Coating thermal noise for arbitrary shaped beams

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.Comment: 3 pages. Originally performed in August 2004. Submitted to CQG. (v2) : Corrections from referee and other

Sensitivity of a cavityless optomechanical system

We study the possibility of revealing a weak coherent force by using a pendular mirror as a probe, and coupling this to a radiation field, which acts as the meter, in a cavityless configuration. We determine the sensitivity of such a scheme and show that the use of an entangled meter state greatly improves the ultimate detection limit. We also compare this scheme with that involving an optical cavity.Comment: 4 pages, RevTex file, 2 eps figures, provisionally accepted by Phys. Rev.

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

Quantum statistical properties of the radiation field in a cavity with a movable mirror

A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve in principle as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.Comment: REVTeX, 9 pages, 5 figures. More info on http://www.ligo.caltech.edu/~cbrif/science.htm

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

Speed Meter As a Quantum Nondemolition Measuring Device for Force

Quantum noise is an important issue for advanced LIGO. Although it is in principle possible to beat the Standard Quantum Limit (SQL), no practical recipe has been found yet. This paper dicusses quantum noise in the context of speedmeter-a devise monitoring the speed of the testmass. The scheme proposed to overcome SQL in this case might be more practical than the methods based on monitoring position of the testmass.Comment: 7 pages of RevTex, 1 postscript figur

How to reduce the suspension thermal noise in LIGO without improving the Q's of the pendulum and violin modes

The suspension noise in interferometric gravitational wave detectors is caused by losses at the top and the bottom attachments of each suspension fiber. We use the Fluctuation-Dissipation theorem to argue that by careful positioning of the laser beam spot on the mirror face it is possible to reduce the contribution of the bottom attachment point to the suspension noise by several orders of magnitude. For example, for the initial and enhanced LIGO design parameters (i.e. mirror masses and sizes, and suspension fibers' lengths and diameters) we predict a reduction of $\sim 100$ in the "bottom" spectral density throughout the band $35-100\hbox{Hz}$ of serious thermal noise. We then propose a readout scheme which suppresses the suspension noise contribution of the top attachment point. The idea is to monitor an averaged horizontal displacement of the fiber of length $l$; this allows one to record the contribution of the top attachment point to the suspension noise, and later subtract it it from the interferometer readout. For enhanced LIGO this would allow a suppression factor about 100 in spectral density of suspension thermal noise.Comment: a few misprints corrected; submitted to Classical and Quantum Gravit

Reduction and possible elimination of coating thermal noise using a rigidly controlled cavity with a QND technique

Thermal noise of a mirror is one of the most important issues in high precision measurements such as gravitational-wave detection or cold damping experiments. It has been pointed out that thermal noise of a mirror with multi-layer coatings can be reduced by mechanical separation of the layers. In this paper, we introduce a way to further reduce thermal noise by locking the mechanically separated mirrors. The reduction is limited by the standard quantum limit of control noise, but it can be overcome with a quantum-non-demolition technique, which finally raises a possibility of complete elimination of coating thermal noise

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