M. L. Gorodetsky

Noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization

It is shown that photon shot noise and radiation-pressure back-action noise are the sole forms of quantum noise in interferometric gravitational wave detectors that operate near or below the standard quantum limit, if one filters the interferometer output appropriately. No additional noise arises from the test masses initial quantum state or from reduction of the test-mass state due to measurement of the interferometer output or from the uncertainty principle associated with the test-mass state. Two features of interferometers are central to these conclusions: (i) The interferometer output [the photon number flux [script N]-hat(t) entering the final photodetector] commutes with itself at different times in the Heisenberg picture, [[script N]-hat(t),[script N]-hat(t[prime])] = 0 and thus can be regarded as classical. (ii) This number flux is linear to high accuracy in the test-mass initial position and momentum operators x-hato and p-hato, and those operators influence the measured photon flux [script N]-hat(t) in manners that can easily be removed by filtering. For example, in most interferometers x-hato and p-hato appear in [script N]-hat(t) only at the test masses ~1 Hz pendular swinging frequency and their influence is removed when the output data are high-pass filtered to get rid of noise below ~10 Hz. The test-mass operators x-hato and p-hato contained in the unfiltered output [script N]-hat(t) make a nonzero contribution to the commutator [[script N]-hat(t),[script N]-hat(t[prime])]. That contribution is precisely canceled by a nonzero commutation of the photon shot noise and radiation-pressure noise, which also are contained in [script N]-hat(t). This cancellation of commutators is responsible for the fact that it is possible to derive an interferometers standard quantum limit from test-mass considerations, and independently from photon-noise considerations, and get identically the same result. These conclusions are all true for a far wider class of measurements than just gravitational-wave interferometers. To elucidate them, this paper presents a series of idealized thought experiments that are free from the complexities of real measuring systems.

Energetic Quantum Limit in Large-Scale Interferometers

For each optical topology of an interferometric gravitational wave detector, quantum mechanics dictates a minimum optical power (the energetic quantum limit) to achieve a given sensitivity. For standard topologies, when one seeks to beat the standard quantum limit by a substantial factor, the energetic quantum limit becomes impossibly large. Intracavity readout schemes may do so with manageable optical powers.

Optical microsphere resonators: optimal coupling and the ultimate Q

A general model is presented for coupling of high-Q whispering-gallery modes in optical microsphere resonators with coupler devices possessing discrete and continuous spectrum of propagating modes. By contrast to Fabry-Perot resonators, in microspheres independent high intrinsic quality-factor and controllable parameters of coupling via evanescent field offer variety of regimes earlier available in RF devices. Latest results on realization of material- limited Q approximately 1010 in microspheres in the visible and near-infrared band and preservation of very-high Q in surface-hydration-preventing environment are presented.

Optical whispering-gallery microresonators

Quality factor 2.5 X 109 at the wavelength (lambda) equals 0.63 micrometers is reported in approximately 100 micrometers spherical resonators of fused silica with whispering-gallery modes (equivalent finesse F equals 2.5 X 106). Quality-factor 3 X 107 and effective thermal tunability of modes (up to 0.1%) is demonstrated in whispering-gallery microresonators of optical glass. Dispersive bistability and other nonlinear effects are observed at the level of input power about tens of microwatts. Nonlinear properties of optical whispering-gallery modes are investigated by mode cross-modulation technique. Prospects of applications in linear signal processing and quantum-nondemolition measurements are outlined.

Thermorefractive noise in microspheres

Thermodynamical fluctuations of temperature in microspheres transform to fluctuations of its resonance frequencies due to coefficient of thermal refraction. These fluctuations produce additional phase and amplitude noise in the output of the cavity. The implications of this noise for laser stabilization and other applications are discussed. Experimental conditions for the direct observation of this new effect are given.

Intracavity Rayleigh scattering in microspheres: limits imposed on quality factor and mode coupling

We present a detailed analysis of the effect of volumetric and surface inhomogeneities as a source of quality-factor limitation and intracavity resonant backscattering in optical microsphere cavities of fused silica. Intrinsic scattering in microspheres is shown to be significantly inhibited as compared to standard Rayleigh scattering in the bulk material. This reassessment of fundamental losses indicates that Q-factors substantially exceeding the previously expected limit of approximately 1011 can be obtained in microspheres, as soon as surface hydration is prevented. The intracavity backscattering is analyzed as a source of whispering-gallery mode splitting and resonant optical feedback in presence of a mode-matched travelling- wave coupler.

The measurement of thermo-refractive noise in microspheres

We present the results of measurements of thermal fluctuations in microspheres. Experimental noise spectra are in good agreement with the theoretical model of recently predicted thermorefractive noise.

Ultimate Q of optical microsphere resonators

We demonstrate the quality factor Q equals (0.8 plus or minus 0.1) multiplied by 1010 of whispering-gallery modes in fused silica microspheres at 633 nm, close to the limit determined by fundamental material attenuation. The lifetime of ultimate Q is limited by adsorption of atmospheric water. Optical effects of adsorption are investigated and conditions for fabrication of long-lifetime microspheres are clarified.