Exact decoherence in an environment-free measurement model brought by a position-limited initial state of the probe and pointer

Abstract

We demonstrate the implementation of the measurement of the energy observable of a quantum harmonic oscillator by using the environment-free measurement model wherein the probe and the pointer of the apparatus are treated as different quantum systems. When the probe and pointer are initially in position-limited initial states, exact decoherence can be induced at a finite time and the emerging pointer states are exactly orthogonal at a finite time after the former has occurred. Closed forms for the functions and time scales relevant to decoherence and orthogonality of pointer states are obtained.