Simon Barke

Experimental demonstration of weak-light laser ranging and data communication for LISA

Interferometric gravitational wave detectors with an unequal and time-varying arm length configuration like the Laser Interferometer Space Antenna rely on time-delay interferometry (TDI) for laser frequency noise subtraction. However, the TDI algorithm requires a laser ranging scheme with meter accuracy over a five million kilometer arm length. At the end of each arm only about 100 pW of light power will be detected for gravitational wave measurements and only 1% of this power can be used for laser ranging in order to avoid degradation in the phase stability of the science measurements. Here, we present the first experimental demonstration of such a ranging scheme at 1 pW power levels using a Direct Sequence Spread Spectrum (DS/SS) modulation. This type of modulation also enables optical communication by encoding data with ranging signals and provides significant noise reduction against spurious interfering signals for bidirectional ranging. Experimental results show ranging measurements of 42 cm at 3 Hz and the viability of highly reliable data transfer at several kilobits per second.

Auxiliary functions of the LISA laser link: ranging, clock noise transfer and data communication

The Laser Interferometer Space Antenna (LISA) is required to reduce two important noise sources by post-processing on the ground using time-delay interferometry (TDI): phase noise of the on-board reference clocks and laser frequency noise. To achieve the desired suppression, the TDI algorithm needs measurements of the differential clock noise between any two spacecraft and inter-spacecraft ranging measurements with at least 1 m accuracy, which is beyond the precision of ground-based measurements for deep space missions. Therefore, we need on-board measurements by transmitting clock noise and ranging information between the spacecraft as auxiliary functions of the laser link. This paper reports our current experimental results in clock noise transfer and ranging for noise subtraction via post-processing as well as additional data transfer.

Octahedron configuration for a displacement noise-cancelling gravitational wave detector in space

We study for the first time a three-dimensional octahedron constellation for a space-based gravitational wave detector, which we call the octahedral gravitational observatory (OGO). With six spacecraft the constellation is able to remove laser frequency noise and acceleration disturbances from the gravitational wave signal without needing LISA-like drag-free control, thereby simplifying the payloads and placing less stringent demands on the thrusters. We generalize LISA’s time-delay interferometry to displacement noise free interferometry (DFI) by deriving a set of generators for those combinations of the data streams that cancel laser and acceleration noise. However, the three-dimensional configuration makes orbit selection complicated. So far, only a halo orbit near the Lagrangian point L1 has been found to be stable enough, and this allows only short arms up to 1400 km. We derive the sensitivity curve of OGO with this arm length, resulting in a peak sensitivity of about \(2\times 10^{-23}\,\) Hz \({}^{-1/2}\) near 100 Hz. We compare this version of OGO to the present generation of ground-based detectors and to some future detectors. We also investigate the scientific potentials of such a detector, which include observing gravitational waves from compact binary coalescences, the stochastic background, and pulsars as well as the possibility to test alternative theories of gravity. We find a mediocre performance level for this short arm length detector, between those of initial and advanced ground-based detectors. Thus, actually building a space-based detector of this specific configuration does not seem very efficient. However, when alternative orbits that allow for longer detector arms can be found, a detector with much improved science output could be constructed using the octahedron configuration and DFI solutions demonstrated in this chapter. Also, since the sensitivity of a DFI detector is limited mainly by shot noise, we discuss how the overall sensitivity could be improved by using advanced technologies that reduce this particular noise source.

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.

Lasers for LISA: overview and phase characteristics

We have investigated two alternative laser systems for the Laser Interferometer Space Antenna (LISA). One consisted of the laser of LISAs technology precursor LISA Pathfinder and a fiber amplifier originally designed for a laser communication terminal onboard TerraSar-X. The other consisted of a commercial fiber distributed feedback (DFB) laser seeding a fiber amplifier. We have shown that the TerraSar-X amplifier can emit more than 1W without the onset of stimulated Brillouin scattering as required by LISA. We have measured power noise and frequency noise of the LISA Pathfinder laser (LPL) and the fiber laser. The fiber laser shows comparable or even lower power noise than the LPL. LISA will use electro-optical modulators (EOMs) between seed laser and amplifier for clock noise comparison between spacecraft. This scheme requires that the excess noise added by the amplifiers be negligible. We have investigated the phase characteristics of two fiber amplifiers emitting 1 W and found them to be compatible with the LISA requirement on amplifier differential phase noise.

Phase noise contribution of EOMs and HF cables

Two key components of LISAs inter-spacecraft clock tone transfer chain are electro-optic modulators (EOMs) and high-frequency (HF) cable assemblies. At modulation frequencies of 2GHz, we characterized the excess phase noise of these components in the LISA frequency range (0.1 mHz to 1 Hz). The upper phase noise limit was found to be almost an order of magnitude better than required. In addition, phase dependencies on temperature were determined. The measured coefficients are within a few milliradians per Kelvin and thereby negligible due to the specified on-board temperature stability.

Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors

The most promising concept for low frequency (millihertz to hertz) gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal readout. For this to be true, a careful balance of mission parameters is crucial to keep all other parasitic disturbances below shot noise. We developed a web application that uses over 30 input parameters and considers many important technical noise sources and noise suppression techniques to derive a realistic position noise budget. It optimizes free parameters automatically and generates a detailed report on all individual noise contributions. Thus one can easily explore the entire parameter space and design a realistic gravitational wave observatory. In this document we describe the different parameters, present all underlying calculations, and compare the final observatory’s sensitivity with astrophysical sources of gravitational waves. We use as an example parameters currently assumed to be likely applied to a space mission proposed to be launched in 2034 by the European Space Agency. The web application itself is publicly available on the Internet at http://spacegravity.org/designer. Future versions of the web application will incorporate the frequency dependence of different noise sources and include a more detailed model of the observatory’s residual acceleration noise.

Transportable setup for amplifier phase fidelity measurements

One possible laser source for the Laser Interferometer Space Antenna (LISA) consists of an Ytterbium-doped fiber amplifier originally developed for inter-satellite communication, seeded by the laser used for the technology demonstrator mission LISA Pathfinder. LISA needs to transmit clock information between its three spacecraft to correct for phase noise between the clocks on the individual spacecraft. For this purpose phase modulation sidebands at GHz frequencies will be imprinted on the laser beams between spacecraft. Differential phase noise between the carrier and a sideband introduced within the optical chain must be very low. We report on a transportable setup to measure the phase fidelity of optical amplifiers.