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Creation of coherence in Bose-Einstein condensates by atom detection

Péter Horák, Barnett, S M

Published Jan 1, 1999• 17 citations
OpenAlex

Abstract

We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for the creation of the interference is of the order of the detection time for a few single atoms and another, for the preparation of coherent states, of the order of the detection time for a significant fraction of the total number of atoms. Approximate analytic solutions are derived and compared with exact numerical results.

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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 15, 1997•7 citations
We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for the creation of the interference is of the order of the detection time for a few single atoms and another, for the preparation of coherent states, of the order of the detection time for a significant fraction of the total number of atoms. Approximate analytic solutions are derived and compared with exact numerical results.
We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for the creation of the interference is of the order of the detection time for a few single atoms and another, for the preparation of coherent states, is of the order of the detection time for a significant fraction of the total number of atoms. Approximate analytic solutions are derived and compared with exact numerical results.
We study the buildup of quantum coherence between two Bose-Einstein condensates that are initially in mixed states. We consider in detail the two cases where each condensate is initially in a thermal or a Poisson distribution of atom number. Although initially there is no relative phase between the condensates, a sequence of spatial atom detections produces an interference pattern with arbitrary but fixed relative phase. The visibility of this interference pattern is close to one for the Poisson distribution of two condensates with equal counting rates but it becomes a stochastic variable in the thermal case, where the visibility will vary from run to run around an average visibility of $\ensuremath{\pi}/4.$ In both cases, the variance of the phase distribution is inversely proportional to the number of atom detections in the regime where this number is large compared to one but small compared with the total mean number of atoms in the condensates.
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.
We show that, when two Bose-Einstein condensates are combined, a spatial interference pattern ensues even if the condensates are in number states with no spontaneously broken gauge symmetry. In our measurement-theoretical approach the interference pattern arises from correlations between the detected positions of the atoms. We also simulate numerically experiments intended to distinguish number-state condensates and spontaneous symmetry breaking, the latter being modelled by coherent-state condensates. To detect the difference in the pair correlation functions, the experiment has to be repeated about a thousand times even for condensates with as few as five atoms each.
We study the interaction of light with two Bose-Einstein condensates as an open quantum system. The two overlapping condensates occupy two different Zeeman sublevels and two driving light beams induce a coherent quantum tunneling between the condensates. We derive the master equation for the system. It is shown via stochastic simulations that the measurements of spontaneously scattered photons establish the relative phase between two Bose-Einstein condensates, even though the condensates are initially in pure number states. These measurements are nondestructive for the condensates, because only light is scattered and no atoms are removed from the system. Due to macroscopic quantum interference the detection rate of photons depends strongly on the relative phase between the condensates. This may provide a way to distinguish between initial number states and initial symmetry-breaking states of the condensates.