M.Sc Thesis

M.Sc StudentElla Lior
SubjectNonlinear Phenomena in Optomechanical Devices
DepartmentDepartment of Electrical and Computer Engineering
Supervisor ASSOCIATE PROF. Eyal Buks
Full Thesis textFull thesis text - English Version


In this work we investigate several aspects of these nonlinear phenomena both theoretically and experimentally, with the aim of understanding how they may be utilized to enhance desired effects in optomechanical devices.

The work presented here includes three main parts. In the first part we present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the control parameters of the SQUID. We detect the position of the beam by placing it in an optical cavity, which frees the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a periodic dependence on applied magnetic flux. To account for this, we develop a model based on the standard model for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the response of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.

In the second chapter we present a theory describing the semiclassical dynamics of a superconducting flux qubit inductively coupled to a nanomechanical resonator. Focusing on the influence of the qubit on the mechanical element, and on the nonlinear phenomena displayed by this device, we show that it exhibits retardation effects and self-excited oscillations. These can be harnessed for the generation of non-classical states of the mechanical resonator. In addition, we find that this system shares several fundamental properties with cavity optomechanical systems, and elucidate the analogy between these two classes of devices.

The third chapter is a theoretical investigation of the nonlinear dynamics of a hybrid opto-microwave-mechanical system. We show by a perturbative calculation that in the presence of a Duffing nonlinearity of the microwave system, the standard optomechanical addition to the mechanical frequency and dissipation become hysteretic. In all cases, the research is motivated by the question of how these effects can be used to enhance coherent quantum effects in these devices.