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arXiv:cond-mat/0507154 · Physical Review Letters

Optical Weak Link between Two Spatially Separated Bose-Einstein Condensates

Yong-il Shin, Gyu-Boong Jo, Michele Saba, Thomas A. Pasquini, Wolfgang Ketterle, David E. Pritchard

Published Oct 17, 2005• 86 citations
arXivHTMLPDF

Abstract

Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite directions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.

DOI
10.1103/physrevlett.95.170402

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A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 microm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.
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We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles or particles in the two condensates get entangled due to quantum communication between the condensates via the probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables and depends strongly on the relative detuning of the two pumps and the relative atom-field coupling strengths of the two condensates. We present two methods of detecting the generated entanglement.
We theoretically analyse the Bragg spectroscopic interferometer of two spatially separated atomic Bose–Einstein condensates that was experimentally realized by Saba et al (2005 Science 307 1945) by continuously monitoring the relative phase evolution. Even though atoms in the light-stimulated Bragg scattering interact with intense coherent laser beams, we show that the phase is created by quantum measurement-induced backaction on the homodyne photocurrent of the lasers, opening the possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a running phase regime observed in the experiment of Saba et al , which is sensitive to an energy offset and suitable for an interferometer, and a trapped phase regime, which can be insensitive to the applied forces and detrimental to interferometric applications.
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In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.