We present a theoretical and numerical analysis of a quantum system that is capable of functioning as a heat engine. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath.

Quantum decay of a relativistic scalar field from a false vacuum is a fundamental idea in quantum field theory. It is relevant to models of the early Universe, where the nucleation of bubbles gives rise to an inflationary universe and the creation of matter. Here we propose a laboratory test using an experimental model of an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated radiofrequency coupling of the spin components. Numerical simulations demonstrate the spontaneous formation of true vacuum bubbles with realistic parameters and time-scales.As proposed by Coleman in a seminal paper [1], the false vacuum is a metastable state of the relativistic scalar field that can decay by quantum tunneling, locally forming bubbles of true vacuum that expand at the speed of light. It has a close analogy with the ubiquitous phenomenon of bubble nucleation during a first order phase transition in condensed matter [2], e.g. the spontaneous creation of vapor bubbles in superheated water [3]. Applied to a quantum field such as the inflaton or Higgs field, bubble nucleation is an event of cosmological significance in some early universe models. Indeed, the Coleman decay scenario of the inflaton field features prominently in the theory of eternal inflation [4,5], where bubbles continuously nucleating from a false vacuum grow into separate universes, each subsequently undergoing exponential growth of space [6]. This scenario, which could potentially explain the value of the cosmological constant by the anthropic principle, is currently being tested against observational evidence in astrophysical experiments [7,8]. For an observer inside the bubble, the tunneling event -occurring in the observer's past -appears like a cosmological "big-bang", prior to inflation.From a theoretical point of view, quantum tunneling from a false vacuum is a problem that can only be solved approximately [1,9] (except for simplified models [10]) due to the exponential complexity of quantum field dynamics. This motivates the search for an analog quantum system that is accessible to experimental scrutiny, to test these models. The utility of such experiments, which complement astrophysical investigations, is that they would provide data that allow verification of widely used approximations inherent in current theories [11].Here we demonstrate how to use an ultra-cold atomic two-component Bose-Einstein condensate (BEC) as a quantum simulator that generates a decaying, relativistic false vacuum. Quantum field dynamics occurs for the relative phase of two spin components that are linearly coupled by a radio-frequency field. In this proposal the speed of sound in the condensate models the speed of light, and the "universe" is less than a millimeter across. Domains of true vacuum are observable using interferometric techniques [12] over millisecond time-scales with realistic parameters.Modulating the radio-frequency coupling in time allows one to cr...

The quantum decay of a relativistic scalar field from a metastable state ("false vacuum decay") is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal [EPL 110, 56001 (2015)] for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component 7 Li or 41 K bosonic condensates in one-dimensional traps of ∼ 100 µm size. arXiv:1607.01460v4 [cond-mat.quant-gas]

Atomic Bose-Einstein condensates confined to a dual-ring trap support Josephson vortices as topologically stable defects in the relative phase. We propose a test of the scaling laws for defect formation by quenching a Bose gas to degeneracy in this geometry. Stochastic Gross-Pitaevskii simulations reveal a -1/4 power-law scaling of defect number with quench time for fast quenches, consistent with the Kibble-Zurek mechanism. Slow quenches show stronger quench-time dependence that is explained by the stability properties of Josephson vortices, revealing the boundary of the Kibble-Zurek regime. Interference of the two atomic fields enables clear long-time measurement of stable defects and a direct test of the Kibble-Zurek mechanism in Bose-Einstein condensation.

Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark-soliton excitations that show periodic density dynamics in real space. In addition to the density feature, the solitons also carry a localized pseudospin magnetization that exhibits a rich and tunable dynamics. Analytical results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.

Key words optical lattice, quantum phase transition, Mott insulator, functional integrals PACS 05.30. Jp,03.75.Hh,03.75.Lm Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the GrossPitaevskii equation to the dense regime by introducing renormalized parameters in the latter.

Finite topological quantum systems can undergo continuous metastable quantum phase transitions to change their topological nature. Here we show how to nucleate the transition between ring currents and dark soliton states in a toroidally trapped Bose-Einstein condensate. An adiabatic passage to wind and unwind its phase is achieved by explicit global breaking of the rotational symmetry. This could be realized with current experimental technology.

We study soliton collisions and the decay of solitons into sound in superfluid Fermi gases across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover by performing numerical simulations of the time-dependent Bogoliubov-de Gennes equations. This decay process occurs when the solitons are accelerated to the bulk pair-breaking speed by an external potential. A similar decay process may occur when solitons are accelerated by an inelastic collision with another soliton. We find that soliton collisions become increasingly inelastic as we move from the BEC to the BCS regime, and the excess energy is converted into sound. We interpret this effect as being due to the evolution of Andreev bound states localized within the soliton.