Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators

Abstract

Parametric coupling of optical and mechanical degrees of freedom forms the basis of many ultra-sensitive measurements of both force and mechanical displacement. An optical cavity with a mechanically compliant boundary enhances the optomechanical interaction, which gives rise to qualitatively new behavior which can modify the dynamics of the mechanical motion. As early as 1967, in a pioneering work, V. Braginsky analyzed theoretically the role of radiation pressure in the interferometric measurement process, but it has remained experimentally unexplored for many decades. Here, we use whispering-gallery-mode optical microresonators to study these radiation pressure phenomena. Optical microresonators simultaneously host optical and mechanical modes, which are systematically analyzed and optimized to feature ultra-low mechanical dissipation, photon storage times exceeding the mechanical oscillation period (i.e. the "resolved-sideband regime") and large optomechanical coupling. In this manner, it is demonstrated for the first time that dynamical backaction can be employed to cool mechanical modes, i.e., to reduce their thermally excited random motion. Utilizing this novel technique together with cryogenic pre-cooling of the mechanical oscillator, the phonon occupation of mechanical radial-breathing modes could be reduced to n = 63 ± 20 excitation quanta. The corresponding displacement fluctuations are monitored interferometrically with a sensitivity at the level of 1 · 10 −18 m/ √ Hz, which is below the imprecision at the standard quantum limit (SQL). This implies that the readout is already in principle sufficient to measure the quantum mechanical zero-point position fluctuations of the mechanical mode. Moreover, it is shown that optical measurement techniques employed here are operating in a near-ideal manner according to the principles of quantum measurement, displaying a backaction-imprecision product close to the quantum limit.

Optoelectronic Oscillators Phase Noise and Stability Measurements

“…Figure 6 then gives the noise floor of the instrument versus Fourier frequencies. The noise floor is respectively better than -90 and -170 dBc/Hz at 10 3 and 5x10 6 Hz from the carrier.…”

“…One can note that the use of a shorter delay line in a optoelectronic phase noise measurement system working in X-band, allow a characterization of the phase noise far from the carrier. Fourier frequency analysis can be extended from 10 5 to 2x10 6 Hz by introducing a 100 m delay line in addition of a 2 km optical fiber [12]. As the Fast Fourier Transform (FFT) analyzer (Hewlett-Packard 3562A) used for characterizing the noise up to 100 kHz from the carrier is not operating for higher frequencies, it is necessary to use another FFT such as an Agilent 89600 for instance.…”

“…100 m fiber corresponds to a 500 ns delay. So the 10 5 Hz limit due to the 2 km fiber can be extended from 10 5 to 2x10 6 Hz from the carrier. This system works for any microwave signal in X-band (8.2 -12.4 GHz) especially for those delivered by optoelectronic oscillators.…”

Extremely high Q-factor mechanical modes in quartz bulk acoustic wave resonators at millikelvin temperature

“…To achieve the operation of hybrid mechanical systems in their quantum ground state, it is vital to develop acoustic resonators with very low losses at temperatures approaching absolute zero [1]. The frequencies accessible using mechanical systems are low, and thus a lower temperature is required.…”

Synchronization in coupled mechanical resonator arrays

“…This is largely because of the increased experimental expertise at the smaller scales where mechanisms such as nano and micromechanical cantilevers [9][10][11][12][13][14] and membranes [15] operate. In the last 10 years, the scale of the applications has even approached the quantum mechanical regime, with the fabrication of devices such as nano-scale beams coupled to microwave cavities [16], photonic-phononic crystals [17], toroidal optical micro-resonators [18], doubly clamped beams with integrated mirrors [19] and drumhead capacitors in superconductive microwave resonators [20], among others. However, applications can also be found in the larger scale-for example, in manipulating the center of mass motion of mechanical oscillators like the mirrors in the LIGO project [21,22].…”