Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks

Abstract

The quantum dynamics of open many-body systems poses a challenge for computational approaches. Here we develop a stochastic scheme based on the positive P phase-space representation to study the nonequilibrium dynamics of coupled spin-boson networks that are driven and dissipative. Such problems are at the forefront of experimental research in cavity and solid state realizations of quantum optics, as well as cold atom physics, trapped ions and superconducting circuits. We demonstrate and test our method on a driven, dissipative two-site system, each site involving a spin coupled to a photonic mode, with photons hopping between the sites, where we find good agreement with Monte Carlo Wavefunction simulations. In addition to numerically reproducing features recently observed in an experiment [Phys. Rev. X 4, 031043 (2014)], we also predict a novel steady state quantum dynamical phase transition for an asymmetric configuration of drive and dissipation.

arXiv comment15 pages, 8 figures

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• Nonequilibrium many-body steady states via Keldysh formalism
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• Introduction to Supersymmetric Theory of Stochastics
• Fully quantum scalable description of driven dissipative lattice models
• Universal distributed quantum computing on superconducting qutrits with dark photons
• Second quantization of open quantum systems in Liouville space
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Frustrated polaritons
• Fock space localization of polaritons in the Jaynes-Cummings dimer model
• Time-Evolving Weiss Fields in the Stochastic Approach to Quantum Spins
• Conservation of Quantum Correlations in Multimode Systems with $U(1)$ Symmetry
• Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics