Quantum simulation of discrete curved spacetime by the Bose-Hubbard model: from analog acoustic black hole to quantum phase transition
arXiv:1612.09094 · doi:10.1016/j.aop.2017.11.010
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.
References in corpus (14)
- Many-Body Physics with Ultracold Gases
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Quantum simulations and many-body physics with light
- Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
- Quantum Simulation with Interacting Photons
- Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates
- "Cosmological" quasiparticle production in harmonically trapped superfluid gases
- Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
- Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate
- Gravitational dynamics in Bose Einstein condensates
- Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model
- Step-like discontinuities in Bose-Einstein condensates and Hawking radiation: dispersion effects
- Analog curved spacetimes in the reversed dissipation regime of cavity optomechanics