Holographic Superfluid Solitons with Backreaction

Abstract

Solitons are important nonperturbative excitations in superfluids. For holographic superfluids, we numerically construct dark solitons that have the symmetry-restored phase at their core. A central point is that we include the gravitational back-reaction of the matter fields, which becomes important at low temperatures. We study in detail the properties of these solitons under variation of the back-reaction strength via tuning the gravitational constant. In particular, the depletion fraction of the particle number density at the core of the solitons is carefully investigated. In agreement with the probe-limit analysis, the depletion fraction shows the same qualitative behavior as in Bogoliubov-de Gennes (BdG) theory, even if the back-reaction is included. We find that the depletion decreases with increasing back-reaction strength. Moreover, the inclusion of back-reaction enables us to obtain the effective energy density of solitons within holography, which together with an evaluation of the surface tension leads to a simple physical explanation for the snake instability of dark solitons.