Single and coupled cavity mode sensing schemes using a diagnostic field.

Precise optical mode matching is of critical importance in experiments using squeezed-vacuum states. Automatic spatial-mode matching schemes have the potential to reduce losses and improve loss stability. However, in quantum-enhanced coupled-cavity experiments, such as gravitational-wave detectors, one must also ensure that the sub-cavities are also mode matched. We propose what we believe to be a new mode sensing scheme, which works for simple and coupled cavities. The scheme requires no moving parts, nor tuning of Gouy phases. Instead a diagnostic field tuned to the HG20/LG10 mode frequency is used. The error signals are derived to be proportional to the difference in waist position, and difference in Rayleigh ranges, between the sub-cavity eigenmodes. The two error signals are separable by 90 degrees of demodulation phase. We demonstrate reasonable error signals for a simplified Einstein Telescope optical design. This work will facilitate routine use of extremely high levels of squeezing in current and future gravitational-wave detectors.

Observing the optical modes of parametric instability.

Parametric instability (PI) is a phenomenon that results from resonant interactions between optical and acoustic modes of a laser cavity. This is problematic in gravitational wave interferometers where the high intracavity power and low mechanical loss mirror suspension systems create an environment where three-mode PI will occur without intervention. We demonstrate a technique for real-time imaging of the amplitude and phase of the optical modes of PI yielding, to the best of the authors' knowledge, the first ever images of this phenomenon which could form part of active control strategies for future detectors.

Revealing optical loss from modal frequency degeneracy in a long optical cavity.

Optical loss plays a significant role in optical experiments involving optical cavities such as recycling cavities and filter cavities in laser interferometer gravitational-wave detectors. For those cavities, modal frequency degeneracy, where the fundamental and a higher order mode resonate inside the cavity simultaneously, is a potential mechanism which may bring extra optical loss to the cavity thus degrade detection sensitivity. In this paper, we report observation of modal frequency degeneracy in a large-scale suspended Fabry-Pérot cavity. The cavity g-factor is tuned by a CO2 laser heating one test mass, and the cavity finesse is obtained from a ring-down measurement of the transmitted light. We demonstrate that the modal frequency degeneracy can cause a reduction of the cavity finesse by up to ∼30%, corresponding to a ∼2-fold increase in total optical loss. To minimize optical loss in gravitational-wave detectors, the effect of modal frequency degeneracy needs to be taken into account in the design and operation of the detector.

Two dimensional photonic crystal angle sensor design.

We present a novel design for an angle sensor based on photon coupling to internal optical modes of a two dimensional photonic crystal. We show in simulation that an implementation of this design could achieve sensitivities as high as 1.61 × 106 V/rad, which in principle allows for angle measurements with a noise floor of 2.98 × 10-14 rad$/\sqrt{\textrm{Hz}}$ at the photodiode noise equivalent power. We discuss the limitations of this design and predict the impact these limitations have on the sensitivity as well as the possible ways to further increase the devices sensitivity. As a proof of concept, we demonstrate experimentally a photonic crystal with an angle sensitive mode.

Pump RIN coupling to frequency noise of a polarization-maintaining 2 µm single frequency fiber laser.

We investigated the frequency noise coupling mechanism of a 2 µm polarization-maintaining single frequency fiber laser (SFFL) theoretically and experimentally. The coupling of pump's relative intensity noise (RIN) to frequency noise of a single-frequency high-gain silica fiber laser is shown experimentally to be consistent with a theoretical model where thermal expansion and thermo-optic effect mediate the coupling. The measured and theoretical frequency noise of the 2 µm SFFL with three pump sources is compared. We find using a 1550 nm single frequency laser pump source produces the lowest frequency noise, less than 100 Hz/Hz at frequencies higher than 100 Hz.

5 W ultra-low-noise 2 µm single-frequency fiber laser for next-generation gravitational wave detectors.

We demonstrated an ultra-low-noise polarization-maintaining (PM) single-frequency fiber laser at 2 µm. Both relative intensity noise (RIN) and frequency noise were improved by suppressing the pump source RIN using feedback control. After a two-stage Tm3+-doped PM fiber amplifier, the output power reached about 5 W, and the amplifier did not introduce any observable extra frequency noise. The frequency noise was less than 100Hz/Hz above 13 Hz, which is comparable to the frequency noise of a typical seed laser of the Advanced LIGO high-power laser. The central wavelength was measured to be 1990.25 nm, with a polarization extinction ratio above 24 dB.

Modular suspension system with low acoustic coupling to the suspended test mass in a prototype gravitational wave detector.

Low acoustic loss suspension systems are essential components in low thermal noise instruments including gravitational wave detectors. Monolithic fused silica suspensions have been used successfully with fused silica test masses but may not be suitable in next generation detectors that may use sapphire or silicon test masses. Here we report a study of a modular suspension system with high replaceability. The system is based on high pressure gravitationally attached mechanical contacts which have been previously shown to contribute low acoustic losses to sapphire resonators. Here we combine high pressure contacts with cantilevers and fibres to create sets of four suspension modules which are shown to have low loss contributions to fused silica test masses in a 74-m high-finesse optical cavity. Results are combined with finite element simulations to estimate the strain energy distributions of the eigenmodes. By combining the simulations and measurement results, the test mass loss angle due to the coupling to the suspension system was estimated. The modular suspension system is shown to contribute <10% to the total test mass acoustic loss. Such suspension systems could have applications for test masses or subsystems in next generation gravitational wave detectors.

First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO.

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electrostatic actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nN was required to maintain the acoustic mode at its minimum amplitude.

Enhancing the Bandwidth of Gravitational-Wave Detectors with Unstable Optomechanical Filters.

Advanced interferometric gravitational-wave detectors use optical cavities to resonantly enhance their shot-noise-limited sensitivity. Because of positive dispersion of these cavities-signals at different frequencies pick up different phases, there is a tradeoff between the detector bandwidth and peak sensitivity, which is a universal feature for quantum measurement devices having resonant cavities. We consider embedding an active unstable filter inside the interferometer to compensate the phase, and using feedback control to stabilize the entire system. We show that this scheme in principle can enhance the bandwidth without sacrificing the peak sensitivity. However, the unstable filter under our current consideration is a cavity-assisted optomechanical device operating in the instability regime, and the thermal fluctuation of the mechanical oscillator puts a very stringent requirement on the environmental temperature and the mechanical quality factor.

Linear negative dispersion with a gain doublet via optomechanical interactions.

Optical cavities containing a negative dispersion medium have been proposed as a means of improving the sensitivity of laser interferometric gravitational wave detectors through the creation of white-light signal recycling cavities. Here we demonstrate that negative dispersion can be realized using an optomechanical cavity pumped by a blue detuned doublet. We used an 85-mm cavity with an intracavity silicon nitride membrane. Tunable negative dispersion is demonstrated, with a phase derivative dφ/df from -0.14 Deg·Hz(-1) to -4.2×10(-3) Deg·Hz(-1).

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.

Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction.

We propose using optomechanical interaction to narrow the bandwidth of filter cavities for achieving frequency-dependent squeezing in advanced gravitational-wave detectors, inspired by the idea of optomechanically induced transparency. This can allow us to achieve a cavity bandwidth on the order of 100 Hz using small-scale cavities. Additionally, in contrast to a passive Fabry-Pérot cavity, the resulting cavity bandwidth can be dynamically tuned, which is useful for adaptively optimizing the detector sensitivity when switching amongst different operational modes. The experimental challenge for its implementation is a stringent requirement for very low thermal noise of the mechanical oscillator, which would need a superb mechanical quality factor and a very low temperature. We consider one possible setup to relieve this requirement by using optical dilution to enhance the mechanical quality factor.

Compact vibration isolation and suspension for Australian International Gravitational Observatory: local control system.

High performance vibration isolators are required for ground based gravitational wave detectors. To attain very high performance at low frequencies we have developed multistage isolators for the proposed Australian International Gravitational Observatory detector in Australia. New concepts in vibration isolation including self-damping, Euler springs, LaCoste springs, Roberts linkages, and double preisolation require novel sensors and actuators. Double preisolation enables internal feedback to be used to suppress low frequency seismic noise. Multidegree of freedom control systems are required to attain high performance. Here we describe the control components and control systems used to control all degrees of freedom. Feedback forces are injected at the preisolation stages and at the penultimate suspension stage. There is no direct actuation on test masses. A digital local control system hosted on a digital signal processor maintains alignment and position, corrects drifts, and damps the low frequency linear and torsional modes without exciting the very high Q-factor test mass suspension. The control system maintains an optical cavity locked to a laser with a high duty cycle even in the absence of an autoalignment system. An accompanying paper presents the mechanics of the system, and the optical cavity used to determine isolation performance. A feedback method is presented, which is expected to improve the residual motion at 1 Hz by more than one order of magnitude.

Three-mode optoacoustic parametric amplifier: a tool for macroscopic quantum experiments.

We introduce the three-mode optoacoustic parametric amplifier (OAPA), a close analog of the optical parametric amplifier, for macroscopic quantum mechanics experiments. The radiation pressure reaction of light on the reflective surface of an acoustic resonator provides a nonlinearity similar to the Kerr effect in the optical parametric amplifier. The OAPA can be tuned to operate in a positive gain regime where acoustic signals are amplified or in a negative gain regime where acoustic modes are cooled. Compared with conventional optoacoustic devices, (i) the OAPA incorporates two transverse cavity modes such that the carrier and sideband fields simultaneously resonate, and (ii) it is less susceptible to the laser phase and amplitude noise. These two features significantly ease the experimental requirements for cooling of acoustic modes to their quantum-ground state and creating entangled pairs of phonons and photons.

Optical design of the proposed Australian International Gravitational Observatory.

Marginally stable power recycling cavities are being used by nearly all interferometric gravitational wave detectors.With stability factors very close to unity the frequency separation of the higher order optical modes is smaller than the cavity bandwidth. As a consequence these higher order modes will resonate inside the cavity distorting the spatial mode of the interferometer control sidebands. Without losing generality we study and compare two designs of stable power recycling cavities for the proposed 5 kilometer long Australian International Gravitational Observatory (AIGO), a high power advanced interferometric gravitational wave detector. The length of various optical cavities that form the interferometer and the modulation frequencies that generate the control sidebands are also selected.

Direct measurement of absorption-induced wavefront distortion in high optical power systems.

Wavefront distortion due to absorption in the substrates and coatings of mirrors in advanced gravitational wave interferometers has the potential to compromise the operation and sensitivity of these interferometers [Opt. Lett.29, 2635-2637 (2004)]. We report the first direct spatially-resolved measurement, to our knowledge, of such wavefront distortion in a high optical power cavity. The measurement was made using an ultrahigh sensitivity Hartmann wavefront sensor on a dedicated test facility. The sensitivity of the sensor was lambda/730, where lambda=800 nm.

Rayleigh scattering, absorption, and birefringence of large-size bulk single-crystal sapphire.

While the thermomechanical properties of sapphire make it an excellent candidate of test mass for advanced laser interferometers, its optical quality is not well understood or well controlled. We have studied the results from high-resolution measurements of scattering, absorption, and birefringence in test-mass samples to better understand issues of quality. Samples show large-scale scattering structures clearly linked to the crystal-growth process. Samples characterized by the presence of point defects have significantly lower scattering (except at the point defects). In general on a large scale, high scattering also correlates with higher absorption and higher average birefringence inhomogeneity. However, on a smaller scale there is not a clear point-to-point correlation between scattering and absorption. Often a large-scale scattering structure is spatially displaced by tens of millimeters from a similar absorption structure, indicating that quite separate microscopic mechanisms give rise to scattering and absorption. The spatial displacements indicate that absorption centers and scattering centers are laid down during crystal growth at different distances from the solid-liquid interface. We suggest that absorption may be linked to F centers, while scattering may be linked to impurities such as iron.