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arXiv:cond-mat/9905409 · Physical Review Letters

Interference of Bose-Einstein Condensates in Momentum Space

Лев П. Питаевский, S. Stringari

Published Nov 22, 1999• 57 citations
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Abstract

We suggest an experiment to investigate interference effects between two spatially separated Bose-Einstein condensates. In the presence of coherence, the dynamic structure factor, measurable through inelastic photon scattering, is predicted to exhibit, at high momentum transfer $q$, interference fringes with frequency period $\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q/\mathrm{md}$, where $d$ is the distance between the condensates. We show that this coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates can be, hence, created through the measurement process.

DOI
10.1103/physrevlett.83.4237

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We suggest an experiment to investigate interference effects between two spatially separated Bose-Einstein condensates. In the presence of coherence, the dynamic structure factor, measurable through inelastic photon scattering, is predicted to exhibit, at high momentum transfer qqq, interference fringes with frequency period \ensuremathΔ\ensuremathν=q/md\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q/\mathrm{md}\ensuremathΔ\ensuremathν=q/md, where ddd is the distance between the condensates. We show that this coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that the relative phase of the condensates can be, hence, created through the measurement process.
We present experimental and theoretical studies of the coherence properties of a Bose-Einstein condensate (BEC) using an interference technique. Two optical standing wave pulses of duration 100 ns and separation $\ensuremath{\Delta}t$ are applied to a condensate. Each standing wave phase grating makes small copies of the condensate displaced in momentum space. The quantum mechanical amplitudes of each copy interfere, depending on $\ensuremath{\Delta}t$ and on spatial phase variations across the condensate. We find that the behavior of a trapped BEC is consistent with a uniform spatial phase. A released BEC, however, exhibits large phase variation across the condensate.
Interference between two freely expanding Bose-Einstein condensates has been observed. Two condensates separated by approximately 40 micrometers were created by evaporatively cooling sodium atoms in a double-well potential formed by magnetic and optical forces. High-contrast matter-wave interference fringes with a period of approximately 15 micrometers were observed after switching off the potential and letting the condensates expand for 40 milliseconds and overlap. This demonstrates that Bose condensed atoms are "laser-like"; that is, they are coherent and show long-range correlations. These results have direct implications for the atom laser and the Josephson effect for atoms.
We study the dynamic structure factor of two coherent bright solitary waves in attractive Bose- Einstein condensates confined in a harmonic trap. We demonstrate that the wave function of the two solitary waves with a fixed relative phase shows interference in momentum space. The fringes are shifted depending on the values of the phase. This momentum interference can be extracted from the dynamic structure factor of the system using stimulated two-photon Bragg scattering. Thus our method provides a way to measure the relative phase directly.
We study theoretically the macroscopic interference of two independent Bose condensates released from a double potential trap. The observation of fringes could serve as a test for the paradigm of broken gauge symmetry. By numerical solution of the nonlinear Schr\"odinger equation in three dimensions, the consecutive stages of expansion, overlap, and interference are investigated in order to facilitate the design of future experiments. The phase-space dynamics of the condensates is analyzed by means of the Wigner function. It turns out that the distance of interference fringes grows linearly in time with a velocity inversely proportional to the initial distance of the two condensates. The collisional reduction of the fringe visibility is estimated.
We demonstrated an experimental technique based on stimulated light scattering to continuously sample the relative phase of two spatially separated Bose-Einstein condensates of atoms. The phase measurement process created a relative phase between two condensates with no initial phase relation, read out the phase, and monitored the phase evolution. This technique was used to realize interferometry between two trapped Bose-Einstein condensates without need for splitting or recombining the atom cloud.