The Study Of Microwave Squeezing In A Superconducting Quantum Circuit

In quantum optics,the quantum fluctuations of squeezed states are anisotropic(i.e.,the fluctuations are reduced in one quadrature component but increased in the other canonically conjugate one),which have promising applications in,e.g.,precision measurement,detection of weak signal and quantum information.The degenerate parametric down conversion(PDC)is one of the important methods for generating the squeezed states.Due to the advantages of good coherence and easy tunability,the superconducting-quantum circuit system is a good platform for exploring exotic phenomena in quantum optics.Up to now,the microwave squeezing via degenerate PDC has been studied preliminarily in superconducting quantum circuits.However,the squeezing parameters in these theoretical schemes are too small because of the limitation of the dispersive conditions.In addition,it is difficult to achieve those proposals in the experiment,since they are limited by the experiment parameters.In this thesis,we propose a superconducting quantum circuit to generate the microwave squeezing via degenerate PDC.In our scheme,two coplanar waveguide resonators(CWRs)are nonlinearly coupled together via a superconducting quantum interference device(SQUID)embedded in one of the CWRs.This is equivalent to replacing the transmission line in a flux-driven Josephson parametric amplifier(JPA)by a CWR.With second quantization,the proposed quantum circuit can be described by a standard Hamiltonian for PDC.Using the Heisenberg-Langevin approach,we numerically investigate the microwave squeezing via degenerate PDC in this system.In contrast to the JPA,our proposed system becomes stable around the critical point and can generate stronger transient squeezing.Compared with the previous schemes,our scheme not only enhances the coefficient of PDC by three orders of magnitude(i.e.,from tens of kilohertz to tens of megahertz)but also promises a much easier implementation in the experiment.In addition,our scheme reaches the strong-coupling regime and thus can be used to engineer the photon blockade based on the three wave mixing process.