QND Measurement Of A Flux Qubit Coupled To A Noisy Detector

This thesis is a record of my research on macroscopic quantum phenomenon in superconducting Josephson quantum devices, including the following contexts:In Chapter 1, some relative background knowledge is introduced. Then, I give a introduction to several kinds of means for qubit construction assembled by super-conducting Josephson circuit:Phase qubit, Flux qubit and Charge qubit. Also, their coupling types, measurement and a short review about recent experiments are also in-troduced. At last, according to the rapid development of circuit QED (cQED), I give a brief introduction to cQED and derive the quantum Hamiltonian of circuit from classi-cal coplanar waveguid (CPW) circuit.In Chapter 2,I present the quantum nondemolition (QND) measurement of a flux qubit coupled to a noisy detector. Firstly, I introduce the concept and the prerequisite for a perfect QND measurement. Secondly, I discuss the noise effect that impact on measurement rate and measurement time, the result shows that noise can influence the measurement time directly, which make the the qubit information gaining time become longer. This result can be interpreted by quantum limit theory. Also, the identity of measurement-induced dephasing and probability distribution curves also confirm the result which can be explained by quantum limit:the easier we gain information about one variable, the faster we lose information about its conjugate variable. Finally in this chapter, we analyze nonideal QND measurement which caused by the coupling between external noise and nondiagonal term of qubit. This type of coupling cause the transition between these two quantum states of qubit. In other words, the initial information of qubit is destroyed due to quantum tunneling between the qubit states. In Chapter 3,I present the design precept of a coplanar waveguide resonator. I first introduce the application and foreground of coplanar waveguide in cQED experi-ments. After that, I give the microwave theory in coplanar waveguide, according to the dielectric character of CPW, and derive the quantitive relationship of these parameter. The result shows that the width of the center stripe and the gap determine the CPW's transmission behavior. Another parameter, resonance frequency, is determined by the length of the center stripe which must be confirmed by the particular experiment type. At the end of this chapter, I give the perquisite of the CPW's measurement, including the design of PCB board and the connector type.