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

Journal Article · Mon Jan 15 04:00:00 EST 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2017.11.010· OSTI ID:22848277

Bemani, F. ^[1]; Naderi, M. H. ^[1]

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1. Department of Physics, Faculty of Science, University of Isfahan, Hezar Jerib, 81746-73441, Isfahan (Iran, Islamic Republic of)

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 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.

• OSTI ID: 22848277
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 388; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
COMPUTERIZED SIMULATION
FLUCTUATIONS
HAMILTONIANS
HUBBARD MODEL
HYDRODYNAMICS
KLEIN-GORDON EQUATION
PHASE TRANSFORMATIONS
QUANTUM FIELD THEORY
SCALAR FIELDS
SINGULARITY
SPACE-TIME
SUPERFLUIDITY
TRAPPING