Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Phase-space dynamics of Bose condensates: Interference versus interaction

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

Published Mar 1, 1997• 77 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.55.2109

Related papers

Interference of Bose condensates

M. Naraschewski, Hartmut Wallis, Axel Schenzle +2 more

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.

arXiv:atom-ph/9606005•Physical Review A•Sep 1, 1996•129 citations

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

Andreas Röhrl, M. Naraschewski, Axel Schenzle +1 more

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.

Physical Review Letters•Jun 2, 1997•108 citations

Interference of two Bose-Einstein condensates

В. А. Алексеев

The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ →∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al. , Science 275 , 6367 (1997), the computed correlation time τ ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms.

Journal of Experimental and Theoretical Physics Letters•Apr 1, 1999•3 citations

Density–density correlation and interference mechanism for two initially independent Bose–Einstein condensates

Shujuan Liu, Hongwei Xiong

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.

arXiv:cond-mat/0612133•New Journal of Physics•Nov 21, 2007•7 citations

Evolution of the Interference of Bose Condensates Released from a Double-Well Potential

Bihui Zhu, Shujuan Liu, Hong-Wei Xiong

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.

Chinese Physics Letters•Sep 1, 2011•1 citation

Phase dynamics and Bose–broken symmetry in atomic Bose–Einstein condensates

Daniel F. Walls, Matthew J. Collett, T. Wong +2 more

Collisions lead to the collapse and revival of the interference fringes between two atomic Bose–Einstein condensates. We study the collapses and revivals of the relative phase between the condensates for two different initial states. One state invokes Bose–broken symmetry allowing us to write the wavefunction as a superposition of total number (of both condensates) states whereas the other does not.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 15, 1997•7 citations
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.
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.
The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ →∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al. , Science 275 , 6367 (1997), the computed correlation time τ ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms.
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.