Bayesian inference to characterize Josephson oscillations in a double-well trap

Juha Javanainen; Renuka Rajapakse

doi:10.1103/PhysRevA.92.023613

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Bayesian inference to characterize Josephson oscillations in a double-well trap

Juha Javanainen, Renuka Rajapakse

DOI 10.1103/PhysRevA.92.023613 · Physical Review A

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Abstract

We use quantum trajectories to simulate Josephson oscillations of atomic condensates between the two sides of a double-well potential. In the simulations the atoms in both wells are monitored using off-resonant light scattering, and the ultimate outcome of our thought experiment is a sequence of photon counts probing the numbers of the atoms in each potential well. We show how to reconstruct the Josephson oscillations from the observed photon counts using Bayesian inference, and study the oscillations quantitatively by averaging the inferred time-dependent oscillation amplitude over a large number of realizations. Scaling behaviors that characterize the oscillations are uncovered and related to physics principles such as measurement back-action. It turns out that the scalings hold true for quite small atom numbers, so that in this sense four atoms in a potential well may already make a Bose-Einstein condensate.