Quantum Zeno effect in a double-well potential: A model of a physical measurement

Abstract

In this paper we study the quantum Zeno effect in real space due to a position measurement. The motion of a particle is decelerated or comes to a complete stop when its position is observed. Instead of using the von Neumann collapse hypothesis, we treat a real measurement process. The measurement consists of coupling a two-level atom in a double-weil potential to a resonant laser beam. Subsequent resonance fluorescence can be used to determine the atom's position within the double well, provided the laser wavelength is short enough to ensure a resolvable scattering pattern of the fluorescence photons. Treating this process in the framework of dissipative quantum mechanics, we derive a master equation which describes the measurement process in all relevant details. Solving the master equation analytically as weil as numerically we study the conditions for the decay of the nondiagonal elements. This leads directly to the inhibition of the center-of-mass motion, i.e. , to a quantum Zeno effect. Because we treat the measurement process in detail we are able to investigate the conditions for a complete measurement.In particular, we study the role of the intensity and the wavelength of the probing laser field. PACS number(s): 42.50.Wm, 06.20.Dk

Zeno Effect in Parametric Down-Conversion

“…This would link the Zeno effect directly with the quantum measurement theory. Since then, other approaches have been presented by means of purely dynamical terms without having to appeal to the reduction postulate [3,4,6].In most cases, in order to observe the intermediate stages of the evolution, it is necessary to modify the observed system in some way. The effect of these changes can be determined and understood only by a full quantum mechanical treatment of the whole process, which shows that even the most careful of all these observations inevitably leaves a trace on the observed system.…”

“…This would link the Zeno effect directly with the quantum measurement theory. Since then, other approaches have been presented by means of purely dynamical terms without having to appeal to the reduction postulate [3,4,6].…”

“…In the limit of very frequent measurements, continuous observation, or arbitrary high resolution, it may happen that the system is locked on its initial state and the evolution, which was the aim of the observation, is in fact inhibited and does not occur. It has been studied in atomic transitions [2], double-well potentials [3], and neutron spin dynamics [4], for example. Parallels can also be drawn with the interaction-free measurements [5].…”

Evolution of Cancer: A Quantum Mechanical Approach

“…The idea of directed or adaptive mutation suggests that, at least on occasion, consciousness may play a direct role in evolution [1]. The phenomenon bears many similarities to the inverse quantum Zeno effect, as described by [70][71][72], whereby a dense series of measurements along a particular path will force a quantum system to evolve along that path [19]. It might be apparent to say the inverse quantum zeno effect is analogous to the canalized pathway of change which was proposed for the extension of unitary field concept in order to cover the temporal aspect of development (Fig.…”

Dynamics of quantum zeno and anti-zeno effects in an open system

“…As shown below, in this interaction picture our calculations are significantly simplified and we can express all the effects from the measurements in terms of the decoherence factor γ n e iθn defined in Eq. (23). In the following two sections we will derive the short-time and long-time evolutions of the TLS with the calculations in this interaction picture.…”