Theoretical Studies On Quantum Simultaneous Continuous Measurement And Feedback Control

Quantum measurement is not only an important approach to understand the nature of the microscopic world,but also a cornerstone for demonstrating the quantum superiority via feedback control.In contrast with its classical counterpart,the dynamics of the quantum system monitored is inevitably disturbed by the quantum measurement.Furthermore,the outcomes of simultaneous measurement of two observables are restricted by Heisenberg uncertainty principle,which make it attractive and meaningful to discuss the evolution of the system under the simultaneous measurement.In the present thesis,we consider simultaneous and continuous measurement of two noncommutative observables of the system whose commutator is not necessarily a c-number.We revisit the Arthurs-Kelly model and generalize it to describe the simultaneous measurement of two arbitrary observables of the system.Using this generalized model,we continuously measure the system by following the scheme proposed by Scott and Milburn.We find that the non-selective master equation always reduces to the Lindblad form in the continuous limit.More importantly,this master equation does not contain a cross term describing the interplay effect of two measurements even if these two observables are noncommutative.In addition,the selective master equation can be approximated by a Ito stochastic differential equation whose noise terms are independent with each other.As an important application,we propose schemes to prepare the state of a two-level system and a one-dimensional harmonic oscillator system,respectively,by the feedback control based on such type of measurement of noncommutative observables.Firstly,we discuss the state preparation of a two-level system in an external field.Focusing on an asymptotic steady state,we find the static external field together with the measurement and feedback control allows us to manipulate the state of a two-level system in a versatile manner.Then,we propose a scheme to generate a pure ideal quadrature-squeezed state in a one-dimensional harmonic oscillator system by the feedback control.We find that,by appropriately setting the strengths of the measurement and the feedback control,the pure ideal quadrature-squeezed state with arbitrary squeezedness can be produced.This is in contrast to the scheme based on the single-observable measurement and the feedback control,where only nonideal squeezed states are produced.Furthermore,we discuss the transient dynamics of the harmonic oscillator and the experimental feasibility of this scheme.