Cavity Optomechanics in Photonic and Phononic Crystals: Engineering the Interaction of Light and Sound at the Nanoscale

Abstract

The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical and microwave cavities is of growing interest. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimeter- or micrometer-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass. In this thesis, two different nanometer-scale structures that use combinations of gradient and radiation pressure optical forces are described theoretically and demonstrated experimentally. These structures merge the fields of cavity optomechanics and nanomechanics into nano-optomechanical systems (NOMS). The first device, the Zipper optomechanical cavity, consists of a pair of doubly-clamped nanoscale beams separated by approximately 100 nanometers, each beam having a mass of 20 picograms and being patterned with a quasi-1D photonic crystal bandgap cavity. The optical mode of the coupled system is exquisitely sensitive to differential motion of the beams, producing optomechanical coupling right at the fundamental limit set by optical diffraction. The mechanical modes of the beam probed with a background sensitivity only a factor of 4 above the standard quantum limit, and the application of less than a milliwatt of optical power is shown to increase the mechanical rigidity of the system by almost an order of magnitude. The second device focuses on just one of the doubly-clamped nanoscale beams of the Zipper. We show that, in addition to a photonic bandgap cavity, the periodic patterning of the beam also produces a phononic bandgap cavity with localized mechanical modes having frequencies in the microwave regime. We call these photonic and phononic crystal bandgap cavities optomechanical crystals. Because the optical and mechanical modes occupy a volume more than 100,000 times smaller than the volume of a single human cell, the optomechanical interaction in this system is again at the fundamental limit set by optical diffraction. The miniscule effective volume of the mechanical mode corresponds to effective motional masses in the femtogram regime, which, coupled with the enormous optomechanical interaction and high optical and mechanical quality factors, allows transduction of microwave-frequency mechanical motion nearly at the standard quantum limit, with the standard quantum limit easily within reach with simple modifications of the experimental apparatus. The combination of the small motional mass and strong optomechanical coupling allows each trapped photon to drive motion of an acoustic mode with a force more than 15 times the weight of the structure. This provides a powerful method for optically actuating microwave-frequency mechanical oscillators on a chip, and we demonstrate an on-chip phonon laser that emits over 1012 microwave-frequency phonons per second with a ratio of frequency to linewidth of 2 million—characteristics similar to those of the first optical lasers. With the ability to readily interconvert photons and microwave-frequency phonons on the surface of a microchip, new chip-scale technologies can be created. We discuss the future of optomechanical crystals and provide new methods of calculating all the otptomechanical properties of the structures.