A procedure is described whereby a linearly coupled spinor Bose condensate can be used as a physically accessible quantum simulator of the early universe. In particular, an experiment to generate an analog of an unstable vacuum in a relativistic scalar field theory is proposed. This is related to quantum theories of the inflationary phase of the early universe. There is an unstable vacuum sector whose dynamics correspond to the quantum sine‐Gordon equations in one, two or three space dimensions. Numerical simulations of the expected behavior are reported using a truncated Wigner phase‐space method, giving evidence for the dynamical formation of complex spatial clusters. Preliminary results showing the dependence on coupling strength, condensate size and dimensionality are obtained.
A procedure is described whereby a linearly coupled spinor Bose condensate can be used as a physically accessible quantum simulator of the early universe. In particular, an experiment to generate an analog of an unstable vacuum in a relativistic scalar field theory is proposed. This is related to quantum theories of the inflationary phase of the early universe. There is an unstable vacuum sector whose dynamics correspond to the quantum sine‐Gordon equations in one, two or three space dimensions. Numerical simulations of the expected behavior are reported using a truncated Wigner phase‐space method, giving evidence for the dynamical formation of complex spatial clusters. Preliminary results showing the dependence on coupling strength, condensate size and dimensionality are obtained.
Cosmic inflation is the theory that the universe underwent a violent, rapid expansion at the beginning of time, giving rise to much of the observed structure in the universe 1. This theory is supported by indirect observational evidence from many different sources (e.g. see 2). However, direct experimental investigation of inflation is of course impossible. For this reason there has been considerable interest in analog models for astrophysics (e.g. see 3), in which analogous behavior is studied in systems that are experimentally convenient. Due to their cleanness and great flexibility, dilute ultra-cold atomic gases (particularly Bose-Einstein condensates) form an attractive system for realizing such analog models. Indeed, a number of such table-top-astrophysics experiments have been conducted with Bose-Einstein condensates. For example, supernova-like collapse and explosion dynamics 4, controlled by modifying inter-atomic interactions using Feshbach resonances, and later interpreted as cosmological particle creation 5; Faster-than-sound flow of a condensate has been used to produce a sonic black hole analog 6; The in situ measurements of density fluctuations in a quenched quasi-two-dimensional condensate have demonstrated Sakharov like oscillations, analogous to the process thought to give rise to the anisotropy in the cosmic microwave background radiation 7. In Quantum simulations of the early universe Opanchuk and collaborators 8 propose using a two component condensate to simulate the inflationary phase of the early universe (see Fig. 1). In appropriate limits the relative phase between the two fields describing the condensate components is known to obey the sine-Gordon equation 9. The sine-Gordon model (SGM) is one of many scalar models for inflation that have been investigated in cosmology. It is thought to provide an acceptable model of the beginning of inflation where, starting from an unstable vacuum state, quantum fluctuations seed the cosmological inhomogeneities that lead to structure formation. However, the SGM likely fails to describe the end of inflation as its scalar potential does not generate efficient parametric resonances needed to ensure reheating of the universe 10, 11. The SGM also has applications in cosmology beyond inflation, and is a model for the “axion” matter field considered as a promising candidate for dark matter12. An important innovation in the scheme proposed by Opanchuk et al. is the introduction of a microwave (linear) coupling between the components that provides a practical way to initialize the system into an unstable vacuum state and controllably explore the subsequent evolution. Approximate numerical simulations, performed using the truncated Wigner approach, verify dynamical clustering can occur within experimentally realistic parameter regimes. The main challenge to realizing the proposed scenario will be finding an atom, and a pair of internal states, with suitable interaction parameters. It is likely that such an atom will be available given the increasing diversity of atomic species that have been Bose-condensed, and the great control over interactions afforded by Feshbach resonances. Aided by the rich toolbox of techniques available to ultra-cold atomic physics an array of opportunities present themselves for developing this line of research, such as: Engineering gravitational-like effects through including long range interactions, e.g. through electromagnetically induced gravity 13; Enhancing quantum fluctuations through stronger interactions or by confining the system in an optical lattice; Engineering richer models by including more spin states and other species of atoms.
We consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent to the spatial expansion of a one-dimensional toy-Universe, with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss how to observe the 'freezing' of quantum fluctuations during an accelerating expansion in a possible experiment. We also analyze an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field, seeded by quantum fluctuations.
Abstract 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 (Fialko O et al 2015 Europhys. Lett. 110 56001 ) 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 μ m size.
Despite being at the heart of the theory of the "Big Bang" and cosmic inflation, the quantum-field-theory prediction of false vacuum tunneling has not been tested.To address the exponential complexity of the problem, a table-top quantum simulator in the form of an engineered Bose-Einstein condensate (BEC) has been proposed to give dynamical solutions of the quantum-field equations.In this paper, we give a numerical feasibility study of the BEC quantum simulator under realistic conditions and temperatures, with an approximate truncated Wigner phase-space method.We report the observation of false vacuum tunneling in these simulations, and the formation of multiple bubble "universes" with distinct topological properties.The tunneling gives a transition of the relative phase of coupled Bose fields from a metastable to a stable "vacuum."We include finite-temperature effects that would be found in a laboratory experiment and also analyze the cutoff dependence of modulational instabilities in Floquet space.Our numerical phase-space model does not use thin-wall approximations, which are inapplicable to cosmologically interesting models.It is expected to give the correct quantum treatment, including superpositions and entanglement during dynamics.By analyzing a nonlocal observable called the topological phase entropy (TPE), our simulations provide information about phase structure in the true vacuum.We observe a cooperative effect in which true vacua bubbles representing distinct universes each have one or the other of two distinct topologies.The TPE initially increases with time, reaching a peak as multiple universes are formed, and then decreases with time to the phase-ordered vacuum state.This gives a model for the formation of universes with one of two distinct phases, which is a possible solution to the problem of particle-antiparticle asymmetry.
Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often challenging, particularly in more than one spatial dimension. Analog simulation using tunable synthetic quantum systems can both verify existing theoretical predictions and lead to new physical insights. Here, we realize analog simulation of massive relativistic quantum fields in 2+1 dimensions (two spatial dimensions and time), using two coherently coupled spin components in a uniform two-dimensional atomic Bose--Einstein condensate. Specifically, we encode the paradigmatic sine-Gordon model in the long-wavelength modes of the field describing the relative phase, φ, of the two components. In the perturbative regime, collective field excitations exhibit a relativistic dispersion with a tunable mass gap. We also observe explicitly non-perturbative phenomena, including the existence of topological domain walls across which φ rapidly winds by 2π. Our work opens possibilities for studies of cosmologically relevant phenomena including preheating, dynamics of topological defects, and relativistic false-vacuum decay.
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 radio-frequency coupling of the spin components. Numerical simulations demonstrate the spontaneous formation of true vacuum bubbles with realistic parameters and time-scales.