Theoretical Investigations of Early Universe Simulators

Abstract

The very early universe remains a mystery, with the nature of phase transitions such as inflation and electroweak symmetry breaking still uncertain. Whilst we cannot probe the early universe itself, we may simulate it, using laboratory analogues, such as ultracold gases. Here, we explore the possibility of first-order transitions, and carry out theoretical investigations to determine the strengths and experimental viability of a range of candidate cold-atom models. We begin by considering a one-dimensional, two-component, finite-temperature Bose gas. We perform simulations using the stochastic projected Gross-Pitaevskii equation (SPGPE) and verify the validity of this approach, by demonstrating that thermal fluctuations in the relative phase are characteristic of a relativistic thermal system. We go on to simulate vacuum-decay in this system and find agreement between the resultant rates of vacuum decay and those predicted by instanton theory. In line with experimental protocol, we go on to incorporate time-dependent interactions into this system. This is known to give rise to parametric instabilities. We use analytical methods to locate the resultant resonance bands and determine the dependence of their amplitude on damping rate. Subsequently, we demonstrate that the resonances may be supressed by raising the damping rate. However, we find the required rate to be unrealistically high, casting doubt on the viability of this model. We move on to consider a three-component system, free from resonant instabilities, whereby components interact via radio frequency and Raman couplings. Within the elaborate phase structure of the system, we identify an effective Klein-Gordon field. Initially, we examine a one-dimensional, zero-temperature system and use Gross-Pitaevskii simulations within the truncated Wigner approximation to model vacuum-decay. We investigate the dependence of the rate of vacuum decay on particle density and find reasonable agreement with instanton methods. Next, we extend our three-component investigations to a two-dimensional, finite-temperature gas, and return to SPGPE simulations. This improves the agreement between numerical and theoretical decay rates. Finally, we introduce an optical box trap and find that the trap walls seed vacuum decay.