Stable optical spring in aLIGO detector with unbalanced arms and in Michelson-Sagnac interferometer

Optical rigidity in aLIGO gravitational-wave detector, operated on dark port regime, is unstable. We show that the same interferometer with excluded symmetric mechanical mode but with unbalanced arms allows to get stable optical spring for antisymmetric mechanical mode. Arm detuning necessary to get stability is shown to be a small one - it corresponds to small power in signal port. We show that stable optical spring may be also obtained in Michelson-Sagnac interferometer with both power and signal recycling mirrors and unbalanced arms

Accurate calculation of thermal noise in multilayer coating

We derive accurate formulas for thermal fluctuations in multilayer interferometric coating taking into account light propagation inside the coating. In particular, we calculate the reflected wave phase as a function of small displacements of the boundaries between the layers using transmission line model for interferometric coating and derive formula for spectral density of reflected phase in accordance with Fluctuation-Dissipation Theorem. We apply the developed approach for calculation of the spectral density of coating Brownian noise.Comment: 10 pages, 9 figure

Stable Optical Rigidity Based on Dissipative Coupling

We show that the stable optical rigidity can be obtained in a Fabry-Perot cavity with dissipative optomechanical coupling and with detuned pump, corresponding conditions are formulated. An optical detection of a weak classical mechanical force with usage of this rigidity is analyzed. The sensitivity of small force measurement can be better than the standard quantum limit (SQL).Comment: 10 pages, 6 figure

Squeezing of optomechanical modes in detuned Fabry-Perot interferometer

We carry out analysis of optomechanical system formed by moveable mirror of Fabry-Perot cavity pumped by detuned laser. Optical spring arising from detuned pump creates in the system several eigen modes which could be treated as high-Q oscillators. Modulation of laser power results in parametric modulation of oscillators spring constants thus allowing to squeeze noise in quadratures of the modes. Evidence of the squeezing could be found in the light reflected from the cavity.Comment: 8 pages, 2 figure

Displacement-noise-free gravitational-wave detection with two Fabry-Perot cavities

We propose two detuned Fabry-Perot cavities, each pumped through both the mirrors, positioned in line as a toy model of the gravitational-wave (GW) detector free from displacement noise of the test masses. It is demonstrated that the noise of cavity mirrors can be completely excluded in a proper linear combination of the cavities output signals. This model is illustrated by a simplified round trip model (without Fabry-Perot cavities). We show that in low-frequency region the obtained displacement-noise-free response signal is stronger than the one of the interferometer recently proposed by S.Kawamura and Y.Chen.Comment: 10 pages, 5 figure

Back action cancellation in resolved sideband regime

We consider the simple model of measurement of mechanical oscillator position via Fabry-Pero cavity pumped by detuned laser (end mirror of cavity is mass of oscillator) in resolved sideband regime when laser is detuned from cavity's frequency by frequency of mechanical oscillator $\pm\omega_m$ and relaxation rate $\gamma$ of cavity is small: $\gamma\ll \omega_m$. We demonstrate fluctuation back action cancellation in reflected wave. However, it does not allow to circumvent Standard Quantum Limit, the reason of it is the dynamic back action.Comment: 5 pages, 1 figur

Electromagnetic Continuum Induced Nonlinearity

A nonrelativistic Hamiltonian describing interaction between a mechanical degree of freedom and radiation pressure is commonly used as an ultimate tool for studying system behavior in opto-mechanics. This Hamiltonian is derived from the equation of motion of a mechanical degree of freedom and the optical wave equation with time-varying boundary conditions. We show that this approach is deficient for studying higher order nonlinear effects in an open resonant opto-mechanical system. Opto-mechanical interaction induces a large mechanical nonlinearity resulting from a strong dependence of the power of the light confined in the optical cavity on the mechanical degrees of freedom of the cavity due to coupling with electromagnetic continuum. This dissipative nonlinearity cannot be inferred from the standard Hamiltonian formalism.Comment: 5 pages, 1 figur

On sensitivity limitations of a dichromatic optical detection of a classical mechanical force

We apply the strategy of the back action evading measurement of a quadrature component of mechanical motion of a test mass to detection of a classical force acting on the mass (Science, 209, (1980) 547) and study both classical and quantum limitations of the technique. We are considering a resonant displacement transducer interrogated with a dichromatic optical pump as a model system in this study. The transducer is represented by a Fabry Perot cavity with a totally reflecting movable end mirror the resonant force of interest acts upon. The cavity is pumped with two coherent optical carriers equally detuned from one of the cavity resonances. We show that the quantum back action cannot be completely excluded from the measurement result due to the dynamic instability of the opto-mechanical system that either limits the allowable power of the optical pump or calls for introducing an asymmetry to the pump configuration destroying the quantum nondemolition nature of the measurement.Comment: 8 pages, 1 figur

Displacement- and laser-noise-free gravitational-wave detection with two Fabry-Perot cavities

We propose two Fabry-Perot cavities, each pumped through both the mirrors, positioned in line as a toy model of the gravitational-wave (GW) detector free from displacement noise of the test masses. It is demonstrated that the displacement noise of cavity mirrors as well as laser noise can be completely excluded in a proper linear combination of the cavities output signals. We show that in low-frequency approximation (gravitational wave length $\lambda-\text{gw}$ is much greater than distance $L$ between mirrors $\lambda_\text{gw}\gg L$) the decrease of response signal is about $(L/\lambda_\text{gw})^2$, i.e. signal is stronger than the one of the interferometer recently proposed by S. Kawamura and Y. Chen.Comment: 7 pages, 4 figur

Polarization loss in reflecting coating

In laser gravitational waves detectors optical loss restricts sensitivity. We discuss polarization scattering as one more possible mechanism of optical losses. Circulated inside interferometer light is polarized and after reflection its plane of polarization can turn a little due to reflecting coating of mirror can have slightly different refraction index along axes $x,\, y$ in plane of mirror surface (optical anisotropy). This anisotropy can be produced during manufacture of coating (elasto-optic effect). This orthogonal polarized light, enhanced in cavity, produces polarization optical loss. Polarization map of mirrors is very important and we propose to measure it. Polarization loss can be important in different precision optical experiments based on usage of polarized light, for example, in quantum speed meter