Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame

We analyze the interaction of plane '+'-polarized gravitational waves with a Fabry-Perot cavity in the local Lorentz frame of the cavity input mirror outside of the range of long-wave approximation with the force of radiation pressure taken into account. The obtained detector response signal is represented as a sum of two parts: (i) the phase shift due to displacement of the movable mirror under the influence of gravitational wave and the force of light pressure, and (ii) the phase shift due to direct interaction of gravitational wave with light wave inside the cavity. We obtain formula for the movable mirror law of motion paying close attention to the phenomena of optical rigidity, radiative friction and direct coupling of gravitational wave to light wave. Some issues concerning the detection of high-frequency gravitational waves and the role of optical rigidity in it are discussed. We also examine in detail special cases of optical resonance and small detuning from it and compare our results with the known ones.Comment: 17 pages, 9 figures; corrected references [7,8,34], added 2 new references (currently [35,36]), added comments on (i) relativistic corrections, (ii) detector angular pattern, (iii) quantized electromagnetic field, increased font in figure

Sub-SQL Sensitivity via Optical Rigidity in Advanced LIGO Interferometer with Optical Losses

The ``optical springs'' regime of the signal-recycled configuration of laser interferometric gravitational-wave detectors is analyzed taking in account optical losses in the interferometer arm cavities. This regime allows to obtain sensitivity better than the Standard Quantum Limits both for a free test mass and for a conventional harmonic oscillator. The optical losses restrict the gain in sensitivity and achievable signal-to-noise ratio. Nevertheless, for parameters values planned for the Advanced LIGO gravitational-wave detector, this restriction is insignificant.Comment: 15 pages, 9 figure

Proof of the Standard Quantum Limit for Monitoring Free-Mass Position

The measurement result of the moved distance for a free mass m during the time t between two position measurements cannot be predicted with uncertainty smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit (SQL) and it has been proven to always hold for the following position measurement: a probe is set in a prescribed position before the measurement. Just after the interaction of the mass with the probe, the probe position is measured, and using this value, the measurement results of the pre-measurement and post-measurement positions are estimated.Comment: 4 pages, no figur

Dual-Resonator Speed Meter for a Free Test Mass

A description and analysis are given of a ``speed meter'' for monitoring a classical force that acts on a test mass. This speed meter is based on two microwave resonators (``dual resonators''), one of which couples evanescently to the position of the test mass. The sloshing of the resulting signal between the resonators, and a wise choice of where to place the resonators' output waveguide, produce a signal in the waveguide that (for sufficiently low frequencies) is proportional to the test-mass velocity (speed) rather than its position. This permits the speed meter to achieve force-measurement sensitivities better than the standard quantum limit (SQL), both when operating in a narrow-band mode and a wide-band mode. A scrutiny of experimental issues shows that it is feasible, with current technology, to construct a demonstration speed meter that beats the wide-band SQL by a factor 2. A concept is sketched for an adaptation of this speed meter to optical frequencies; this adaptation forms the basis for a possible LIGO-III interferometer that could beat the gravitational-wave standard quantum limit h_SQL, but perhaps only by a factor 1/xi = h_SQL/h ~ 3 (constrained by losses in the optics) and at the price of a very high circulating optical power --- larger by 1/xi^2 than that required to reach the SQL.Comment: RevTex: 13 pages with 4 embedded figures (two .eps format and two drawn in TeX); Submitted to Physical Review

Phase diffusion pattern in quantum nondemolition systems

We quantitatively analyze the dynamics of the quantum phase distribution associated with the reduced density matrix of a system, as the system evolves under the influence of its environment with an energy-preserving quantum nondemolition (QND) type of coupling. We take the system to be either an oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a spin-1/2 system), and model the environment as a bath of harmonic oscillators, initially in a general squeezed thermal state. The impact of the different environmental parameters is explicitly brought out as the system starts out in various initial states. The results are applicable to a variety of physical systems now studied experimentally with QND measurements.Comment: 18 pages, REVTeX, 8 figure

Imprinting interference fringes in massive optomechanical systems

An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for the observation of signatures of momentum superpositions in a massive macroscopic system at non-zero temperatures. It is robust against thermalized initial states, displacement and movement, mirror imperfections, and the measurements' back-actions.Comment: 4 pages, 3 figures, 7 subfigure

Random surface roughness influence on gas damped nanoresonators

The author investigates quantitatively the influence of random surface roughness on the quality factor Q of nanoresonators due to noise by impinging gas molecules. The roughness is characterized by the amplitude w, the correlation length ξ, and the roughness exponent H that describes fine roughness details at short wavelengths. Surface roughening (decreasing H and increasing ratio w/ξ) leads to lower Q, which translates to lower sensitivity to external perturbations, and a higher limit to mass sensitivity. The influence of the exponent H is shown to be important as that of w/ξ, indicating the necessity for precise control of the surface morphology.

Optical noise correlations and beating the standard quantum limit in advanced gravitational-wave detectors

The uncertainty principle, applied naively to the test masses of a laser-interferometer gravitational-wave detector, produces a Standard Quantum Limit (SQL) on the interferometer's sensitivity. It has long been thought that beating this SQL would require a radical redesign of interferometers. However, we show that LIGO-II interferometers, currently planned for 2006, can beat the SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their thermal noise can be pushed low enough. This is due to dynamical correlations between photon shot noise and radiation-pressure noise, produced by the LIGO-II signal-recycling mirror.Comment: 12 pages, 2 figures; minor changes, some references adde

Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer

We present an optomechanical displacement transducer, that relies on three cavity modes parametrically coupled to a mechanical oscillator and whose frequency spacing matches the mechanical resonance frequency. The additional resonances allow to reach the standard quantum limit at substantially lower input power (compared to the case of only one resonance), as both, sensitivity and quantum backaction are enhanced. Furthermore, it is shown that in the case of multiple cavity modes, coupling between the modes is induced via reservoir interaction, e.g., enabling quantum backaction noise cancellation. Experimental implementation of the schemes is discussed in both the optical and microwave domain.Comment: 5 pages, 3 figures. Revised and amended versio

Quantum Signatures of the Optomechanical Instability

In the past few years, coupling strengths between light and mechanical motion in optomechanical setups have improved by orders of magnitude. Here we show that, in the standard setup under continuous laser illumination, the steady state of the mechanical oscillator can develop a non-classical, strongly negative Wigner density if the optomechanical coupling is large at the single-photon level. Because of its robustness, such a Wigner density can be mapped using optical homodyne tomography. These features are observed near the onset of the instability towards self-induced oscillations. We show that there are also distinct signatures in the photon-photon correlation function $g^{(2)}(t)$ in that regime, including oscillations decaying on a time scale not only much longer than the optical cavity decay time, but even longer than the \emph{mechanical} decay time.Comment: 6 pages including 1 appendix. 6 Figures. Correcte