Theory Of The Quantum Non-demolition Measurements In A Dirac Oscillator

Quantum precision measurements has witnessed spectacular advances in the last few years and especially a lot of research efforts are put in the quantum non-demolition(QND)measurement.In a QND measurement,the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a non-commuting observable is avoided.It has been exploited in particular in optical and atomic interferometry,weak force and gravitational wave detection,and the preparation of squeezed states.The goal of this paper is to theoretically show the QND measurements can also be realized on the Dirac oscillator,which is a relativistic counterpart of the harmonic oscillator and is frequently used to investigate relativistic extensions of non-relativistic quantum effects.It has also been found wide applications in nuclear physics,condensed matter physics and cosmology.Because of its non-equidistant excitation spectrum and the presence of a spin-orbit coupling in the Hamiltonian,the dynamics of the Dirac oscillator differs significantly from that of the harmonic oscillator.The effects of this coupling are formally eliminated in the FoldyWouthuysen(FW)representation,through which we derive general expressions for its QND observables and find that they are intricate combinations of the position,momentum,and spin operators in the physical representation,which makes the experimental realizations of the measurement more challenging.However,the situation is considerably simplified in both the weakly and strongly relativistic limits,where we give out the possible experimental proposals.This research result will help to improve the accuracy of measurement by using quantum measurement theory in relativistic physical systems.