N. Mavalvala

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 g mirror. The observed optical spring has an inferred Youngs 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.

A quantum-enhanced prototype gravitational-wave detector

The quantum nature of the electromagnetic field imposes a fundamental limit on the sensitivity of optical precision measurements such as spectroscopy, microscopy and interferometry. The so-called quantum limit is set by the zero-point fluctuations of the electromagnetic field, which constrain the precision with which optical signals can be measured. In the world of precision measurement, laser-interferometric gravitational-wave detectors, are the most sensitive position meters ever operated, capable of measuring distance changes of the order of 10- 18 m r.m.s. over kilometre separations caused by gravitational waves from astronomical sources. The sensitivity of currently operational and future gravitational-wave detectors is limited by quantum optical noise. Here, we demonstrate a 44% improvement in displacement sensitivity of a prototype gravitational-wave detector with suspended quasi-free mirrors at frequencies where the sensitivity is shot-noise-limited, by injecting a squeezed state of light. This demonstration is a critical step towards implementation of squeezing-enhancement in large-scale gravitational-wave detectors.

Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK

We report on the use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 g suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of approximately 40 000 below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experiment we infer an increase in the dynamical lifetime of the state by a factor of approximately 200.

Alignment of an interferometric gravitational wave detector

Interferometric gravitational wave detectors are designed to detect small perturbations in the relative lengths of their kilometer-scale arms that are induced by passing gravitational radiation. An analysis of the effects of imperfect optical alignment on the strain sensitivity of such an interferometer shows that to achieve maximum strain sensitivity at the Laser Interferometer Gravitational Wave Observatory requires that the angular orientations of the optics be within 10(-8) rad rms of the optical axis, and the beam must be kept centered on the mirrors within 1 mm. In addition, fluctuations in the input laser beam direction must be less than 1.5 x 10(-14) rad/ radicalHz in angle and less than 2.8 x 10(-10) m/ radicalHz in transverse displacement for frequencies f > 150 Hz in order that they not produce spurious noise in the gravitational wave readout channel. We show that seismic disturbances limit the use of local reference frames for angular alignment at a level approximately an order of magnitude worse than required. A wave-front sensing scheme that uses the input laser beam as the reference axis is presented that successfully discriminates among all angular degrees of freedom and permits the implementation of a closed-loop servo control to suppress the environmentally driven angular fluctuations sufficiently.

Principles of calculating alignment signals in complex resonant optical interferometers

In the long-baseline laser interferometers that are now under construction to measure gravitational waves, the alignment of the optical components with respect to the incoming laser beam is crucial for maintaining maximum phase sensitivity. We present a basic formalism to calculate the effects of misalignment and beam distortions analytically in an arbitrarily complex optical system, including coupled cavities and Michelson interferometer configurations coupled with cavities. The electromagnetic field is decomposed into a superposition of higher-order Gaussian modes, while misaligned and distorting optical components along with free-space propagators are represented by matrix operators that act on the state vectors in this basis. We show how to deduce useful alignment signals generally, in order to design angular control systems.

Quantum noise locking

Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, cannot rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.

Gravitational wave detector with cosmological reach

Twenty years ago, construction began on the Laser Interferometer Gravitational-wave Observatory (LIGO). Advanced LIGO, with a factor of 10 better design sensitivity than Initial LIGO, will begin taking data this year, and should soon make detections a monthly occurrence. While Advanced LIGO promises to make first detections of gravitational waves from the nearby universe, an additional factor of 10 increase in sensitivity would put exciting science targets within reach by providing observations of binary black hole inspirals throughout most of the history of star formation, and high signal to noise observations of nearby events. Design studies for future detectors to date rely on significant technological advances that are futuristic and risky. In this paper we propose a different direction. We resurrect the idea of using longer arm lengths coupled with largely proven technologies. Since the major noise sources that limit gravitational wave detectors do not scale trivially with the length of the detector, we study their impact and find that 40 km arm lengths are nearly optimal, and can incorporate currently available technologies to detect gravitational wave sources at cosmological distances ðz ≳ 7Þ.

Squeezed quadrature fluctuations in a gravitational wave detector using squeezed light

Squeezed states of light are an important tool for optical measurements below the shot noise limit and for optical realizations of quantum information systems. Recently, squeezed vacuum states were deployed to enhance the shot noise limited performance of gravitational wave detectors. In most practical implementations of squeezing enhancement, relative fluctuations between the squeezed quadrature angle and the measured quadrature (sometimes called squeezing angle jitter or phase noise) are one limit to the noise reduction that can be achieved. We present calculations of several effects that lead to quadrature fluctuations, and use these estimates to account for the observed quadrature fluctuations in a LIGO gravitational wave detector. We discuss the implications of this work for quantum enhanced advanced detectors and even more sensitive third generation detectors.

Review: Quantum noise in gravitational-wave interferometers

We present an overview of quantum noise in gravitational-wave interferometers. Current gravitational-wave detectors are modified variants of a Michelson interferometer and the quantum noise limits are strongly influenced by the optical configuration of the interferometer. We describe recent developments in the treatment of quantum noise in the complex interferometers of present-day and future gravitational-wave detectors and explore prospects for beating the standard quantum limit by use of both injected and ponderomotive squeezing in future interferometers.

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.