Quantum sine-Gordon dynamics on analogue curved spacetime in a weakly imperfect scalar Bose gas

TL;DR

This paper demonstrates how the sine-Gordon model on an analogue curved spacetime can be realized through phase fluctuations in a weakly imperfect Bose gas, revealing new ways to simulate quantum field theories in curved spacetime.

Contribution

It introduces a novel approach to simulate sine-Gordon dynamics on curved spacetime using ultracold Bose gases with controlled quantum states and bipartitions.

Findings

Effective sine-Gordon model arises from phase fluctuations in Bose gases.

Quantum control allows tuning of background spacetime geometry.

Superpositions of modes produce variable curved spacetime effects.

Abstract

Using the coherent state functional integral expression of the partition function, we show that the sine-Gordon model on an analogue curved spacetime arises as the effective quantum field theory for phase fluctuations of a weakly imperfect Bose gas on an incompressible background superfluid flow when these fluctuations are restricted to a subspace of the single-particle Hilbert space. We consider bipartitions of the single-particle Hilbert space relevant to experiments on ultracold bosonic atomic or molecular gases, including, e.g., restriction to high- or low-energy sectors of the dynamics and spatial bipartition corresponding to tunnel-coupled planar Bose gases. By assuming full unitary quantum control in the low-energy subspace of a trapped gas, we show that (1) appropriately tuning the particle number statistics of the lowest-energy mode partially decouples the low- and high-energy sectors, allowing any low-energy single-particle wave function to define a background for sine-Gordon dynamics on curved spacetime and (2) macroscopic occupation of a quantum superposition of two states of the lowest two modes produces an analogue curved spacetime depending on two background flows, with respective weights continuously dependent on the corresponding weights of the superposed quantum states.