Nonlinearities induced by parametric resonance in effectively 1D atomic Bose condensates

Abstract

We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the system. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking, as is the similarity of techniques used to study them. arXiv:1802.00739v2 [cond-mat.quant-gas] 3 Sep 2018

Dynamical response of Bose–Einstein condensates to oscillating gravitational fields

“…For example, this could be the direct driving or parametric driving from the vacuum, where the latter is equivalent to the dynamical Casimir effect in Bose-Einstein condensates [42]. See also [58], where parametric amplification of excitations of phonons modes due to a modulation of the transverse trapping frequency of a BEC is discussed in detail.…”

Quantum fluctuations of the friction force induced by the dynamical Casimir emission

“…Even though our work is based on a simplest, yet realistic model of dynamical Casimir emission in an optical cavity that is amenable to exact calculations at a fully quantum level, we expect that our findings on the dramatic breakdown of the semiclassical approximation and the non-trivial quantum statistics of the mechanical oscillation are very general and may have deep consequences for a variety of problems in quantum field theories on curved spacetimes and in gravitation. Next steps will include an investigation of the conceptual links between our findings and stochastic gravity models [15] and the extension of our study of backreaction effects to those multimode configurations that naturally appear in dynamical Casimir experiments with atomic fluids [41,43,59,60]. These investigations will pave the way towards the more challenging task of understanding quantum fluctuation features in the black hole evaporation process [13].…”

Particle creation in the spin modes of a dynamically oscillating two-component Bose-Einstein condensate

“…This feature holds a great promise in view of studying how the parametrically excited quantum field back-reacts onto the background and modifies its dynamics, e.g. by inducing a friction onto the density oscillations [59,61]. Understanding such back-reaction phenomena in condensed-matter toy models provides a promising avenue to shine light on a number of questions of cosmological interest, related for example to the early inflationary stage of the Universe, or the ultimate stage of existence of a black hole.…”

“…On the other hand, a clearly visible signal is found in every dimension for a resonantly oscillating condensate [panel (e)], which looks very promising in view of experiments. The large contrast of the oscillations in the spin density fluctuations is a signature of squeezing effects, which have been predicted to lead to non-separable behaviours [58,59].…”