Spacetime analogue of Bose-Einstein condensates: Bogoliubov-de Gennes formulation

Abstract

We construct quantum field theory in an analogue curved spacetime in Bose-Einstein condensates based on the Bogoliubov-de Gennes equations, by exactly relating quantum particles in curved spacetime with Bogoliubov quasiparticle excitations in Bose-Einstein condensates. Here, we derive a simple formula relating the two, which can be used to calculate the particle creation spectrum by solving the time-dependent Bogoliubov-de Gennes equations. Using our formulation, we numerically investigate particle creation in an analogue expanding Universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate. We obtain its spectrum, which follows the thermal Maxwell-Boltzmann distribution, the temperature of which is experimentally attainable. Our derivation of the analogy is useful for general Bose-Einstein condensates and not limited to homogeneous ones, and our simulation is the first example of particle creations by solving the Bogoliubov-de Gennes equation in an inhomogeneous condensate.

8 pages, 6 figures

References in corpus (24)

• Analogue Gravity
• Numerical observation of Hawking radiation from acoustic black holes in atomic Bose-Einstein condensates
• Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
• Non-local density correlations as signal of Hawking radiation in BEC acoustic black holes
• Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates
• "Cosmological" quasiparticle production in harmonically trapped superfluid gases
• Hawking radiation in sonic black holes
• Analogue model of a FRW universe in Bose-Einstein condensates: Application of the classical field method
• Cosmological particle production in emergent rainbow spacetimes
• Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate
• Aspects of Cosmic Inflation in Expanding Bose-Einstein Condensates
• Superradiance from BEC vortices: a numerical study
• The Quantum de Laval Nozzle: stability and quantum dynamics of sonic horizons in a toroidally trapped Bose gas containing a superflow
• Stability analysis of sonic horizons in Bose-Einstein condensates
• Trans-Planckian physics and signature change events in Bose gas hydrodynamics
• Conditions for one-dimensional supersonic flow of quantum gases
• Analog model for an expanding universe
• Limits to the analogue Hawking temperature in a Bose-Einstein condensate
• Quasinormal Ringing for Acoustic Black Holes at Low Temperature
• Quasi-normal mode analysis in BEC acoustic black holes
• Phonon background versus analogue Hawking radiation in Bose-Einstein condensates
• Formation of a sonic horizon in isotropically expanding Bose-Einstein condensates
• Quantum fluctuations in trapped time-dependent Bose-Einstein condensates
• Zel'dovich-Starobinsky Effect in Atomic Bose-Einstein Condensates: Analogy to Kerr Black Hole

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• Bose-Einstein condensation in the Rindler space
• Bose-Einstein Condensates with Derivative and Long-Range Interactions as Set-Ups for Analog Black Holes
• Scalar Field as a Bose-Einstein Condensate?
• The two faces of quantum sound
• Particle creation in Bose--Einstein condensates: Theoretical formulation based on conserving gapless mean field theory
• Exact surface-wave spectrum of a dilute quantum liquid
• Analog cosmology with spinor BECs