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-well 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 well 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.