The two faces of quantum sound

TL;DR

This paper explores the dual nature of quantum sound in Bose-Einstein condensates, showing that quasiparticles are consistently described across different regimes and formalisms, with implications for analog gravity and Hawking radiation.

Contribution

It demonstrates the equivalence of quasiparticle concepts in both Bogolubov and Klein-Gordon frameworks across energy regimes and analyzes vacuum states in acoustic horizons.

Findings

Quasiparticles are consistent in low and high energy regimes.

Different formalisms yield equivalent quasiparticle descriptions.

Vacuum state choices affect Hawking radiation predictions.

Abstract

Fluctuations around a Bose-Einstein condensate can be described by means of Bogolubov theory leading to the notion of quasiparticle and antiquasiparticle familiar to non-relativistic condensed matter practitioners. On the other hand, we already know that these perturbations evolve according to a relativistic Klein-Gordon equation in the long wavelength approximation. For shorter wavelengths, we show that this equation acquires nontrivial corrections which modify the Klein-Gordon product. In this approach, quasiparticles can also be defined (up to the standard ambiguities due to observer-dependence). We demonstrate that---in the low as well as in the high energy regimes---both concepts of quasiparticle are actually the same, regardless of the formalism (Bogolubov or Klein-Gordon) used to describe them. These results also apply to any barotropic, inviscid, irrotational fluid, with or without quantum potential. Finally, we illustrate how the quantization of these systems of quasiparticles proceeds by analyzing a stationary configuration containing an acoustic horizon. We show that there are several possible choices of a regular vacuum state, including a regular generalization of the Boulware vacuum. Issues such us Hawking radiation crucially depend on this vacuum choice.