A model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation, derived from a density operator equation such as the Bloch equation, and consistent with it. The advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described. The method is applied to the nonlinear absorber, cascades of quantum transitions, second-harmonic generation and a measurement reduction process. The model provides graphic illustrations of these processes, with statistical fluctuations that mimic those of experiments. The stochastic differential equations originated from studies of the measurement problem in the foundations of quantum mechanics. The model is compared with the quantum-jump model of Dalibard (1992), Carmichael and others, which originated among experimenters looking for intuitive pictures and rules of computation.

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The quantum-state diffusion model applied to open systems

In theory, the decay of any unstable quantum state can be inhibited by sufficiently frequent measurements--the quantum Zeno effect. Although this prediction has been tested only for transitions between two coupled, essentially stable states, the quantum Zeno effect is thought to be a general feature of quantum mechanics, applicable to radioactive or radiative decay processes. This generality arises from the assumption that, in principle, successive observations can be made at time intervals too short for the system to change appreciably. Here we show not only that the quantum Zeno effect is fundamentally unattainable in radiative or radioactive decay (because the required measurement rates would cause the system to disintegrate), but also that these processes may be accelerated by frequent measurements. We find that the modification of the decay process is determined by the energy spread incurred by the measurements (as a result of the time-energy uncertainty relation), and the distribution of states to which the decaying state is coupled. Whereas the inhibitory quantum Zeno effect may be feasible in a limited class of systems, the opposite effect--accelerated decay--appears to be much more ubiquitous.

Acceleration of quantum decay processes by frequent observations

https://www.tmd.ac.jp/artsci/physics/ikuzak/2005PhysRep.pdf

Quantum Zeno effect by general measurements

We review the principles and some recent advances in the theory of coherent control of molecular processes and discuss some of its experimental realizations. Amongst the topics discussed are: bichromatic and pump-dump control; the interference between N-photons and M-photon processes; the optical conversion of a mixture of left- and right-handed chiral molecules into an ensemble containing molecules of the handedness of choice; control of collisional processes; control over chaotic dynamics; effects of decoherence; the solution of the non-degenerate quantum control problem; and control over spontaneous emission and other decay processes.

https://iopscience.iop.org/article/10.1088/0034-4885/66/6/201/pdf

Coherent control of molecular dynamics

A Conceptual Analysis of Quantum Zeno; Paradox, Measurement, and Experiment

The change of dynamics in a quantum system under frequent or continuous observation, known as the quantum Zeno effect, is generally derived from the projection or reduction of the wave-packet hypothesis that is the central postulate in the theory of quantum measurements The only experiment in which the Zeno effect has yet been clearly demonstrated, though, allows no conclusion on the necessity or validity of the projection postulate This is shown by calculating, in detail, the outcome of the experiment on the basis of the standard three-level Bloch equations These equations follow from the quantum theory of irreversible processes with no additional assumptions necessary, such as which part of the system serves as measuring apparatus or how efficient the measurement would be

Vera Frerichs

Papers

Quantum Zeno effect without collapse of the wave packet