The origin of the phase in the interference of Bose-Einstein condensates

Abstract

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.We show that a phase can also arise from experiments using condensates in Fock states, that is, having known particle numbers. Analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of "spontaneously broken gauge symmetry" and to "hidden variables" is mentioned.

Readout of the atomtronic quantum interference device

“…(1), combining them with the wave function of the central condensate and simulating the detection sequence of all particles of the expanding wavefunction [37,38]. In our case, however, the latter approach does not produce the spiral patterns because the numerics are limited to a small number of particles.…”

“…This is confirmed by Fig.9 in the Appendix. However, if we measure two or more particles, information about the particle origin is lost [37,38], as the measured particles could be either from the ring or from the central condensate. As the particle number distribution between ring and central condensate becomes uncertain, phase certainty is gained.…”

“…We calculate the density-density covariance [37,38,43,44] cov(r, r , t) = n(r, t)n(r , t) − n(r, t) n(r , t) .…”

Dynamical effects of exchange symmetry breaking in mixtures of interacting bosons

“…(39) for m φ = ±j φ can be obtained in a semiclassical picture. A Fock state corresponds to a Bloch vector with fixed z component, but uncertain x and y component-the phase between the wells is maximally uncertain, since the particle number in each well is fixed [48][49][50][51]. A single-species Fock state is thus described by a vector of constant length that lies on a cone around the z axis.…”

Nonlocal Appearance of a Macroscopic Angular Momentum

“…Suppose we have two Bose-Einstein condensates (BEC) polarized in opposite directions along the z-direction [2] and we perform a measurement of the spin (angular momentum) along a transversal direction by absorbing particles emerging from one cloud or the other. Then it can be shown that a macroscopic angular momentum along a random transversal direction appears after the detection of only a few particles [3][4][5][6][7][8][9][10]. Moreover, owing to the fact that the clouds can be imagined as having a very large spatial extension, apparently a large macroscopic angular momentum can be made to appear almost instantaneously at a distance.…”