Theoretical study of quantum correlations and nonlinear fluctuations in quantum gases
par
Mathieu Isoard
Jury:
Matteo Conforti, Université Lille, rapporteur
Patrik Öhberg, Heriot-Watt University, rapporteur
Élisabeth Giacobino, CNRS, examinatrice
Sandro Stringari, University of Trento, examinateur
Chris Westbrook, Institut d’Optique, examinateur
Nicolas Pavloff, Université Paris-Saclay/CNRS , directeur de thèse
Resumé
This thesis is dedicated to the study of nonlinear-driven phenomena in two quantum gases which bear important similarities: Bose-Einstein condensates of ultracold atomic vapors and paraxial nonlinear laser beam.
These systems can be described within a hydrodynamic framework which make it possible to investigate their short and long time propagation by means of mathematical methods developed by Riemann and Whitham. In particular, we study the formation and the propagation of dispersive shock waves which arise after a wave breaking event. We obtain a kind of a weak shock theory, from which we can extract a quantitative description of experimentally relevant parameters, such as the velocity of the solitonic edge of the shock or the contrast of its fringes.
In a second part, we study sonic analogues of black holes. In a Bose-Einstein condensate, it is possible to implement a stationary configuration with a current flowing from a subsonic region to a supersonic one. This mimics a black hole, since sonic excitations cannot escape the supersonic region. Besides, quantizing the phonon field leads to a sonic analogue of Hawking radiation. In this thesis, we have shown that a correct account of zero modes is essential for an accurate description of the Hawking process, and results in a excellent comparison with recent experimental datas. In addition, we characterize the entanglement shared among quantum excitations and show that they exhibit tripartite entanglement.