Phonon spectrum and correlations in a transonic flow of an atomic Bose gas
Résumé
Motivated by a recent experiment of J. Steinhauer, we reconsider the spectrum and the correlations of the phonons spontaneously emitted in stationary transonic flows. The latter are described by “waterfall” configurations which form a one-parameter family of stable flows. For parameters close to their experimental values, in spite of high gradients near the sonic horizon, the spectrum is accurately Planckian in the relevant frequency domain, where the temperature differs from the relativistic prediction by less than 10%. We then study the density correlations across the horizon and the nonseparable character of the final state. We show that the relativistic expressions provide accurate approximations when the initial temperature is not too high. We also show that the phases of the scattering coefficients introduce a finite shift of the location of the correlations which has so far been overlooked. This shift is due to the asymmetry of the flow across the horizon, and persists in the dispersionless regime. Finally we show how the formation of the sonic horizon modifies both local and nonlocal density correlations.