Quantum Simulation of Inflationary Cosmology: Probing Analogue Trans-Planckian Spectra in Dipolar Bose-Einstein Condensates

Abstract

This study concerns the emergence of effective curved spacetime in the quasi two dimensional dipolar Bose-Einstein condensates, in which Bogoliubov quasiparticle excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential.<br/> <br/> The study can generally be divided into two parts. Firstly, an analogue de Sitter cosmos in an expanding dipolar condensate is considered.<br/> It is demonstrated that a hallmark signature of inflationary cosmology, the scale invariance of the power spectrum (SIPS) of inflaton field correlations, experiences strong modifications when, at the initial stage of expansion, the excitation spectrum displays roton minimum.<br/> This exemplifies that dipolar quantum gases furnish a viable laboratory tool to experimentally investigate, with well-defined and controllable initial conditions, whether excitation spectra deviating from Lorentz invariance at trans-Planckian momenta violate standard predictions of inflationary cosmology.<br/> <br/> Secondly, it is investigated whether a rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect (DCE), which can be characterized by measuring the density-density correlation function.<br/> It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of quasiparticle pairs with opposite momenta, resulting from the quench, displays an enhanced potential for the presence of entanglement, when compared to a gas with repulsive contact interactions only.<br/> Entangled quasiparticle pairs contain momenta close to the roton, and hence the quantum correlation significantly increases in the presence of deep roton minimum.