Simulating seeded vacuum decay in a cold atom system

Open Access

Simulating seeded vacuum decay in a cold atom system

Thomas P. Billam, Ruth Gregory, Florent Michel, and Ian G. Moss

Phys. Rev. D 100, 065016 – Published 23 September 2019

Abstract

We propose to test the concept of seeded vacuum decay in cosmology using a Bose-Einstein condensate system. The role of the nucleation seed is played by a vortex within the condensate. We present two complementary theoretical analyses that demonstrate seeded decay is the dominant decay mechanism of the false vacuum. First, we adapt the standard instanton methods to the Gross-Pitaevskii equation. Second, we use the truncated Wigner method to study vacuum decay.

Received 30 November 2018
Revised 12 April 2019

DOI:https://doi.org/10.1103/PhysRevD.100.065016

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Instantons Particle astrophysics Vacuum stability

Bose-Einstein condensates

Gravitation, Cosmology & AstrophysicsAtomic, Molecular & OpticalGeneral PhysicsParticles & Fields

Authors & Affiliations

Thomas P. Billam^1,*, Ruth Gregory^2,3,†, Florent Michel^2,‡, and Ian G. Moss^4,§

¹Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
²Centre for Particle Theory, Durham University, South Road, Durham DH1 3LE, United Kingdom
³Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
⁴School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom

^*thomas.billam@ncl.ac.uk
^†r.a.w.gregory@durham.ac.uk
^‡florent.c.michel@durham.ac.uk
^§ian.moss@ncl.ac.uk

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Issue

Vol. 100, Iss. 6 — 15 September 2019

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Images

Figure 1
The field potential $V$ plotted as a function of the relative phase of the two atomic wave functions, $φ$ . The false vacuum is the minimum at $φ = π$ and the true vacuum the global minimum at $φ = 0$ . $Δ V$ is the difference in vacuum energy.
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Figure 2
Vortex density profile $\hat{ρ} = ρ / ρ_{m}$ plotted as a function of radius $r$ . The density vanishes at the center and approaches the false vacuum density as $r \to \infty$ . Its physical thickness scales as $ε R_{0}$ .
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Figure 3
The dimensionless exponent $\hat{S}$ of the vacuum decay rate plotted as a function of the parameter $ε^{2}$ . The solid lines represent unseeded vacuum decay and the dashed lines are for bubbles seeded by vortices. The action is lower for the seeded bubbles.
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Figure 4
Typical examples of the decay of the false vacuum with and without imprinted vortices in a two-dimensional periodic system. The plots show the cosine of the relative phase between the two spin states. Dimensionless parameters are $λ = 1.15$ , $ε = 0.316$ , $ρ_{m} R_{0}^{2} = 60.0$ , and $L = 42.67 R_{0}$ . Our numerical grid has $P = 128$ . (a) Initially, the false vacuum predominates. (b) As time progresses, bubbles of true vacuum (yellow) nucleate, predominantly around the vortices. (c) Later still, nucleated bubbles expand to fill the system. (d–f) Typical trajectories without imprinted vortices [same times as (a–c)] illustrate the nucleation of bubbles at random locations, which occurs at a slower rate than vortex-seeded nucleation.
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Figure 5
Fraction of trajectories failing to nucleate a bubble of true vacuum by a given time, $F (t)$ , both with and without vortices (dashed and solid lines respectively). The straight grey lines show exponential decays, fitted over selected regions.
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Figure 6
Examples of the decay of the false vacuum with and without an imprinted vortex in a two-dimensional “bucket” trap. The plots show the cosine of the relative phase between the two spin states. Dimensionless parameters are $λ = 1.15$ , $ε = 0.316$ , $ρ_{m} R_{0}^{2} = 32.0$ , and $L = 170.68 R_{0}$ . Our numerical grid has $P = 512$ . The BEC is contained inside a circular bucket trap, ${\hat{V}}_{T} (r) = {\hat{V}}_{0} {1 + \tanh [(r - R) / w]} / 2$ , parametrized by strength ${\hat{V}}_{0} = 100$ , radius $R = 64 R_{0}$ and wall steepness $w = 2 R_{0}$ . (a) Initially, the false vacuum predominates within the circular trap, but bubbles of true vacuum rapidly form around the walls of the trap. (b) Later, a bubble of true vacuum (yellow) forms around the vortex in the center. (c) Later still, the true vacuum regions grow, and eventually merge. (d–f) Typical trajectory without an initially imprinted vortex [same times as (a–c)].
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