We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physics of fermionized bosons in disordered one-dimensional chains; (ii) for weak interactions, we investigate the role of on-site inhomogeneities on a first-order dissipative phase transition in a two-dimensional square lattice.We propose an efficient numerical method to compute configuration averages of observables in disordered open quantum systems whose dynamics can be unraveled via stochastic trajectories. We prove that the optimal sampling of trajectories and disorder configurations is simply achieved by considering one random disorder configuration for each individual trajectory. As a first application, we exploit the present method to study the role of disorder on the physics of the driven-dissipative Bose-Hubbard model in two different regimes: (i) for strong interactions, we explore the dissipative physics of fermionized bosons in disordered one-dimensional chains; (ii) for weak interactions, we investigate the role of on-site inhomogeneities on a first-order dissipative phase transition in a two-dimensional square lattice.

arXiv:1812.08582Physical Review AMar 14, 201921 citations

Stochastic Processes in Quantum Optics

B. Shore

Jan 1, 19860 citations

Driven-dissipative quantum Monte Carlo method for open quantum systems

Alexandra Nagy, Vincenzo Savona

We develop a real-time full configuration-interaction quantum Monte Carlo approach to model driven-dissipative open quantum systems with Markovian system-bath coupling. The method enables stochastic sampling of the Liouville--von Neumann time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the nonequilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional $XYZ$ spin- $\frac{1}{2}$ model on a lattice.We develop a real-time full configuration-interaction quantum Monte Carlo approach to model driven-dissipative open quantum systems with Markovian system-bath coupling. The method enables stochastic sampling of the Liouville--von Neumann time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the nonequilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional $XYZ$ spin-$\frac{1}{2}$ model on a lattice.

arXiv:1802.05931Physical Review AMay 30, 201842 citations

Stochastic Simulations of Dissipation in Quantum Optics: Quantum Superpositions

B. M. Garraway, P. L. Knight

Springer eBooksJan 1, 19950 citations

Optical and atomic stochastic resonances in the driven dissipative Jaynes-Cummings model

Qingyang Qiu, Shengdan Tao, Cunjin Liu +3 more

In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.

arXiv:1708.01345Physical Review ADec 6, 20175 citations

Applications of Quantum Stochastic Processes in Quantum Optics

Lue Bouten

Lecture notes in mathematicsOct 15, 20082 citations

XYZ

spin-

\frac{1}{2}

model on a lattice.