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arXiv:1712.02356 · Journal of High Energy Physics

Towards the cold atom analog false vacuum

Jonathan Braden, Matthew C. Johnson, Hiranya V. Peiris, Silke Weinfurtner

Published Jul 1, 2018• 46 citations
arXivHTMLPDF

Abstract

A bstract Analog condensed matter systems present an exciting opportunity to simulate early Universe models in table-top experiments. We consider a recent proposal for an analog condensed matter experiment to simulate the relativistic quantum decay of the false vacuum. In the proposed experiment, two ultra-cold condensates are coupled via a time-varying radio-frequency field. The relative phase of the two condensates in this system is approximately described by a relativistic scalar field with a potential possessing a series of false and true vacuum local minima. If the system is set up in a false vacuum, it would then decay to a true vacuum via quantum mechanical tunnelling. Should such an experiment be realized, it would be possible to answer a number of open questions regarding non-perturbative phenomena in quantum field theory and early Universe cosmology. In this paper, we illustrate a possible obstruction: the time-varying coupling that is invoked to create a false vacuum for the long-wavelength modes of the condensate leads to a destabilization of shorter wavelength modes within the system via parametric resonance. We focus on an idealized setup in which the two condensates have identical properties and identical background densities. Describing the system by the coupled Gross-Pitaevskii equations (GPE), we use the machinery of Floquet theory to perform a linear stability analysis, calculating the wavenumber associated with the first instability band for a variety of experimental parameters. However, we demonstrate that, by tuning the frequency of the time-varying coupling, it may be possible to push the first instability band outside the validity of the GPE, where dissipative effects are expected to damp any instabilities. This provides a viable range of experimental parameters to perform analog experiments of false vacuum decay.

DOI
10.1007/jhep07(2018)014

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Abstract We investigate the nonlinear dynamics of cold atom systems that can in princi- ple serve as quantum simulators of false vacuum decay. The analog false vacuum manifests as a metastable vacuum state for the relative phase in a two-species Bose-Einstein con- densate (BEC), induced by a driven periodic coupling between the two species. In the appropriate low energy limit, the evolution of the relative phase is approximately governed by a relativistic wave equation exhibiting true and false vacuum configurations. In previous work, a linear stability analysis identified exponentially growing short-wavelength modes driven by the time-dependent coupling. These modes threaten to destabilize the analog false vacuum. Here, we employ numerical simulations of the coupled Gross-Pitaevski equa- tions (GPEs) to determine the non-linear evolution of these linearly unstable modes. We find that unless a physical mechanism modifies the GPE on short length scales, the analog false vacuum is indeed destabilized. We briefly discuss various physically expected correc- tions to the GPEs that may act to remove the exponentially unstable modes. To investigate the resulting dynamics in cases where such a removal mechanism exists, we implement a hard UV cutoff that excludes the unstable modes as a simple model for these corrections. We use this to study the range of phenomena arising from such a system. In particular, we show that by modulating the strength of the time-dependent coupling, it is possible to observe the crossover between a second and first order phase transition out of the false vacuum.
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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.
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+12+12+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, φφφ, 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 φφφ rapidly winds by 2π2π2π. Our work opens possibilities for studies of cosmologically relevant phenomena including preheating, dynamics of topological defects, and relativistic false-vacuum decay.
Ultracold atomic gases can undergo phase transitions that mimic relativistic vacuum decay, allowing us to empirically test early Universe physics in tabletop experiments. We investigate the physics of these analog systems, going beyond previous analyses of the classical equations of motion to study quantum fluctuations in the cold-atom false vacuum. We show that the fluctuation spectrum of this vacuum state agrees with the usual relativistic result in the regime where the classical analogy holds, providing further evidence for the suitability of these systems for studying vacuum decay. Using a suite of semiclassical lattice simulations, we simulate bubble nucleation from this analog vacuum state in a 1D homonuclear potassium-41 mixture, finding qualitative agreement with instanton predictions. We identify realistic parameters for this system that will allow us to study vacuum decay with current experimental capabilities, including a prescription for efficiently scanning over decay rates, and show that this setup will probe the (rather than thermal) decay regime at temperatures T≲10 nK . Our results help lay the groundwork for using upcoming cold-atom experiments as a new probe of nonperturbative early Universe physics. Published by the American Physical Society 2024