Mathematical framework for simulations 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

Readout and Control of a Power-recycled Interferometric Gravitational-wave Antenna

Interferometric gravitational wave antennas are based on Michelson interferometers whose sensitivity to small differential length changes has been enhanced by adding multiple coupled optical resonators. The use of optical cavities is essential for reaching the required sensitivity, but sets challenges for the control system which must maintain the cavities near resonance. The goal for the strain sensitivity of the Laser Interferometer Gravitational-wave Observatory (LIGO) is 10^-21 rms, integrated over a 100 Hz bandwidth centered at 150 Hz. We present the major design features of the LIGO length and frequency sensing and control system which will hold the differential length to within 5 10^-14 m of the operating point. We also highlight the restrictions imposed by couplings of noise into the gravitational wave readout signal and the required immunity against them.Comment: Presentation at ICALEPCS 2001, San Jose, November 2001, (WECT003), 3 page

Optimal Alignment Sensing of a Readout Mode Cleaner Cavity

Critically coupled resonant optical cavities are often used as mode cleaners in optical systems to improve the signal to noise ratio (SNR) of a signal that is encoded as an amplitude modulation of a laser beam. Achieving the best SNR requires maintaining the alignment of the mode cleaner relative to the laser beam on which the signal is encoded. An automatic alignment system which is primarily sensitive to the carrier field component of the beam will not, in general, provide optimal SNR. We present an approach that modifies traditional dither alignment sensing by applying a large amplitude modulation on the signal field, thereby producing error signals that are sensitive to the signal sideband field alignment. When used in conjunction with alignment actuators, this approach can improve the detected SNR; we demonstrate a factor of 3 improvement in the SNR of a kilometer-scale detector of the Laser Interferometer Gravitational-wave Observatory. This approach can be generalized to other types of alignment sensors

An all-optical trap for a gram-scale mirror

We report on a stable optical trap suitable for a macroscopic mirror, wherein the dynamics of the mirror are fully dominated by radiation pressure. The technique employs two frequency-offset laser fields to simultaneously create a stiff optical restoring force and a viscous optical damping force. We show how these forces may be used to optically trap a free mass without introducing thermal noise; and we demonstrate the technique experimentally with a 1 gram mirror. The observed optical spring has an inferred Young's modulus of 1.2 TPa, 20% stiffer than diamond. The trap is intrinsically cold and reaches an effective temperature of 0.8 K, limited by technical noise in our apparatus.Comment: Major revision. Replacement is version that appears in Phy. Rev. Lett. 98, 150802 (2007

Squeezed light for advanced gravitational wave detectors and beyond

Recent experiments have demonstrated that squeezed vacuum states can be injected into gravitational wave detectors to improve their sensitivity at detection frequencies where they are quantum noise limited. Squeezed states could be employed in the next generation of more sensitive advanced detectors currently under construction, such as Advanced LIGO, to further push the limits of the observable gravitational wave Universe. To maximize the benefit from squeezing, environmentally induced disturbances such as back scattering and angular jitter need to be mitigated. We discuss the limitations of current squeezed vacuum sources in relation to the requirements imposed by future gravitational wave detectors, and show a design for squeezed light injection which overcomes these limitations

Frequency-Dependent Squeezing for Advanced LIGO

The first detection of gravitational waves by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 launched the era of gravitational wave astronomy. The quest for gravitational wave signals from objects that are fainter or farther away impels technological advances to realize ever more sensitive detectors. Since 2019, one advanced technique, the injection of squeezed states of light is being used to improve the shot noise limit to the sensitivity of the Advanced LIGO detectors, at frequencies above $\sim 50$ Hz. Below this frequency, quantum back action, in the form of radiation pressure induced motion of the mirrors, degrades the sensitivity. To simultaneously reduce shot noise at high frequencies and quantum radiation pressure noise at low frequencies requires a quantum noise filter cavity with low optical losses to rotate the squeezed quadrature as a function of frequency. We report on the observation of frequency-dependent squeezed quadrature rotation with rotation frequency of 30Hz, using a 16m long filter cavity. A novel control scheme is developed for this frequency-dependent squeezed vacuum source, and the results presented here demonstrate that a low-loss filter cavity can achieve the squeezed quadrature rotation necessary for the next planned upgrade to Advanced LIGO, known as "A+."Comment: 6 pages, 2 figures, to be published in Phys. Rev. Let

Advanced interferometry, quantum optics and optomechanics in gravitational wave detectors

Currently operating laser interferometric gravitational wave detectors are limited by quantum noise above a few hundred Hertz. Detectors that will come on line in the next decade are predicted to be limited by quantum noise over their entire useful frequency band (from 10 Hz to 10 kHz). Further sensitivity improvements will, therefore, rely on using quantum optical techniques such as squeezed state injection and quantum nondemolition, which will, in turn, drive these massive mechanical systems into quantum states. This article reviews the principles behind these optical and quantum optical techniques and progress toward there realization