Spontaneous Breaking of a Translational Symmetry and Analogue Gravity

Florent Michel (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

We study the ground state of Bose-Einstein condensates with a roton-maxon dispersion relation when the fluid velocity is larger than the Landau velocity. This leads to a phase breaking translational invariance, which we call \enquote{undulation}. Stability of the undulation strongly depends on the choice of fixed parameters. We find two stability conditions when fixing the condensate velocity, the total number of atoms and the wave-vector of the undulation on the two-body interaction potential. The first one constraints the condensate velocity, while the second one constraints the two-body interaction potential. The structure of the ground state is investigated numerically. We also comment on analogies with a Chern-Simons theory in 5 dimensions. This work is a first step towards what could be a more general study of such phases breaking translational invariance in different domains like hydrodynamics, condensed matter, cold atoms or quantum field theory in curved space-time.

Mots clés: roton-maxon; symmetry breaking; analogue gravity

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Gaz Quantiques [cond-mat.quant-gas]

Florent Michel. Spontaneous Breaking of a Translational Symmetry and Analogue Gravity. 2014. ⟨hal-01044712⟩