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arXiv:quant-ph/0212104 · Physics Letters A

Quantum dissipative systems from theory of continuous measurements

Michael B. Mensky, Stig Stenholm

Published Feb 17, 2003• 15 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(03)00057-4

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The theory of dissipative quantum systems and its relation to the quantum theory of continuous measurements are reviewed. Constructing a correct theory of a dissipative quantum system requires that the system's interaction with its environment (reservoir) be taken into account. Since information about the system is 'recorded' in the state of the reservoir, the quantum theory of continuous measurements can be used to account for the influence of the reservoir. If based on the use of restricted path integrals, this theory does not require an explicit reservoir model and is therefore much simpler technically.
Decoherence aiid dissipation of a quantum system occurs due to its entanglement with the environment (reservoir) . In the course of interaction of the system with the reservoir information about the system is 'recorded' in the state of the reservoir. This is why influence of the reservoir on the system (i.e. the system's decoherence and dissipation) may be accounted in the framework of quantum theory of continuous measurements. Constructing such a theory with the help of restricted path integrals (RPI) gives a model-independent theory of decoherence and dissipation. The special role of information in decoherence and dissipation is explicitly revealed by this approach. This makes it possible to apply the RPI approach for the analysis of decoherence in quantum informatic devices.
Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while leaving the ensemble-averaged steady state strictly invariant. We identify measurement-invariant steady states whose unconditional density matrix remains unchanged under continuous monitoring, despite pronounced measurement-induced localization in conditioned quantum trajectories. This separation between trajectory-level collapse and ensemble invariance defines a regime of partial collapse, in which measurement-induced localization is continuously counteracted by dissipative dynamics. We derive a necessary and sufficient condition for steady-state invariance under continuous measurement and identify Liouvillian symmetry as a concrete dynamical mechanism enforcing it. Our results clarify the distinction between conditional collapse and physical disturbance in open quantum systems and provide a framework for non-invasive continuous monitoring in driven-dissipative settings.
The restricted-path-integral (RPI) theory of continuous quantum measurements including the evolution of the measured systems and phenomenon of decoherence is reviewed. The measured system is considered as an open quantum system but without usage of any model of the measurement (of the measuring medium or the system's environment). The propagator of a measured system (conditioned by the measurement readout) is presented by RPI. In the important special case of monitoring an observable the propagator and the system's wave function satisfy Schroedinger equation with a complex Hamiltonian (depending on the measurement readout). Going over to the non-selective description of the measurement leads to the Lindblad master equation. In case of non-minimally disturbing measurements this gives theory of dissipative systems avoiding difficulties of other approaches. The whole theory is deduced from first principles of quantum mechanics. This proves that quantum mechanics includes theory of measurements and is therefore conceptually closed.