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

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

Bypassing Cowling's theorem in axisymmetric fluid dynamos

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. At small enough Reynolds number, Re, the flow is axisymmetric and generates an equatorial dipole above a critical magnetic Reynolds number Rmc . The magnetic field thus breaks axisymmetry, in agreement with Cowling's theorem. This structure of the magnetic field is however replaced by a dominant axial dipole when Re is larger and allows non axisymmetric fluctuations in the flow. We show here that even in the absence of such fluctuations, an axial dipole can also be generated, at low Re, through a secondary bifurcation, when Rm is increased above the dynamo threshold. The system therefore always find a way to bypass the constraint imposed by Cowling's theorem. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.Comment: 4 pages, 6 figure

Influence of gravitational field on quantum-nondemolition measurement of atomic momentum in the dispersive Jaynes-Cummings model

We present a theoretical scheme based on su(2) algebra to investigate the influence of homogeneous gravitational field on the quantum nondemolition measurement of atomic momentum in dispersive Jaynes-Cummings model. In the dispersive Jaynes-Cummings model, when detuning is large and the atomic motion is in a propagating light wave, we consider a two-level atom with quantized cavity-field in the presence of a homogeneous gravitational field. We derive an effective Hamiltonian describing the dispersive atom-field interaction in the presence of gravitational field. We can see gravitational influence both on the momentum filter and momentum distribution. Moreover, gravitational field decreases both tooth spacing of momentum and the width of teeth of momentum.Comment: 21 pages, 8 figure

To the practical design of the optical lever intracavity topology of gravitational-wave detectors

The QND intracavity topologies of gravitational-wave detectors proposed several years ago allow, in principle, to obtain sensitivity significantly better than the Standard Quantum Limit using relatively small anount of optical pumping power. In this article we consider an improved more ``practical'' version of the optical lever intracavity scheme. It differs from the original version by the symmetry which allows to suppress influence of the input light amplitude fluctuation. In addition, it provides the means to inject optical pumping inside the scheme without increase of optical losses. We consider also sensitivity limitations imposed by the local meter which is the key element of the intracavity topologies. Two variants of the local meter are analyzed, which are based on the spectral variation measurement and on the Discrete Sampling Variation Measurement, correspondingly. The former one, while can not be considered as a candidate for a practical implementation, allows, in principle, to obtain the best sensitivity and thus can be considered as an ideal ``asymptotic case'' for all other schemes. The DSVM-based local meter can be considered as a realistic scheme but its sensitivity, unfortunately, is by far not so good just due to a couple of peculiar numeric factors specific for this scheme. From our point of view search of new methods of mechanical QND measurements probably based on improved DSVM scheme or which combine the local meter with the pondermotive squeezing technique, is necessary.Comment: 27 pages, 6 figure

Forced and self-excited oscillations of an optomechanical cavity

We experimentally study forced and self oscillations of an optomechanical cavity which is formed between a fiber Bragg grating that serves as a static mirror and between a freely suspended metallic mechanical resonator that serves as a moving mirror. In the domain of small amplitude mechanical oscillations, we find that the optomechanical coupling is manifested as changes in the effective resonance frequency, damping rate and cubic nonlinearity of the mechanical resonator. Moreover, self oscillations of the micromechanical mirror are observed above a certain optical power threshold. A comparison between the experimental results and a theoretical model that we have recently presented yields a good agreement. The comparison also indicates that the dominant optomechanical coupling mechanism is the heating of the metallic mirror due to optical absorption.Comment: 11 pages, 6 figure

High-sensitivity force measurement using entangled probes

We show the possibility to improve the measurement sensitivity of a weak force by using two meters in an entangled state. This latter can be achieved by exploiting radiation pressure effects.Comment: ReVTeX file, 11 pages, 2 eps figure

Conversion of conventional gravitational-wave interferometers into QND interferometers by modifying their input and/or output optics

The LIGO-II gravitational-wave interferometers (ca. 2006--2008) are designed to have sensitivities at about the standard quantum limit (SQL) near 100 Hz. This paper describes and analyzes possible designs for subsequent, LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad-band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a "squeezed-input interferometer" (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer's dark port; (ii) a "variational-output" interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a "squeezed-variational interferometer" with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Perot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology and with laser powers comparable to that planned for LIGO-II, these interferometers can beat the amplitude SQL by factors in the range from 3 to 5, corresponding to event rate increases between ~30 and ~100 over the rate for a SQL-limited interferometer.Comment: Submitted to Physical Review D; RevTeX manuscript with 16 figures; prints to 33 pages in Physical Review double column format. Minor revisions have been made in response to referee repor

Quantum Zeno Effect Explains Magnetic-Sensitive Radical-Ion-Pair Reactions

Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70's cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high-magnetic-field radical-ion-pair reactions.Comment: 10 pages, 5 figure

Suspensions Thermal Noise in the LIGO Gravitational Wave Detector

We present a calculation of the maximum sensitivity achievable by the LIGO Gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all its 6 degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational waver detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.Comment: 28 pages, 13 figure