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arXiv:0805.0260

Directly determining the relative phase of two coherent solitary waves in attractive Bose-Einstein condensates

Weibin Li

Published May 2, 2008• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.0805.0260

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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 $\ensuremath{\Delta}\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q/\mathrm{md}$, 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 propose to utilize the Bose–Einstein condensate (BEC) for precision phase sensitive measurement of position and momentum displacements. The controlled two-soliton dynamics can be turned into a quantum probe to measure these parameters with high precision in an experimentally verified system of bright solitary trains. A careful phase space analysis of the dynamics of the mesoscopic wave packet is carried out through Wigner phase space picture for finding out the parameter domain exhibiting sub-Planck structures, required for precision quantum metrology. We propose two experimentally feasible scenarios, one involving the overall phase and the other through the relative phase between the two-solitons when they are oscillating inside the trap. In both the cases, detailed analytical studies are carried out through the overlap functions which reveal the sensitivity issue. A careful analysis is also performed to find the parametric domain relevant for the use of BEC for weak value estimation.
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Using a model many-body wave function I analyze the standard criterion for Bose-Einstein condensation and its relation to coherence properties of the system. I pay special attention to an attractive condensate under such a condition that a characteristic length scale of the spatial extension of its center of mass differs significantly from length scales of relative coordinates. I show that although no interference fringes are produced in the two-slit Young interference experiment performed on this system, fringes of a high visibility can be observed in a conditional simultaneous detection of two particles.