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Physical Review A

Optical detection of the relative phase between two Bose-Einstein condensates

Juha Javanainen

Published Dec 1, 1996• 45 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.r4629

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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.
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Summary form only given.We consider two overlapping and optically thin dilute gas Bose-Einstein condensates occupying two different Zeeman sublevels. We propose an optical method for increasing the number of condensate atoms. Two laser beams drive Raman transitions between the Zeeman states and induce a coherent quantum tunneling between the Bose-Einstein condensates. The scattering of photons is dominantly coherent and in the forward direction due to the Bose enhancement. This corresponds to the scattering of atoms between the two condensates. Some laser-driven Raman transitions also scatter atoms between the condensate and noncondensate atom fractions. For a range of condensate phase differences there is destructive quantum interference of the amplitudes for scattering atoms out of the condensates. Because the total atom scattering rate into the condensates is unaffected the condensates grow. This mechanism is analogous to that responsible for optical lasing without inversion, and it may find application as a pump for an atom laser.
We study an elementary model of two tunneling Bose-Einstein condensates with an atom detector in one of the traps. Stochastic simulations of atom detection in one trap show an oscillation of atom number between traps even though the condensates are initially in equal number Fock states. The oscillation has a random amplitude depending on the phase difference between the condensates, which coincides with that given by a spontaneously broken symmetry argument. \textcopyright{} 1996 The American Physical Society.
We calculate the spectrum of the scattered light from quantum degenerate atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy two ground states, which are optically coupled through a common excited state by two low-intensity off-resonant light beams. In the presence of a Bose condensate in both ground states, the atoms may exhibit light-induced oscillations between the two condensates analogous to the Josephson effect. The spectrum of the scattered light is calculated in the limit of a low oscillation frequency. In the spectrum we are able to observe qualitative features depending on the phase difference between the macroscopic wave functions of the two condensates. Thus, our optical scheme could possibly be used as an experimental realization of the spontaneous breakdown of the U(1) gauge symmetry in the Bose-Einstein condensation.
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.