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arXiv:cond-mat/0404149 · Physical Review A

Double-slit interferometry with a Bose-Einstein condensate

Lee A. Collins, Luca Pezzè, Augusto Smerzi, G. P. Berman, A. R. Bishop

Published Mar 25, 2005• 13 citations
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Abstract

A Bose-Einstein ``double-slit'' interferometer has been recently realized experimentally by Y. Shin et al., Phys. Rev. Lett. 92 050405 (2004). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevskii equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong degradation of the interference pattern observed experimentally. The role of quantum fluctuations is discussed.

DOI
10.1103/physreva.71.033628

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Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.
The interference between two condensates with repulsive interaction is investigated numerically by solving the one-dimensional time-dependent Gross–Pitaevskii equation. The periodic interference pattern forms in two condensates, which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions. Dark solitons are observed when two condensates overlap. Due to the existence of atom–atom interactions, atoms are transferred among the ground state and the excited states, which coincides with the condensate energy change.
We investigate the influence of a Bose-Einstein condensate on the coherence properties of a traversing atomic beam. We derive a master equation describing the interaction between beam atoms and the condensate in sss-wave approximation. Scattering rates are calculated and compared with the case of an ordinary Boltzmann gas. Special attention is paid to the decoherence of the beam, i.e., the decay of spatial coherence in the presence of the condensate. As an application, we explicitly calculate the visibility of the interference pattern in a double-slit experiment and indicate signs for the onset of the condensation.
This work presents a numerical study of a tunnelingbased interferometer implemented using a Bose-Einstein condensate (BEC) confined in a static double-well potential, where the condensate dynamics are simulated using the one-dimensional Gross-Pitaevskii equation to capture the essential mean-field behavior. By carefully configuring the central barrier parameters, the double well is engineered to act as a coherent matterwave beam splitter. A relative phase is introduced between the two arms of the interferometer, enabling the extraction of phase information through interference. We analyze the resulting interference contrast to determine the best barrier configurations that allow the system to function effectively as an interferometer. It was found that the interferometric contrast remains robust under realistic fluctuations in the barrier parameters, confirming experimental feasibility. Using a fixed barrier for both the splitting and recombination steps, we avoid the need to dynamically ramp the barrier, as in other approaches. This allows us to realize a simple and experimentally accessible interferometry scheme in the double-well potential.