Weak Measurement Theory And Its Application In Optomechanical System

The study of quantum mechanical fundamental is not only enriching our scientific knowl-edge, but also enriching our understanding of the natural law. These studies also promote the development of numerous technological application, for example, the question of quantum non-locality has been applied to quantum cryptology, the understanding of wave-particle d-uality made semiconductor technology possible and the investigation of Schrodinger cats advanced the field of quantum information processing and communication.During the examination of the quantum measurement process, Aharonov, Albert and Vaidman introduce weak measurement described by weakly coupling between the system and the pointer, and define weak value of the system observable. Weak value of the system observable can be beyond the usual range of the eigenvalue of the system observable. The feature of weak value is usually referred to as an amplification effect for weak signs. After first optical implement of weak value, it has been applied in different fields to observe very tiny effect, such as beam deflection, frequency shift, phase shift, angular shift, velocity shift, and even temperature shift. Although weak measurement has many applications, its application in quantum optomechanics is seldom reported. As is known to all, when there is only one photon in the optomechanical cavity, the displacement of the mirror caused by one photon is hard to be detected since it is much smaller than the spread of the mirror wave packet. In other word, one photon radiation pressure is difficult to be measured. Therefore, in the current experimental conditions, whether using a weak measurement to amplify a photon radiation pressure is very meaningful.In the first chapter, introduce the background of my paper, and in the second chapter, some basic knowledge is provided. The main work of this paper is illustrated from the third chapter to the fifth chapter. The third and fourth chapters focus on how to improve the displacement of the mirror in optomechanical system for weak measurements with several different quantum pointers. The third chapter is based on optomechanical system combined with weak measurement. When the mirror (quantum pointer) is initialized in the ground state, it's found that, the mirror's displacement can bo amplified. Such amplification effort happens when the postselection state of the photon is orthogonal to its initial state, which cannot be explained by usual weak measurement theory. Moreover, its maximum ampli-fication value can reach the level of the ground state fluctuation. In the fourth chapter, when the mirror is instead initialized in squeezed coherent state, it's found that the mirror's displacement can also be amplified. Such magnification is determined by the increased fluctu-ation of the squeezed coherent state, which is induced by the noncommutativity of quantum mechanics. The fifth chapter is based on the delayed selection experiment combined with optomechanical system. With weak measurement, the controlled Hadamard gate with post-selection is studied, and it's found that the wave-particle duality under its control can be used as a generation mechanism for amplification. Finally, in chapter six the conclusion and prospect is discussed.