Eur. Phys. J. D 56, 391-404 (2010)
https://doi.org/10.1140/epjd/e2009-00314-3

Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates

¹ CNR-INFM BEC Center and Dipartimento di Fisica, Università di Trento, via Sommarive 14, 38050 Povo, Trento, Italy
² Dipartimento di Fisica dell'Università di Bologna and INFN sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
³ Departamento de Fisica Teorica and IFIC, Universidad de Valencia-CSIC, C. Dr.Moliner, 50, 46100 Burjassot, Spain
⁴ Physik-Department, Technische Universität München, 85748 Garching, Germany

Corresponding author: carusott@science.unitn.it

Received: 12 July 2009
Revised: 25 September 2009
Published online: 22 December 2009

Abstract

We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.