Sensor Noise in LISA Pathfinder: In-Flight Performance of the Optical Test Mass Readout.

We report on the first subpicometer interferometer flown in space. It was part of ESA's Laser Interferometer Space Antenna (LISA) Pathfinder mission and performed the fundamental measurement of the positional and angular motion of two free-falling test masses. The interferometer worked immediately, stably, and reliably from switch on until the end of the mission with exceptionally low residual noise of 32.0_{-1.7}^{+2.4} fm/sqrt[Hz], significantly better than required. We present an upper limit for the sensor performance at millihertz frequencies and a model for the measured sensitivity above 200 mHz.

Analysis of the accuracy of actuation electronics in the laser interferometer space antenna pathfinder.

The Laser Interferometer Space Antenna Pathfinder (LPF) main observable, labeled Δg, is the differential force per unit mass acting on the two test masses under free fall conditions after the contribution of all non-gravitational forces has been compensated. At low frequencies, the differential force is compensated by an applied electrostatic actuation force, which then must be subtracted from the measured acceleration to obtain Δg. Any inaccuracy in the actuation force contaminates the residual acceleration. This study investigates the accuracy of the electrostatic actuation system and its impact on the LPF main observable. It is shown that the inaccuracy is mainly caused by the rounding errors in the waveform processing and also by the random error caused by the analog to digital converter random noise in the control loop. Both errors are one order of magnitude smaller than the resolution of the commanded voltages. We developed a simulator based on the LPF design to compute the close-to-reality actuation voltages and, consequently, the resulting actuation forces. The simulator is applied during post-processing the LPF data.

LISA Pathfinder Performance Confirmed in an Open-Loop Configuration: Results from the Free-Fall Actuation Mode.

We report on the results of the LISA Pathfinder (LPF) free-fall mode experiment, in which the control force needed to compensate the quasistatic differential force acting on two test masses is applied intermittently as a series of "impulse" forces lasting a few seconds and separated by roughly 350 s periods of true free fall. This represents an alternative to the normal LPF mode of operation in which this balancing force is applied continuously, with the advantage that the acceleration noise during free fall is measured in the absence of the actuation force, thus eliminating associated noise and force calibration errors. The differential acceleration noise measurement presented here with the free-fall mode agrees with noise measured with the continuous actuation scheme, representing an important and independent confirmation of the LPF result. An additional measurement with larger actuation forces also shows that the technique can be used to eliminate actuation noise when this is a dominant factor.

Matrix heater in the gravitational wave observatory GEO 600.

Large scale laser interferometric gravitational wave detectors (GWDs), such as GEO 600 require high quality optics to reach their design sensitivity. The inevitable surface imperfections, inhomogeneities, and light-absorption induced thermal lensing in the optics, can convert laser light from the fundamental mode to unwanted higher order modes, and pose challenges to the operation and sensitivity of the GWDs. Here we demonstrate the practical implementation of a thermal projection system which reduces those unwanted effects via targeted spatial heating of the optics. The thermal projector consists of 108 individually addressable heating elements which are imaged onto the beam splitter of GEO 600. We describe the optimization of the spatial heating profile and present the obtained results.

Beyond the Required LISA Free-Fall Performance: New LISA Pathfinder Results down to 20 µHz.

In the months since the publication of the first results, the noise performance of LISA Pathfinder has improved because of reduced Brownian noise due to the continued decrease in pressure around the test masses, from a better correction of noninertial effects, and from a better calibration of the electrostatic force actuation. In addition, the availability of numerous long noise measurement runs, during which no perturbation is purposely applied to the test masses, has allowed the measurement of noise with good statistics down to 20 µHz. The Letter presents the measured differential acceleration noise figure, which is at (1.74±0.05) fm s^{-2}/sqrt[Hz] above 2 mHz and (6±1)×10 fm s^{-2}/sqrt[Hz] at 20 µHz, and discusses the physical sources for the measured noise. This performance provides an experimental benchmark demonstrating the ability to realize the low-frequency science potential of the LISA mission, recently selected by the European Space Agency.

Charge-Induced Force Noise on Free-Falling Test Masses: Results from LISA Pathfinder.

We report on electrostatic measurements made on board the European Space Agency mission LISA Pathfinder. Detailed measurements of the charge-induced electrostatic forces exerted on free-falling test masses (TMs) inside the capacitive gravitational reference sensor are the first made in a relevant environment for a space-based gravitational wave detector. Employing a combination of charge control and electric-field compensation, we show that the level of charge-induced acceleration noise on a single TM can be maintained at a level close to 1.0 fm s^{-2} Hz^{-1/2} across the 0.1-100 mHz frequency band that is crucial to an observatory such as the Laser Interferometer Space Antenna (LISA). Using dedicated measurements that detect these effects in the differential acceleration between the two test masses, we resolve the stochastic nature of the TM charge buildup due to interplanetary cosmic rays and the TM charge-to-force coupling through stray electric fields in the sensor. All our measurements are in good agreement with predictions based on a relatively simple electrostatic model of the LISA Pathfinder instrument.

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.

Effects of transients in LIGO suspensions on searches for gravitational waves.

This paper presents an analysis of the transient behavior of the Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) suspensions used to seismically isolate the optics. We have characterized the transients in the longitudinal motion of the quadruple suspensions during Advanced LIGO's first observing run. Propagation of transients between stages is consistent with modeled transfer functions, such that transient motion originating at the top of the suspension chain is significantly reduced in amplitude at the test mass. We find that there are transients seen by the longitudinal motion monitors of quadruple suspensions, but they are not significantly correlated with transient motion above the noise floor in the gravitational wave strain data, and therefore do not present a dominant source of background noise in the searches for transient gravitational wave signals. Using the suspension transfer functions, we compared the transients in a week of gravitational wave strain data with transients from a quadruple suspension. Of the strain transients between 10 and 60 Hz, 84% are loud enough that they would have appeared above the sensor noise in the top stage quadruple suspension monitors if they had originated at that stage at the same frequencies. We find no significant temporal correlation with the suspension transients in that stage, so we can rule out suspension motion originating at the top stage as the cause of those transients. However, only 3.2% of the gravitational wave strain transients are loud enough that they would have been seen by the second stage suspension sensors, and none of them are above the sensor noise levels of the penultimate stage. Therefore, we cannot eliminate the possibility of transient noise in the detectors originating in the intermediate stages of the suspension below the sensing noise.

Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results.

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2±0.1 fm s^{-2}/sqrt[Hz], or (0.54±0.01)×10^{-15} g/sqrt[Hz], with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8±0.3) fm/sqrt[Hz], about 2 orders of magnitude better than requirements. At f≤0.5 mHz we observe a low-frequency tail that stays below 12 fm s^{-2}/sqrt[Hz] down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

Alignment sensing and control for squeezed vacuum states of light.

Beam alignment is an important practical aspect of the application of squeezed states of light. Misalignments in the detection of squeezed light result in a reduction of the observable squeezing level. In the case of squeezed vacuum fields that contain only very few photons, special measures must be taken in order to sense and control the alignment of the essentially dark beam. The GEO 600 gravitational wave detector employs a squeezed vacuum source to improve its detection sensitivity beyond the limits set by classical quantum shot noise. Here, we present our design and implementation of an alignment sensing and control scheme that ensures continuous optimal alignment of the squeezed vacuum field at GEO 600 on long time scales in the presence of free-swinging optics. This first demonstration of a squeezed light automatic alignment system will be of particular interest for future long-term applications of squeezed vacuum states of light.

First long-term application of squeezed states of light in a gravitational-wave observatory.

We report on the first long-term application of squeezed vacuum states of light to improve the shot-noise-limited sensitivity of a gravitational-wave observatory. In particular, squeezed vacuum was applied to the German-British detector GEO 600 during a period of three months from June to August 2011, when GEO 600 was performing an observational run together with the French-Italian Virgo detector. In a second period, the squeezing application continued for about 11 months from November 2011 to October 2012. During this time, squeezed vacuum was applied for 90.2% (205.2 days total) of the time that science-quality data were acquired with GEO 600. A sensitivity increase from squeezed vacuum application was observed broadband above 400 Hz. The time average of gain in sensitivity was 26% (2.0 dB), determined in the frequency band from 3.7 to 4.0 kHz. This corresponds to a factor of 2 increase in the observed volume of the Universe for sources in the kHz region (e.g., supernovae, magnetars). We introduce three new techniques to enable the long-term application of squeezed light, and show that the glitch rate of the detector did not increase from squeezing application. Squeezed vacuum states of light have arrived as a permanent application, capable of increasing the astrophysical reach of gravitational-wave detectors.

External-cavity diode laser in second-order Littrow configuration.

In this Letter, we propose and demonstrate an external-cavity diode laser in second-order Littrow configuration. This topology utilizes a low-efficiency diffraction grating to establish a high-finesse external cavity, strong optical feedback, a high polarization discrimination, and a circular TEM00 output mode. In our proof-of-concept experiment, we realized a cavity with a finesse of 1855, being, to the best of our knowledge, the highest value ever reported for a three-port-grating-coupled cavity. With optical feedback, the laser threshold of the laser diode employed was reduced by a factor of 4.

Stabilized high-power laser system for the gravitational wave detector advanced LIGO.

An ultra-stable, high-power cw Nd:YAG laser system, developed for the ground-based gravitational wave detector Advanced LIGO (Laser Interferometer Gravitational-Wave Observatory), was comprehensively characterized. Laser power, frequency, beam pointing and beam quality were simultaneously stabilized using different active and passive schemes. The output beam, the performance of the stabilization, and the cross-coupling between different stabilization feedback control loops were characterized and found to fulfill most design requirements. The employed stabilization schemes and the achieved performance are of relevance to many high-precision optical experiments.

Translational, rotational, and vibrational coupling into phase in diffractively coupled optical cavities.

All-reflective optical systems are under consideration for future gravitational wave detector topologies. A key feature of these all-reflective systems is the use of Fabry-Perot cavities with diffraction gratings as input couplers; however, theory predicts and experiment has shown that translation of the grating surface across the incident laser light will introduce additional phase into the system. This translation can be induced through simple side-to-side motion of the coupler, yaw motion of the coupler around a central point (i.e., rotation about a vertical axis), and even via internal resonances (i.e., vibration) of the optical element. In this Letter we demonstrate on a prototype-scale suspended cavity that conventional cavity length-sensing techniques used to detect longitudinal changes along the cavity axis will also be sensitive to translational, rotational, and vibrational motion of the diffractive input coupler. We also experimentally verify the amplitude response and frequency dependency of the noise coupling as given by theory.

Differential phase-noise properties of a ytterbium-doped fiber amplifier for the Laser Interferometer Space Antenna.

The interferometric gravitational-wave detector Laser Interferometer Space Antenna (LISA) needs to transfer clock information among its three spacecraft in the form of phase-modulation sidebands. For this reason phase noise introduced by the optical chain between the carrier and a sideband must be low. We have measured this differential phase noise for a ytterbium-doped fiber amplifier emitting up to 2 W. For 1 W of output power as required for LISA, the measured differential phase noise was within its requirement. For 2 W output power the amplifier exhibited stimulated Brillouin scattering and showed a differential phase-noise factor of up to 15 higher. Dependencies on operating parameters and optical length noise of the amplifier were also measured.

Experimental demonstration of a suspended diffractively coupled optical cavity.

All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry-Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound-Drever-Hall length sensing and control techniques to maintain the required operating condition.

Detuned Twin-Signal-Recycling for ultrahigh-precision interferometers.

We propose a new interferometer technique for high-precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provide identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single-sideband recycling topologies of current and planned gravitational wave detectors. Furthermore, the application of squeezed states of light becomes less demanding.

Demonstration of three-port grating phase relations.

We experimentally demonstrate the phase relations of three-port gratings by investigating three-port coupled Fabry-Perot cavities. Two different gratings that have the same first-order diffraction efficiency but differ substantially in their second-order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities, we could validate the results of an earlier theoretical description of the phases at a three-port grating [Opt. Lett. 30, 1183 (2005)].

Optical characterization of ultrahigh diffraction efficiency gratings.

We report on the optical characterization of an ultrahigh diffraction efficiency grating in a first-order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high-reflection mirror. The measurement of the cavity finesse provided precise information about the grating's diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635+/-0.016)% and an overall optical loss due to scattering and absorption of just 0.185%. Such high-quality gratings, including the tool used for their characterization, might apply for future gravitational wave detectors. For example, the demonstrated cavity itself presents an all-reflective, low-loss Fabry-Perot resonator that might replace conventional arm cavities in advanced high-power Michelson interferometers.

Three-port beam splitters-combiners for interferometer applications.

We derive generic phase and amplitude coupling relations for beam splitters-combiners that couple a single port with three output ports or input ports, respectively. We apply the coupling relations to a reflection grating that serves as a coupler to a single-ended Fabry-Perot ring cavity. In the impedance-matched case such an interferometer can act as an all-reflective ring mode cleaner. It is further shown that in the highly undercoupled case almost complete separation of carrier power and phase signal from a cavity strain can be achieved.