James Ira Thorpe

Laser Frequency Stabilization and Control through Offset Sideband Locking to Optical Cavities

We describe a class of techniques whereby a laser frequency can be stabilized to a fixed optical cavity resonance with an adjustable offset, providing a wide tuning range for the central frequency. These techniques require only minor modifications to the standard Pound-Drever-Hall locking techniques and have the advantage of not altering the intrinsic stability of the frequency reference. We discuss the expected performance and limitations of these techniques and present a laboratory investigation in which both the sideband techniques and the standard, on-tunable Pound-Drever- Hall technique reached the 100Hz/square root(Hz) level.

Impact of mergers on LISA parameter estimation for nonspinning black hole binaries

We investigate the precision with which the parameters describing the characteristics and location of nonspinning black hole binaries can be measured with the Laser Interferometer Space Antenna (LISA). By using complete waveforms including the inspiral, merger, and ringdown portions of the signals, we find that LISA will have far greater precision than previous estimates for nonspinning mergers that ignored the merger and ringdown. Our analysis covers nonspinning waveforms with moderate mass ratios, q{>=}1/10, and total masses 10{sup 5} < or approx. M/M{sub {center_dot}}< or approx. 10{sup 7}. We compare the parameter uncertainties using the Fisher-matrix formalism, and establish the significance of mass asymmetry and higher-order content to the predicted parameter uncertainties resulting from inclusion of the merger. In real-time observations, the later parts of the signal lead to significant improvements in sky-position precision in the last hours and even the final minutes of observation. For comparable-mass systems with total mass M/M{sub {center_dot}{approx}1}0{sup 6}, we find that the increased precision resulting from including the merger is comparable to the increase in signal-to-noise ratio. For the most precise systems under investigation, half can be localized to within O(10 arcmin), and 10% can be localized to within O(1 arcmin).

The LISA benchtop simulator at the University of Florida

At the University of Florida, we are developing an experimental Laser Interferometer Space Antenna (LISA) simulator. The foundation for the simulator is a pair of cavity-stabilized lasers that provide realistic, LISA-like phase noise. The light travel time over the five million kilometres between spacecraft is recreated in the lab by use of an electronic phase delay technique. Initial tests will focus on phasemeter implementation, time delay interferometry (TDI) and arm-locking. In this paper we present the frequency stabilization results, results from an electronic arm-locking experiment, software phasemeter performance and results from a first optical experiment to test the TDI concept. In the future, the benchtop simulator will be extended to test several other aspects of LISA interferometry such as clock noise and Doppler shifts of the signals. The eventual long-term use of the LISA simulator will be to provide realistic data streams, including all the noise components, into which model gravitational wave signals can be injected. This will make the simulator a useful testbed for data analysis research groups.

Frequency-tunable pre-stabilized lasers for LISA via sideband locking

Laser frequency noise mitigation is one of the most challenging aspects of the LISA interferometric measurement system. The unstabilized frequency fluctuations must be suppressed by roughly 12 orders of magnitude in order to achieve stability sufficient for gravitational wave detection. This enormous suppression will be achieved through a combination of stabilization and common-mode rejection techniques. The stabilization component will itself be achieved in two stages: pre-stabilization to a local optical reference followed by arm locking to some combination of the inter-spacecraft distances. In order for these two stabilization stages to work simultaneously, the lock-point of the pre-stabilization loop must be frequency tunable. The current baseline stabilization technique, Pound–Drever–Hall locking to an optical cavity, does not provide tunability between cavity resonances. Here we present a modification to the baseline technique that allows the laser to be locked to a cavity resonance with an adjustable frequency offset. This technique requires no modifications to the optical cavity itself, thus preserving the stability of the frequency reference. We present measurements of the system performance and demonstrate that the offset locking techniques are compatible with arm locking.

Implementation of armlocking with a delay of 1 second in the presence of Doppler shifts

LISA relies on several techniques to reduce the initial laser frequency noise in order to achieve an interferometric length measurement with an accuracy of ≈ 10pm/. LISA will use ultra-stable reference cavities as a first step to reduce the laser frequency noise. In a second step the frequency will be stabilized to the LISA arms which provide a better reference in the frequency band of interest. We present experimental results demonstrating Arm locking with LISA-like light travel times and Doppler shifts. We also integrated this system with a LISA-like pre-stabilization system using our ultra-stable cavities. The addition of realistic Doppler shifts led to further refinements of the arm locking controllers compared to the controller architecture discussed in the past. A first experimental result of the new controller is also presented.

Electronic phase delay—a first step towards a bench-top model of LISA

Electronic phase delay (EPD), a new technique for delaying the phase of a signal by an arbitrary amount, is presented as the basis for a model of the Laser Interferometer Space Antenna (LISA). The validity of EPD is demonstrated by constructing a synthetic interferometer (SI) with a single-arm time delay of 1 s. Schemes for studying the phase noise reduction techniques of arm-locking and time delay interferometry using EPD units are presented and discussed, with preliminary results for arm-locking. EPD can also be used as the basis for a bench-top model of LISA which will be used to study LISA interferometry and data analysis methods.

Data series subtraction with unknown and unmodeled background noise

LISA Pathfinder (LPF), the precursor mission to a gravitational wave observatory of the European Space Agency, will measure the degree to which two test masses can be put into free fall, aiming to demonstrate a suppression of disturbance forces corresponding to a residual relative acceleration with a power spectral density (PSD) below (30 fm/sq s/Hz)(sup 2) around 1 mHz. In LPF data analysis, the disturbance forces are obtained as the difference between the acceleration data and a linear combination of other measured data series. In many circumstances, the coefficients for this linear combination are obtained by fitting these data series to the acceleration, and the disturbance forces appear then as the data series of the residuals of the fit. Thus the background noise or, more precisely, its PSD, whose knowledge is needed to build up the likelihood function in ordinary maximum likelihood fitting, is here unknown, and its estimate constitutes instead one of the goals of the fit. In this paper we present a fitting method that does not require the knowledge of the PSD of the background noise. The method is based on the analytical marginalization of the posterior parameter probability density with respect to the background noise PSD, and returns an estimate both for the fitting parameters and for the PSD. We show that both these estimates are unbiased, and that, when using averaged Welchs periodograms for the residuals, the estimate of the PSD is consistent, as its error tends to zero with the inverse square root of the number of averaged periodograms. Additionally, we find that the method is equivalent to some implementations of iteratively reweighted least-squares fitting. We have tested the method both on simulated data of known PSD and on data from several experiments performed with the LISA Pathfinder end-to-end mission simulator.

Comparison of Atom Interferometers and Light Interferometers as Space-Based Gravitational Wave Detectors

We consider a class of proposed gravitational-wave detectors based on multiple atomic interferometers separated by large baselines and referenced by common laser systems. We compute the sensitivity limits of these detectors due to intrinsic phase noise of the light sources, noninertial motion of the light sources, and atomic shot noise and compare them to sensitivity limits for traditional light interferometers. We find that atom interferometers and light interferometers are limited in a nearly identical way by intrinsic phase noise and that both require similar mitigation strategies (e.g., multiple-arm instruments) to reach interesting sensitivities. The sensitivity limit from motion of the light sources is slightly different and, in principle, favors the atom interferometers in the low-frequency limit, although the limit in both cases is severe.

LISA Parameter Estimation using Numerical Merger Waveforms

Recent advances in numerical relativity provide a detailed description of the waveforms of coalescing massive black hole binaries (MBHBs), expected to be the strongest detectable LISA sources. We present a preliminary study of LISAs sensitivity to MBHB parameters using a hybrid numerical/analytic waveform for equal-mass, non-spinning holes. The Synthetic LISA software package is used to simulate the instrument response, and the Fisher information matrix method is used to estimate errors in the parameters. Initial results indicate that inclusion of the merger signal can significantly improve the precision of some parameter estimates. For example, the median parameter errors for an ensemble of systems with total redshifted mass of 106 M⊙ at a redshift of z ~ 1 were found to decrease by a factor of slightly more than two for signals with merger as compared to signals truncated at the Schwarzchild ISCO.

First step toward a benchtop model of the Laser Interferometer Space Antenna

A technique for simulating large optical path lengths by use of digital delay buffers is presented. This technique is used to generate a synthetic interferometer with one arm having an arbitrary length. The response of the interferometer to phase and frequency modulation is measured and found to be in agreement with predictions. This technique could be used to simulate long-baseline interferometric space missions such as the Laser Interferometer Space Antenna.