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Quantum-Atom Optics Downunder (QAO)

Phase sensitivity of a nonlinear matter-wave interferometer

Agnieszka Górecka, Chaohong Lee, Matthew J. Davis, Elena A. Ostrovskaya

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We present a theoretical study of the Bose-Einstein condensate (BEC) in a one-dimensional time-dependent double-well potential. As the two separate wells merge into a single well, moving nonlinear excitations (dark solitons) are formed in the condensate. The amplitude of either the soliton oscillations or the dipole oscillations in the single-well harmonic trap is sensitive to the relative phase between initially separated condensates. By employing the classical field approximation, we examine the phase sensitivity of the interferometry for different recombination rates and temperatures, and investigate the connection between the dynamics of the nonlinear excitations and the condensate heating.

DOI
10.1364/qao.2007.qme19

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We present a theoretical study of the Bose-Einstein condensate (BEC) in a one-dimensional time-dependent double-well potential. As the two separate wells merge into a single well, moving nonlinear excitations (dark solitons) are formed in the condensate. The amplitude of either the soliton oscillations or the dipole oscillations in the single-well harmonic trap is sensitive to the relative phase between initially separated condensates. By employing the classical field approximation, we examine the phase sensitivity of the interferometry for different recombination rates and temperatures, and investigate the connection between the dynamics of the nonlinear excitations and the condensate heating.
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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.
We study the dynamics of Bose–Einstein condensates in time-dependent microtraps for the purpose of understanding the influence of the mean field interaction on the performance of interferometers. We identify conditions where the nonlinearity due to atom interactions increases the sensitivity of interferometers to a phase shift. This feature is connected with the adiabatic generation of a dark soliton. We analyse the robustness of this phenomenon with respect to thermal fluctuations, due to excited near fields in an electromagnetic surface trap.
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.
We study stability of the first excited state of quasi-one-dimensional Bose-Einstein condensates in a double-well potential, which is called ``$\ensuremath{\pi}$ state.'' The density notch in the $\ensuremath{\pi}$ state can be regarded as a standing dark soliton. From the excitation spectrum, we determine the critical barrier height, above which the $\ensuremath{\pi}$ state is dynamically unstable. We find that the critical barrier height decreases monotonically as the number of condensate atoms increases. We also simulate the dynamics of the $\ensuremath{\pi}$ state by solving the time-dependent Gross-Pitaevskii equation. We show that due to the dynamical instability the dark soliton starts to move away from the trap center and exhibits a large-amplitude oscillation.