Quantum simulation of discrete curved spacetime by the Bose-Hubbard model: from analog acoustic black hole to quantum phase transition

TL;DR

This paper proposes a theoretical method to simulate quantum fields in discrete curved spacetime using the Bose-Hubbard model, enabling analog black hole creation and quantum phase transition studies in optical lattices.

Contribution

It introduces a hydrodynamic framework for the Bose-Hubbard model and demonstrates how phase fluctuations obey the Klein-Gordon equation in a discrete curved spacetime, including black hole analogs.

Findings

Phase fluctuations follow the Klein-Gordon equation in the model.

Effective metrics reveal a singularity in the superfluid phase, modeling an acoustic black hole.

The approach allows tuning system parameters to simulate various spacetime geometries.

Abstract

We present a theoretical scheme to simulate quantum field theory in a discrete curved spacetime based on the Bose-Hubbard model describing a Bose-Einstein condensate trapped inside an optical lattice. Using the Bose-Hubbard Hamiltonian, we first introduce a hydrodynamic presentation of the system evolution in discrete space. We then show that the phase (density) fluctuations of the trapped bosons inside an optical lattice in the superfluid (Mott insulator) state obey the Klein-Gordon equation for a massless scalar field propagating in a discrete curved spacetime. We derive the effective metrics associated with the superfluid and Mott-insulator phases and, in particular, we find that in the superfluid phase the metric exhibits a singularity which can be considered as a the manifestation of an analog acoustic black hole. The proposed approach is found to provide a suitable platform for quantum simulation of various spacetime metrics through adjusting the system parameters.