Ph.D Thesis

Ph.D StudentSuchoi Oren
SubjectNonlinear Phenomena and State Tomography in
Superconducting Microwave Resonators Coupled to
Mechanical Resonators and SQUIDs
DepartmentDepartment of Nanoscience and Nanotechnology
Supervisor ASSOCIATE PROF. Eyal Buks
Full Thesis textFull thesis text - English Version


This thesis is divided into two projects:

1.       Tunable linear and nonlinear inductance in a superconducting  transmission-line resonator coupled to a DC-SQUID

A Kerr nonlinearity in an electromagnetic resonator may lead to dispersive intermode coupling, which can be exploited to allow detection of single photons. While Kerr nonlinearity exists in superconducting resonators due to the effect of kinetic inductance, the resultant intermode coupling is typically too weak to allow for single photon detection. A stronger Kerr nonlinearity is achieved by integrating a superconducting quantum interference device (SQUID) with the microwave resonator. Quantum limited measurement leads to increased dephasing in the measured system.  The main goal of this project was to measure the increased dephasing due to strong and tunable intermode coupling induced by the coupling of a nanobridge DC-SQUID to a superconducting microwave resonator.

The linear inductance of the SQUID, which is periodic in the magnetic flux applied to the SQUIDs' loop, causes the resonance frequency of the microwave resonator to become flux depended. The nonlinear inductance of the SQUID gives rise to a strong Kerr nonlinearity, which results in strong coupling between different modes of the resonator. Experimental demonstration of such intermode coupling is presented. This coupling gives rise to dephasing of microwave photons, manifested in the broadening of the resonance lineshape, which depends periodically on the external magnetic flux applied to the SQUID. Comparison of the experimental results with the theoretical analysis of the coupled system, yields good agreement.

2.       Optomechanics with a microwave cavity coupled to an Al membrane:

Optomechanical cavities are currently a subject of intense basic and applied study. In this project, we experimentally study an optomechanical cavity consisting of an oscillating mechanical resonator embedded in a superconducting microwave transmission line cavity.

Tunable optomechanical coupling between the mechanical resonator and the microwave cavity is introduced by positioning a Nb-coated optical fiber above the mechanical resonator. The capacitance between the mechanical resonator and the coated fiber gives rise to optomechanical coupling, which can be controlled by varying the fiber-resonator distance.

Self-excited mechanical oscillations versus microwave frequency and power are studied. A tomography technique is employed for extracting the phase space distribution (PSD) of the mechanical resonator from the signal reflected by the optical cavity.

The main result of this study is the recording of the time evolution of the transition from an optomechanically cooled state to a state of self-excited oscillations, which is induced by abruptly switching the microwave driving frequency from the red-detuned region to the blue-detuned one. Experimental results are compared with theoretical predictions obtained by numerical integration of the Fokker-Planck equation yielding good agreement.  The feasibility of generating quantum superposition states in such a system is also discussed.

Some of our microwave cavities exhibit Kerr nonlinearity, which modifies the stability region, in the plane of pump parameters, of the mechanical oscillator. Intermittency between limit cycle and steady state is also observed. These experimental results are accounted for by a model that takes into account the Duffing-like nonlinearity of the microwave cavity.