Gaussian quantum operator representation for bosons

Abstract

We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems, and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

23 pages, 1 figure, Revised introduction and discussion

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• Hybrid phase-space simulation method for interacting Bose fields
• Positive-P phase space method simulation in superradiant emission from a cascade atomic ensemble
• Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution
• The time-reversal test for stochastic quantum dynamics
• Quantum probabilistic sampling of multipartite 60-qubit Bell inequality violations
• Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
• Probabilistic Q-function distributions in fermionic phase-space
• Quantum correlations in dipolar droplets: Time-dependent Hartree-Fock-Bogoliubov theory
• Quantum dynamics in ultra-cold atomic physics
• Time evolution with symmetric stochastic action
• A comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates
• Monte Carlo techniques for real-time quantum dynamics
• Linear entropy in quantum phase space
• Solving quantum trajectories for systems with linear Heisenberg-picture dynamics and Gaussian measurement noise
• Grassmann Variables and the Jaynes-Cummings Model
• Two-Mode Theory of BEC Interferometry
• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• Quantum dynamics of long-range interacting systems using the positive-P and gauge-P representations
• First-principles quantum dynamics for fermions: Application to molecular dissociation
• Grassmann Phase Space Methods for Fermions. II. Field Theory
• Initial states and apodisation for quantum field simulations in phase-space
• Quantum dynamics in phase space: From coherent states to the Gaussian representation
• Quantum many-body simulations using Gaussian phase-space representations
• Decoherence effects in Bose-Einstein condensate interferometry. I General Theory
• Quantum phase-space simulations of fermions and bosons
• Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
• Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Ultra-cold fermions in optical lattices
• Matrix phase-space representations for gaussian boson sampling
• Theory of light-matter interactions in cascade and diamond type atomic ensembles