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Conference on Lasers and Electro-Optics

Quantum state of two coupled Bose-Einstein condensates

Michael J. Steel, Matthew J. Collett, Daniel F. Walls, Ewan M. Wright

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.Due to interatomic collisions, the ground state of a Bose-Einstein condensate of dilute atoms is not, as is commonly assumed, a coherent state. First recognizing this point, Lewenstein and You concluded that the condensate is actually an amplitude quadrature eigenstate. We have extended this work by studying the quantum state for two condensates with a linear coupling provided by either spatial tunneling or laser coupling between magnetic substates. As the system is closed, the ground state is unambiguously a pure state, and as we deal only with relative phases, there is no need to invoke broken symmetry.

DOI
10.1109/iqec.1998.680086

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Summary form only given.Due to interatomic collisions, the ground state of a Bose-Einstein condensate of dilute atoms is not, as is commonly assumed, a coherent state. First recognizing this point, Lewenstein and You concluded that the condensate is actually an amplitude quadrature eigenstate. We have extended this work by studying the quantum state for two condensates with a linear coupling provided by either spatial tunneling or laser coupling between magnetic substates. As the system is closed, the ground state is unambiguously a pure state, and as we deal only with relative phases, there is no need to invoke broken symmetry.
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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.
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 propose a light-scattering scheme to measure the relative phase of atomic Bose-Einstein condensates and its diffusion rate. The proposal relies on the existence of two independent condensates coupled to a common excited state. To this end, we consider a two-well ground-state potential together with excited-state trap wave functions that extend over the whole region. When the first trap is driven by a weak monochromatic laser field, the light scattered from the second trap has a nonzero mean-electric field amplitude with a phase shift proportional to the difference of the condensate phases. When both condensates are driven, the phases of the two laser fields can be adjusted to cancel the scattering completely by a quantum interference. The particular value of the laser phase difference that gives zero scattering determines the relative phase of the two condensates.