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Theoretical study of quantum correlations and nonlinear fluctuations in quantum gases

Abstract : 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 “fluids of light”. In a first 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 show that a correct account of “zero modes” – overlooked so far in the context of analogue gravity – is essential for an accurate description of the Hawking process, and results in a excellent comparison with recent experimental data. In addition, we characterize the entanglement shared among quantum excitations and show that they exhibit tripartite entanglement. In a second part, we investigate the short and long time propagation of nonlinear fluids within a hydrodynamic framework and by means of mathematical methods developed by Riemann and Whitham. In particular, we study the oscillating structure and the dynamics of dispersive shock waves which arise after a wave breaking event. We obtain a weak shock theory, from which we can extract a quantitative description of experimentally relevant parameters, such as the wave breaking time, the velocity of the solitonic edge of the shock or the contrast of its fringes.
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Mathieu Isoard. Theoretical study of quantum correlations and nonlinear fluctuations in quantum gases. Pattern Formation and Solitons [nlin.PS]. Université Paris-Saclay, 2020. English. ⟨NNT : 2020UPASP004⟩. ⟨tel-02974737⟩

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