of atomic interference using samples of Bose condensed atoms. First we show the ability of two independent Bose condensates to create an interference pattern. This holds even if both condensates are described by Fock states. Thus, the existence of an experimental signature for a broken gauge symmetry, seen in a single run of the experiment, is not necessarily reflected by a broken symmetry on the level of the quantum mechanical state vector. Based on these results, we simulate numerically a recent experiment with two independent Bose condensates [K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995)]. The existence of interference fringes is predicted based on the nonlinear Schr\"odinger equation. Finally we study theoretically the influence of finite temperatures on the visibility of the interference in a double pinhole configuration. \textcopyright{} 1996 The American Physical Society.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N-body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions.