Interference of Bose condensates

Materials Science and Engineering: B, 1997

We studied 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 non-linear Schriidinger equation in three dimensions, the consecutive stages of expansion, overlap and interference were investigated in order to facilitate the design of future experiments. It turns out that the period of the interference fringes grows linearly in time with a velocity inversely proportional to the initial distance of the two condensates. G 1997 Elsevier Science S.A.

Physical Review A, 1996

1997

We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of atomic detection. In the former case we show that the macroscopic wave function collapses and revives in time, and we calculate the characteristic times for current experiments. Collapses and revivals are also predicted in the interference between two Bose-Einstein condensates which are initially in Fock states, a relative phase between the condensates being established via atomic detections corresponding to uncertainty in the number difference between them.

Physical Review Letters, 1997

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 Schrödinger 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. [S0031-9007(97)03260-2]

American Journal of Physics, 2006

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a so-called condensate wave functions having a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state, for which the particle number is uncertain, but phase is known. However, how one would prepare such a state before an experiment is not obvious.

The Journal of Physical Chemistry B, 2008

A formalism for describing the coherence and interference properties of two atomic clouds of Bose-Einstein condensates (BEC) is presented, which is applicable even in the opposite limits when the BEC clouds are initially coherent and when they are initially independent. First, we develop a mean-field theory wherein one mean-field mode is used, and then, for fragmented (i.e., independent) condensates, we use a mean-field theory with two modes. We then develop a full two-mode field theory, with a field operator composed of a sum of two terms containing matter wave mode functions φ 1 and φ 2 , that multiply the destruction operators of the modes, â 1 and â 2. When atom-atom interactions are present and when the mode functions overlap, the matter wave mode functions φ 1 and φ 2 develop components moving to the right and left, and this results in interference fringes in the density. At the many-body level, another source of interference arises from expectation values of the form 〈â i † â j 〉 with i * j, which become nonzero due to tunneling and interactions. We detail how these two sources of interference affect the density profile and the density-density correlation functions of Bose-Einstein condensates in the coherent and in the fragmented regimes.

Physical Review A, 2006

Additional variables (also often called "hidden variables") are sometimes added to standard quantum mechanics in order to remove its indeterminism or "incompletness," and to make the measurement process look more classical. Here we discuss a case in which an additional variable arises almost spontaneously from the quantum formalism: the emergence of relative phase between two highly populated Fock state Bose-Einstein condensates. The model simulated here involves the interference of two Bose condensates, one with all up spins, and the other with down spins, along a z-axis. With the clouds overlapping, we consider the results of measuring spins in a transverse plane (the general direction is studied in an appendix). The determination of the previously "hidden" phase becomes progressively more definite as additional measurements are made. We also provide an analysis of a recent and closely related experiment.

Physical Review Letters, 2007

The density of two initially independent condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and each condensate consists of a different kind of atoms. Illustrative examples are presented.

We present an elementary model of the collapses and revivals in the visibility of the interference between two atomic Bose-Einstein condensates. We obtain different predictions of the revival times whether we conserve or break atom number conservation from the outset. The validity of Bose-broken symmetry can be tested by observations of these collapses and revivals.

Physical Review A, 2008

Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N -body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions.