Global optimization of multilayer dielectric coatings for precision measurements.

We describe the design of optimized multilayer dielectric coatings for precision laser interferometry. By setting up an appropriate cost function and then using a global optimizer to find a minimum in the parameter space, we were able to realize coating designs that meet the design requirements for spectral reflectivity, thermal noise, absorption, and tolerances to coating fabrication errors. We also present application of a Markov-Chain Monte Carlo (MCMC) based parameter estimation algorithm that can infer thicknesses of dielectric layers in a coating, given a measurement of the spectral reflectivity. This technique can be a powerful diagnostic tool for both commercial coating manufacturers, and the community using dielectric mirrors for precision metrology experiments.

Quantum Precision Limits of Displacement Noise-Free Interferometers.

Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for displacement noise-free interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing; i.e., certain modes contain information about the gravitational waves but are insensitive to the mirror motion (displacement noise). We derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing.

Vacuum Beam Guide for Large Scale Quantum Networks.

The vacuum beam guide (VBG) presents a completely different solution for quantum channels to overcome the limitations of existing fiber and satellite technologies for long-distance quantum communication. With an array of aligned lenses spaced kilometers apart, the VBG offers ultrahigh transparency over a wide range of optical wavelengths. With realistic parameters, the VBG can outperform the best fiber by 3 orders of magnitude in terms of attenuation rate. Consequently, the VBG can enable long-range quantum communication over thousands of kilometers with quantum channel capacity beyond 10^{13} qubit/sec, orders of magnitude higher than the state-of-the-art quantum satellite communication rate. Remarkably, without relying on quantum repeaters, the VBG can provide a ground-based, low-loss, high-bandwidth quantum channel that enables novel distributed quantum information applications for computing, communication, and sensing.

Scattering loss in precision metrology due to mirror roughness.

Optical losses degrade the sensitivity of laser interferometric instruments. They reduce the number of signal photons and introduce technical noise associated with diffuse light. In quantum-enhanced metrology, they break the entanglement between correlated photons. Such decoherence is one of the primary obstacles in achieving high levels of quantum noise reduction in precision metrology. In this work, we compare direct measurements of cavity and mirror losses in the Caltech 40 m gravitational-wave detector prototype interferometer with numerical estimates obtained from semi-analytic intra-cavity wavefront simulations using mirror surface profile maps. We show a unified approach to estimating the total loss in optical cavities (such as the LIGO gravitational detectors) that will lead towards the engineering of systems with minimum decoherence for quantum-enhanced precision metrology.

Point absorbers in Advanced LIGO.

Small, highly absorbing points are randomly present on the surfaces of the main interferometer optics in Advanced LIGO. The resulting nanometer scale thermo-elastic deformations and substrate lenses from these micron-scale absorbers significantly reduce the sensitivity of the interferometer directly though a reduction in the power-recycling gain and indirect interactions with the feedback control system. We review the expected surface deformation from point absorbers and provide a pedagogical description of the impact on power buildup in second generation gravitational wave detectors (dual-recycled Fabry-Perot Michelson interferometers). This analysis predicts that the power-dependent reduction in interferometer performance will significantly degrade maximum stored power by up to 50% and, hence, limit GW sensitivity, but it suggests system wide corrections that can be implemented in current and future GW detectors. This is particularly pressing given that future GW detectors call for an order of magnitude more stored power than currently used in Advanced LIGO in Observing Run 3. We briefly review strategies to mitigate the effects of point absorbers in current and future GW wave detectors to maximize the success of these enterprises.

External quantum efficiency enhancement by photon recycling with backscatter evasion.

The nonunity quantum efficiency (QE) in photodiodes (PD) causes deterioration of signal quality in quantum optical experiments due to photocurrent loss as well as the introduction of vacuum fluctuations into the measurement. In this paper, we report that the external QE enhancement of a PD was demonstrated by recycling the reflected photons. The external QE for an InGaAs PD was increased by 0.01-0.06 from 0.86-0.92 over a wide range of incident angles. Moreover, we confirmed that this technique does not increase backscattered light when the recycled beam is properly misaligned.

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals.

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Probing Microplasticity in Small-Scale FCC Crystals via Dynamic Mechanical Analysis.

In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a steplike plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active preyield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply alternate current load perturbations via dynamic mechanical analysis during quasistatic uniaxial compression experiments on single crystalline Cu nanopillars with diameters of 500 nm and compute dynamic moduli at frequencies 0.1, 0.3, 1, and 10 Hz under progressively higher static loads until yielding. By tracking the collective aspects of the oscillatory stress-strain-time series in multiple samples, we observe an evolving dissipative component of the dislocation network response that signifies the transition from elastic behavior to dislocation avalanches in the globally preyield regime. We postulate that microplasticity, which is associated with the combination of dislocation avalanches and slow viscoplastic relaxations, is the cause of the dependency of dynamic modulus on the driving rate and the quasistatic stress. We construct a continuum mesoscopic dislocation dynamics model to compute the frequency response of stress over strain and obtain a consistent agreement with experimental observations. The results of our experiments and simulations present a pathway to discern and quantify correlated dislocation activity in the preyield regime of deforming crystals.

High power and ultra-low-noise photodetector for squeezed-light enhanced gravitational wave detectors.

Current laser-interferometric gravitational wave detectors employ a self-homodyne readout scheme where a comparatively large light power (5-50 mW) is detected per photosensitive element. For best sensitivity to gravitational waves, signal levels as low as the quantum shot noise have to be measured as accurately as possible. The electronic noise of the detection circuit can produce a relevant limit to this accuracy, in particular when squeezed states of light are used to reduce the quantum noise. We present a new electronic circuit design reducing the electronic noise of the photodetection circuit in the audio band. In the application of this circuit at the gravitational-wave detector GEO 600 the shot-noise to electronic noise ratio was permanently improved by a factor of more than 4 above 1 kHz, while the dynamic range was improved by a factor of 7. The noise equivalent photocurrent of the implemented photodetector and circuit is about 5µA/Hz above 1 kHz with a maximum detectable photocurrent of 20 mA. With the new circuit, the observed squeezing level in GEO 600 increased by 0.2 dB. The new circuit also creates headroom for higher laser power and more squeezing to be observed in the future in GEO 600 and is applicable to other optics experiments.

Observation of Parametric Instability in Advanced LIGO.

Parametric instabilities have long been studied as a potentially limiting effect in high-power interferometric gravitational wave detectors. Until now, however, these instabilities have never been observed in a kilometer-scale interferometer. In this Letter, we describe the first observation of parametric instability in a gravitational wave detector, and the means by which it has been removed as a barrier to progress.

Residual amplitude modulation in interferometric gravitational wave detectors.

The effects of residual amplitude modulation (RAM) in laser interferometers using heterodyne sensing can be substantial and difficult to mitigate. In this work, we analyze the effects of RAM on a complex laser interferometer used for gravitational wave detection. The RAM introduces unwanted offsets in the cavity length signals and thereby shifts the operating point of the optical cavities from the nominal point via feedback control. This shift causes variations in the sensing matrix, and leads to degradation in the performance of the precision noise subtraction scheme of the multiple-degree-of-freedom control system. In addition, such detuned optical cavities produce an optomechanical spring, which also perturbs the sensing matrix. We use our simulations to derive requirements on RAM for the Advanced LIGO (aLIGO) detectors, and show that the RAM expected in aLIGO will not limit its sensitivity.

Angular control of optical cavities in a radiation-pressure-dominated regime: the Enhanced LIGO case.

We describe the angular sensing and control (ASC) of 4 km detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO). Enhanced LIGO, the culmination of the first generation LIGO detectors, operated between 2009 and 2010 with about 40 kW of laser power in the arm cavities. In this regime, radiation-pressure effects are significant and induce instabilities in the angular opto-mechanical transfer functions. Here we present and motivate the ASC design in this extreme case and present the results of its implementation in Enhanced LIGO. Highlights of the ASC performance are successful control of opto-mechanical torsional modes, relative mirror motions of ≤ 1×10(-7) rad rms, and limited impact on in-band strain sensitivity.

Large-angle scattered light measurements for quantum-noise filter cavity design studies.

Optical loss from scattered light could limit the performance of quantum-noise filter cavities being considered for an upgrade to the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO) gravitational-wave detectors. This paper describes imaging scatterometer measurements of the large-angle scattered light from two high-quality sample optics, a high reflector and a beamsplitter. These optics are each superpolished fused silica substrates with silica:tantala dielectric coatings. They represent the current state-of-the art optical technology for use in filter cavities. We present angle-resolved scatter values and integrate these to estimate the total scatter over the measured angles. We find that the total integrated light scattered into larger angles can be as small as 4 ppm.

Multicolor cavity metrology.

Long-baseline laser interferometers used for gravitational-wave detection have proven to be very complicated to control. In order to have sufficient sensitivity to astrophysical gravitational waves, a set of multiple coupled optical cavities comprising the interferometer must be brought into resonance with the laser field. A set of multi-input, multi-output servos then lock these cavities into place via feedback control. This procedure, known as lock acquisition, has proven to be a vexing problem and has reduced greatly the reliability and duty factor of the past generation of laser interferometers. In this article, we describe a technique for bringing the interferometer from an uncontrolled state into resonance by using harmonically related external fields to provide a deterministic hierarchical control. This technique reduces the effect of the external seismic disturbances by 4 orders of magnitude and promises to greatly enhance the stability and reliability of the current generation of gravitational-wave detectors. The possibility for using multicolor techniques to overcome current quantum and thermal noise limits is also discussed.

Technique for in situ measurement of free spectral range and transverse mode spacing of optical cavities.

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational-wave interferometers. This technique and the results of its application to the coupled cavities of a 40 m-long gravitational-wave interferometer prototype are presented here.

Nonlinear Noise Cleaning in Gravitational-Wave Detectors With Convolutional Neural Networks.

Currently, the sub-60 Hz sensitivity of gravitational-wave (GW) detectors like Advanced LIGO (aLIGO) is limited by the control noises from auxiliary degrees of freedom which nonlinearly couple to the main GW readout. One promising way to tackle this challenge is to perform nonlinear noise mitigation using convolutional neural networks (CNNs), which we examine in detail in this study. In many cases, the noise coupling is bilinear and can be viewed as a few fast channels' outputs modulated by some slow channels. We show that we can utilize this knowledge of the physical system and adopt an explicit "slow×fast" structure in the design of the CNN to enhance its performance of noise subtraction. We then examine the requirements in the signal-to-noise ratio (SNR) in both the target channel (i.e., the main GW readout) and in the auxiliary sensors in order to reduce the noise by at least a factor of a few. In the case of limited SNR in the target channel, we further demonstrate that the CNN can still reach a good performance if we use curriculum learning techniques, which in reality can be achieved by combining data from quiet times and those from periods with active noise injections.