Quantum noise in gravitational-wave interferometers: Overview and recent developments

We present an overview of quantum noise in gravitational wave interferometers. Gravitational wave detectors are extensively modified variants of a Michelson interferometer and the quantum noise couplings are strongly influenced by the interferometer configuration. We describe recent developments in the treatment of quantum noise in the complex interferometer configurations of present-day and future gravitational-wave detectors. In addition, we explore prospects for the use of squeezed light in future interferometers, including consideration of the effects of losses, and the choice of optimal readout schemes.Comment: 13 pages, 5 figure

Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field

Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formalism

We present a mathematical framework for simulation of optical fields in complex gravitational-wave interferometers. The simulation framework uses the two-photon formalism for optical fields and includes radiation pressure effects, an important addition required for simulating signal and noise fields in next-generation interferometers with high circulating power. We present a comparison of results from the simulation with analytical calculation and show that accurate agreement is achieved

Experimental test of an alignment-sensing scheme for a gravitational-wave interferometer

An alignment-sensing scheme for all significant angular degrees of freedom of a power-recycled Michelson interferometer with Fabry Perot cavities in the arms was tested on a tabletop interferometer. The response to misalignment of all degrees of freedom was measured at each sensor, and good agreement was found between measured and theoretical values

Frequency-Dependent Squeeze Amplitude Attenuation and Squeeze Angle Rotation by Electromagnetically Induced Transparency for Gravitational Wave Interferometers

We study the effects of frequency-dependent squeeze amplitude attenuation and squeeze angle rotation by electromagnetically induced transparency (EIT) on gravitational wave (GW) interferometers. We propose the use of low-pass, band-pass, and high-pass EIT filters, an S-shaped EIT filter, and an intra-cavity EIT filter to generate frequency-dependent squeezing for injection into the antisymmetric port of GW interferometers. We find that the EIT filters have several advantages over the previous filter designs with regard to optical losses, compactness, and the tunability of the filter linewidth.Comment: 4 page

Gravitationally induced phase shift on a single photon

The effect of the Earth's gravitational potential on a quantum wave function has only been observed for massive particles. In this paper we present a scheme to measure a gravitationally induced phase shift on a single photon travelling in a coherent superposition along different paths of an optical fiber interferometer. To create a measurable signal for the interaction between the static gravitational potential and the wave function of the photon, we propose a variant of a conventional Mach-Zehnder interferometer. We show that the predicted relative phase difference of $10^{-5}$ radians is measurable even in the presence of fiber noise, provided additional stabilization techniques are implemented for each arm of a large-scale fiber interferometer. Effects arising from the rotation of the Earth and the material properties of the fibers are analysed. We conclude that optical fiber interferometry is a feasible way to measure the gravitationally induced phase shift on a single-photon wave function, and thus provides a means to corroborate the equivalence of the energy of the photon and its effective gravitational mass.Comment: 13 pages, 5 figure

A route to observing ponderomotive entanglement with optically trapped mirrors

The radiation pressure of two detuned laser beams can create a stable trap for a suspended cavity mirror; here it is shown that such a configuration entangles the output light fields via interaction with the mirror. Intra-cavity, the opto-mechanical system can become entangled also. The degree of entanglement is quantified spectrally using the logarithmic negativity. Entanglement survives in the experimentally accessible regime of gram-scale masses subject to thermal noise at room temperature.Comment: 4 pages, 4 figure

Generation of a stable low-frequency squeezed vacuum field with periodically-poled KTiOPO4_4 at 1064 nm

We report on the generation of a stable continuous-wave low-frequency squeezed vacuum field with a squeezing level of $3.8\pm0.1$ dB at 1064 nm, the wavelength at which laser interferometers for gravitational wave (GW) detection operate, using periodically poled KTiOPO$_4$ (PPKTP) in a sub-threshold optical parametric oscillator. PPKTP has the advantages of higher nonlinearity, smaller intra-crystal and pump-induced seed absorption, user-specified parametric down-conversion temperature, wider temperature tuning range, and lower susceptibility to thermal lensing over alternative nonlinear materials such as MgO doped or periodically poled LiNbO$_3$, and is, therefore, an excellent material for generation of squeezed vacuum fields for application to laser interferometers for GW detection

Non-invasive Measurements of Cavity Parameters by Use of Squeezed Vacuum

We propose and experimentally demonstrate a method for non-invasive measurements of cavity parameters by injection of squeezed vacuum into an optical cavity. The principle behind this technique is the destruction of the correlation between upper and lower quantum sidebands with respect to the carrier frequency when the squeezed field is incident on the cavity. This method is especially useful for ultrahigh $Q$ cavities, such as whispering gallery mode (WGM) cavities, in which absorption and scattering by light-induced nonlinear processes inhibit precise measurements of the cavity parameters. We show that the linewidth of a test cavity is measured to be $\gamma = 844\pm40$ kHz, which agrees with the classically measured linewidth of the cavity within the uncertainty ($\gamma=856\pm34$ kHz).Comment: 6 pages, 4 figure