How to design quantum-jump trajectories via distinct master equation representations

Abstract

Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing on quantum-jump unravelings, we demonstrate that there exists inherent freedom in how to assign the terms of the underlying master equation to the deterministic and jump parts of the stochastic description, which leads to a number of qualitatively different unravelings. As relevant examples, we show that a fixed basis of post-jump states can be selected under some definite conditions, or that the deterministic evolution can be set by a chosen time-independent non-Hermitian Hamiltonian, even in the presence of external driving. Our approach relies on the definition of rate operators, whose positivity equips each unraveling with a continuous-measurement scheme and is related to a long known but so far not widely used property to classify quantum dynamics, known as dissipativity. Starting from formal mathematical concepts, our results allow us to get fundamental insights into open quantum system dynamics and to enrich their numerical simulations.

v3: 15+5 pages, closer to the published version; v2:12+5 pages, 4 figures, 1 table -- major changes with respect to v1, with two main new results in Secs.3.2 and 5.2 and a new title; v1: 5+7 pages, 1+1 figures, 1 table

References in corpus (17)

• Non-Hermitian Physics
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum trajectories and open many-body quantum systems
• Real-time optimal quantum control of mechanical motion at room temperature
• Observation of quantum jumps in a superconducting artificial atom
• Non-Markovian quantum jumps
• On measures of non-Markovianity: divisibility vs. backflow of information
• Dynamics of simultaneously measured non-commuting observables
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Open system dynamics with non-Markovian quantum jumps
• Pure-state quantum trajectories for general non-Markovian systems do not exist
• Stochastic pure state representation for open quantum systems
• Non-Hermitian physics and master equations
• Non-Markovian continuous quantum measurement of retarded observables
• Incoherent qubit control using the quantum Zeno effect
• Rate operator unravelling for open quantum system dynamics
• Orthogonal jumps of wavefunction in white-noise potentials

Cited by in corpus (4)

• Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
• Generalized Rate Operator Quantum Jumps via Realization-Dependent Transformations
• Dynamics of Open Quantum Systems with Initial System-Environment Correlations via Stochastic Unravelings
• Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics