Continuous position measurements and the quantum Zeno effect
- 1 July 1993
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 48 (1) , 132-142
- https://doi.org/10.1103/physreva.48.132
Abstract
We present a model of continuous (in time) position measurements on a quantum system using a single pseudoclassical meter. The nonselective evolution of the system is described by a master equation which is identical to that obtained from previous models. The selective evolution is described by a stochastic nonlinear Schrödinger equation. The significance of this equation is that the stochastic term has a physical interpretaion. By carefully choosing the parameters which define the meter and the system-meter coupling, we obtain a meter pointer with well-defined position which undergoes fluctuations. This ‘‘jitter’’ in the pointer position gives rise to the stochastic dynamical collapse of the system wave function. By the inclusion of feedback on the meter, the pointer is made to relax towards an appropriate readout. We apply this model to the selective measurement of the position of a particle in a double-well potential. In contrast to a recent claim [H. Fearn and W. E. Lamb, Jr., Phys. Rev. A 46, 1199 (1992)] we show that truly continuous position measurements lead to a quantum Zeno effect in certain parameter regimes. This is manifest by the changing of the particle dynamics from coherent tunneling between the well minima to incoherent flipping, as in a random telegraph. As the measurement strength increases, the average length of time the particle remains stuck in one well increases proportionally.Keywords
This publication has 23 references indexed in Scilit:
- Localized solution of a simple nonlinear quantum Langevin equationPhysics Letters A, 1988
- Continuous quantum measurement and itô formalismPhysics Letters A, 1988
- Quantum-mechanical model for continuous position measurementsPhysical Review A, 1987
- A universal master equation for the gravitational violation of quantum mechanicsPhysics Letters A, 1987
- Gisin RespondsPhysical Review Letters, 1984
- Quantum Measurements and Stochastic ProcessesPhysical Review Letters, 1984
- Continuous measurement: Watchdog effect versus golden rulePhysical Review D, 1984
- Zeno paradox in quantum theoryAmerican Journal of Physics, 1980
- General Principles of Quantum MechanicsPublished by Springer Nature ,1980
- The Zeno’s paradox in quantum theoryJournal of Mathematical Physics, 1977