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Physical Review Letters

Transition from Phase Locking to the Interference of Independent Bose Condensates: Theory versus Experiment

Andreas Röhrl, M. Naraschewski, Axel Schenzle, Hartmut Wallis

Published Jun 2, 1997• 108 citations
Publisher

Abstract

The macroscopic interference of two Bose condensates released from a double minimum potential has been demonstrated recently [M. R. Andrews et al., Science 275, 637 (1997)]. In this Letter we show the excellent agreement between those experiments and theoretical predictions based on the nonlinear Schr\"odinger equation. In addition, the transition from interference of coupled condensates, comparable with the Josephson effect in superconductors, to the interference of independent Bose condensates is studied.

DOI
10.1103/physrevlett.78.4143

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The macroscopic interference of two Bose condensates released from a double minimum potential has been demonstrated recently [M. R. Andrews et al., Science 275, 637 (1997)]. In this Letter we show the excellent agreement between those experiments and theoretical predictions based on the nonlinear Schr"odinger equation. In addition, the transition from interference of coupled condensates, comparable with the Josephson effect in superconductors, to the interference of independent Bose condensates is studied.
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 investigate the prospects of atomic interference using samples of Bose condensed atoms. First we show the ability of two independent Bose condensates to create an interference pattern. This holds even if both condensates are described by Fock states. Thus, the existence of an experimental signature for a broken gauge symmetry, seen in a single run of the experiment, is not necessarily reflected by a broken symmetry on the level of the quantum mechanical state vector. Based on these results, we simulate numerically a recent experiment with two independent Bose condensates [K. B. Davis et al., Phys. Rev. Lett. 75, 3969 (1995)]. The existence of interference fringes is predicted based on the nonlinear Schr\"odinger equation. Finally we study theoretically the influence of finite temperatures on the visibility of the interference in a double pinhole configuration. \textcopyright{} 1996 The American Physical Society.
We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.
In an exciting experiment by MIT's group (Science 275, 637 (1997)), clear interference fringes were observed for two initially independent Bose condensates in dilute gas. Presently, there are two different theories (measurement-induced interference theory and interaction-induced interference theory) which can both explain MIT's experimental results. Based on our interaction-induced interference theory, we consider the evolution of the density-density correlation after the releasing of a double-well potential trapping two independent Bose condensates. Based on the interaction-induced interference theory, we find that the interference fringes in the density-density correlation exhibit a behavior of emergence and disappearance with the development of time. We find essential difference for the density-density correlation based on interaction-induced interference theory and measurement-induced interference theory, and thus we suggest the density-density correlation to experimentally reveal further the interference mechanism for two initially independent Bose condensates.
The interference pattern of two Bose—Einstein condensates released from a double-well potential for different holding times is theoretically investigated using a decoupled two-mode Bose—Hubbard model. For two coherently separated condensates, the interference displays a periodic behavior, which is closely related to the atomic interaction. A remarkable parity effect is found in the interference patterns. For certain holding times, the even/odd total number of atoms would result in different interference fringes. The influences of different initial conditions on the evolution of interference and the observation of parity effects are discussed.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.