Nonlinear dynamics of the cold atom analog false vacuum

Abstract

We investigate the nonlinear dynamics of cold atom systems that can in principle 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 condensate (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 equations (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 corrections 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.

Simulating cosmological supercooling with a cold-atom system

“…This case is similar to some of the examples in Ref. [18], where there was an effective cutoff from the size of the spatial grid used in the numerical simulations. We therefore have agreement between the two sets of results for this case.…”

“…However, Refs. [11,18] showed that the false vacuum state in this scheme can suffer from a parametric instability caused by the time-modulation of the system. The instability causes decay of the false vacuum state by a different mechanism than a first-order phase transition.…”

Phonon redshift and Hubble friction in an expanding BEC

“…The analogy extends to the level of quantum field theory if the fluid is a coherent quantum system, like a Bose-Einstein condensate (BEC) near zero temperature. This opens the possibility of studying, in a laboratory setting, phenomena closely related to those of quantum field theory in curved spacetime, such as particle creation in an expanding universe and Hawking radiation from a black hole [1], the Unruh effect [2], and false vacuum decay [3].…”

“…in its "vacuum". Many proposals for simulating cosmological quantum field theory have been put forth as well [3,[8][9][10][11][12][13][14][15]. Experiments have not yet fully realized the analogy, but related phenomena have been observed.…”

Occurrence of semiclassical vacuum decay

“…Although the instanton approach borrows the wisdom of classically forbidden quantum penetration under the barrier, the physical picture behind the vacuum decay in field theory resembles the bubble nucleation in statistical physics [3,4] with quantum fluctuations replaced by thermodynamic fluctuations. Indeed, there is a cold atom analog of vacuum decay in field theory from experimental [5,6], theoretical [7], and simulational [8,9] perspectives. This inspires the request for vacuum decay in field theory via classically allowed channel, which is recently realized in lattice simulation [10] and formulated in real-time formalism [11].…”