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arXiv:cond-mat/0703006 · Physical Review Letters

Phase-Sensitive Recombination of Two Bose-Einstein Condensates on an Atom Chip

Gyu-Boong Jo, Jongsoo Choi, Caleb A. Christensen, Thomas A. Pasquini, Ye-Ryoung Lee, Wolfgang Ketterle, David E. Pritchard

Published Apr 30, 2007• 109 citations
arXivHTMLPDF

Abstract

The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10% and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.

DOI
10.1103/physrevlett.98.180401

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The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10% and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.
Chip-based atom interferometers bring together the advantages of atom chips and Bose–Einstein condensates. Their central prerequisite is that a condensate can be coherently split into two halves with a determined relative phase. This paper demonstrates the dynamical splitting and merging of an atom cloud with two U-wires on an atom chip. Symmetrical and asymmetrical splittings are realized by applying a bias field with different directions and magnitudes. The trajectories of the splitting are consistent with theoretical calculations. The atom chip is a good candidate for constructing an atom interferometer.
We study the dynamics of Bose-Einstein condensates in time-dependent microtraps in view of applications in atom interferometry. The scheme is based on the slow splitting and recombination of an elongated harmonic trap. It is shown that the nonlinearity due to the mean field atom-atom interaction increases the sensitivity of the interferometers to an applied phase shift. This feature is connected with the adiabatic generation of a dark soliton. The soliton typically oscillates in the recombined trap, and its amplitude provides an alternative readout of the interferometer phase. We analyse the robustness of this phenomenon with respect to thermal fluctuations, due to (i) initially excited Bogoliubov modes and (ii) magnetic near fields in an electromagnetic surface trap.
We show that the decay of a soliton into vortices provides a mechanism for measuring the initial phase difference between two merging Bose-Einstein condensates. At very low temperatures, the mechanism is resonant, operating only when the clouds start in antiphase. But at higher temperatures, phase fluctuations trigger vortex production over a wide range of initial relative phase, as observed in recent experiments at MIT. Choosing the merge time to maximize the number of vortices created makes the interferometer highly sensitive to spatially varying phase patterns and hence atomic movement.
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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Cold-atom interferometers with optical splitting and recombination use off-resonant laser beams to split a cloud of Bose-Einstein condensate (BEC) into two clouds that travel along different paths and are then recombined again using optical beams. After the recombination, the BEC in general populates both the cloud at rest and the moving clouds. Measuring a relative number of atoms in each of these clouds yields information about the relative phase shift accumulated by the atoms in the two moving clouds during the interferometric cycle. We derive the expression for the probability of finding any given number of atoms in each of the clouds, discuss features of the probability density distribution, analyze its dependence on the relative accumulated phase shift as a function of the strength of the interatomic interactions, and compare our results with experiment.