Quantum correlations between light and the kilogram-mass mirrors of LIGO.

The measurement of minuscule forces and displacements with ever greater precision is inhibited by the Heisenberg uncertainty principle, which imposes a limit to the precision with which the position of an object can be measured continuously, known as the standard quantum limit1-4. When light is used as the probe, the standard quantum limit arises from the balance between the uncertainties of the photon radiation pressure applied to the object and of the photon number in the photoelectric detection. The only way to surpass the standard quantum limit is by introducing correlations between the position/momentum uncertainty of the object and the photon number/phase uncertainty of the light that it reflects5. Here we confirm experimentally the theoretical prediction5 that this type of quantum correlation is naturally produced in the Laser Interferometer Gravitational-wave Observatory (LIGO). We characterize and compare noise spectra taken without squeezing and with squeezed vacuum states injected at varying quadrature angles. After subtracting classical noise, our measurements show that the quantum mechanical uncertainties in the phases of the 200-kilowatt laser beams and in the positions of the 40-kilogram mirrors of the Advanced LIGO detectors yield a joint quantum uncertainty that is a factor of 1.4 (3 decibels) below the standard quantum limit. We anticipate that the use of quantum correlations will improve not only the observation of gravitational waves, but also more broadly future quantum noise-limited measurements.

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 ∼50 Hz. Below this frequency, quantum backaction, 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 30 Hz, using a 16-m-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+."

Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy.

The Laser Interferometer Gravitational Wave Observatory (LIGO) has been directly detecting gravitational waves from compact binary mergers since 2015. We report on the first use of squeezed vacuum states in the direct measurement of gravitational waves with the Advanced LIGO H1 and L1 detectors. This achievement is the culmination of decades of research to implement squeezed states in gravitational-wave detectors. During the ongoing O3 observation run, squeezed states are improving the sensitivity of the LIGO interferometers to signals above 50 Hz by up to 3 dB, thereby increasing the expected detection rate by 40% (H1) and 50% (L1).

Relativistic coupling of phase and amplitude noise in optical interferometry.

Extraneous motion of optical elements in an interferometer leads to excess noise. Typically, fluctuations in the effective path length lead to phase noise, while beam pointing fluctuations lead to apparent amplitude noise. For a transmissive optic moving along the optical axis, neither effect should exist. However, relativity of motion suggests that, even in this case, small corrections of order v/c (v the velocity of the optic) give rise to phase and amplitude noise on the light. Here we calculate the effect of this relativistic mechanism of noise coupling and discuss when such an effect would limit the sensitivity of optical interferometers.

Continuously tunable modulation scheme for precision control of optical cavities with variable detuning.

We present a scheme for locking optical cavities with arbitrary detuning by many linewidths from resonance using an electro-optic modulator that can provide arbitrary ratios of amplitude-to-phase modulation. We demonstrate our scheme on a Fabry-Perot cavity, and show that a well-behaved linear error signal can be obtained by demodulating the reflected light from a cavity that is detuned by several linewidths.

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.

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.

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 that 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.

Lock acquisition of a gravitational-wave interferometer.

Interferometric gravitational-wave detectors, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) detectors currently under construction, are based on kilometer-scale Michelson interferometers, with sensitivity that is enhanced by addition of multiple coupled optical resonators. Reducing the relative optic motions to bring the system to the resonant operating point is a significant challenge. We present a new approach to lock acquisition, used to lock a LIGO interferometer, whereby the sensor transformation matrix is dynamically calculated to sequentially bring the cavities into resonance.

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 the addition of 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 x 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.

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.

Determination and optimization of mode matching into optical cavities by heterodyne detection.

We report on a novel high-sensitivity method to characterize and improve mode matching into optical cavities. This method is based on heterodyne detection of cylindrical transverse cavity modes. A specially designed annular-segmented photodiode is used to measure the amplitude of nonresonant modes reflected by the cavity. Our measurements allow us to optimize cavity mode matching to nearly 99.98% and will play an important diagnostic role in gravitational-wave detectors.

High-gain power recycling of a Fabry-Perot Michelson interferometer for a gravitational-wave antenna.

Power recycling was implemented on a fully suspended prototype interferometer with arm lengths of 20 m. A wave-front-sensing technique for alignment control of the suspended mirrors was also implemented, which allowed for several hours of stable operation. A power-recycling gain of greater than 12 was achieved, a significant increase over the highest gain in a suspended mirror Fabry-Perot Michelson interferometer reported to date.

Signal extraction in a power-recycled michelson interferometer with fabry-perot arm cavities by use of a multiple-carrier frontal modulation scheme.

We present a signal extraction scheme for longitudinal sensing and control of an interferometric gravitational-wave detector based on a multiple-frequency heterodyne detection technique. Gravitational-wave detectors use multiple-mirror resonant optical systems where resonance conditions must be satisfied for multiple degrees of freedom that are optically coupled. The multiple-carrier longitudinal-sensing technique provides sensitive signals for all interferometric lengths to be controlled and successfully decouples them. The feasibility of the technique is demonstrated on a tabletop-scale power-recycled Michelson interferometer with Fabry-Perot arm cavities, and the experimentally measured values of the length-sensing signals are in good agreement with theoretical calculations.

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.

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.