Time-Delay Interferometry and Clock-Noise Calibration

The Laser Interferometer Space Antenna is a joint ESA-NASA space-mission to detect and study mHz cosmic gravitational waves. The trajectories followed by its three spacecraft result in unequal- and time-varying arms, requiring use of the Time-Delay Interferometry (TDI) post- processing technique to cancel the laser phase noises affecting the heterodyne one-way Doppler measurements. Although the second-generation formulation of TDI cancels the laser phase noises when the array is both rotating and "flexing", second-generation TDI combinations for which the phase fluctuations of the onboard ultra stable oscillators (USOs) can be calibrated out have not appeared yet in the literature. In this article we present the solution of this problem by generalizing to the realistic LISA trajectory the USO calibration algorithm derived by Armstrong, Estabrook and Tinto for a static configuration.Comment: This article is 17 pages long and contains 2 figure

Gravitational wave detection with single-laser atom interferometers

We present a new general design approach of a broad-band detector of gravitational radiation that relies on two atom interferometers separated by a distance L. In this scheme, only one arm and one laser will be used for operating the two atom interferometers. We consider atoms in the atom interferometers not only as perfect inertial reference sensors, but also as highly stable clocks. Atomic coherence is intrinsically stable and can be many orders of magnitude more stable than a laser. The unique one-laser configuration allows us to then apply time-delay interferometry to the responses of the two atom interferometers, thereby canceling the laser phase fluctuations while preserving the gravitational wave signal in the resulting data set. Our approach appears very promising. We plan to investigate further its practicality and detailed sensitivity analysis.Comment: Paper submitted to General Relativity and Gravitation as part of the prceedings of the International Workshop on Gravitational Waves Detection with Atom Interferometry (Florence, February 2009)

The LISA Time-Delay Interferometry Zero-Signal Solution. I: Geometrical Properties

Time-Delay Interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three LISA spacecraft. Within the space of all possible interferometric combinations TDI can generate, we have derived a specific combination that has zero-response to the gravitational wave signal, and called it the {\it Zero-Signal Solution} (ZSS). This is a two-parameter family of linear combinations of the generators of the TDI space, and its response to a gravitational wave becomes null when these two parameters coincide with the values of the angles of the source location in the sky. Remarkably, the ZSS does not rely on any assumptions about the gravitational waveform, and in fact it works for waveforms of any kind. Our approach is analogous to the data analysis method introduced by G\"ursel & Tinto in the context of networks of Earth-based, wide-band, interferometric gravitational wave detectors observing in coincidence a gravitational wave burst. The ZSS should be regarded as an application of the G\"ursel & Tinto method to the LISA data.Comment: 29 pages, 17 Figure

Spacecraft Doppler Tracking as a Xylophone Detector

We discuss spacecraft Doppler tracking in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine, we derive a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. Our method provides also for reducing by several orders of magnitude, at selected Fourier components, the frequency fluctuations due to other noise sources, such as the clock on board the spacecraft or the antenna and buffeting of the probe by non-gravitational forces. In this respect spacecraft Doppler tracking can be regarded as a xylophone detector. Estimates of the sensitivities achievable by this xylophone are presented for two tests of Einstein's theory of relativity: searches for gravitational waves and measurements of the gravitational red shift. This experimental technique could be extended to other tests of the theory of relativity, and to radio science experiments that rely on high-precision Doppler measurements

Data Combinations Accounting for LISA Spacecraft Motion

LISA is an array of three spacecraft in an approximately equilateral triangle configuration which will be used as a low-frequency gravitational wave detector. We present here new generalizations of the Michelson- and Sagnac-type time-delay interferometry data combinations. These combinations cancel laser phase noise in the presence of different up and down propagation delays in each arm of the array, and slowly varying systematic motion of the spacecraft. The gravitational wave sensitivities of these generalized combinations are the same as previously computed for the stationary cases, although the combinations are now more complicated. We introduce a diagrammatic representation to illustrate that these combinations are actually synthesized equal-arm interferometers.Comment: 10 pages, 3 figure

Nano-Hertz Gravitational Waves Searches with Interferometric Pulsar Timing Experiments

We estimate the sensitivity to nano-Hertz gravitational waves of pulsar timing experiments in which two highly-stable millisecond pulsars are tracked simultaneously with two neighboring radio telescopes that are referenced to the same time-keeping subsystem (i.e. "the clock"). By taking the difference of the two time-of-arrival residual data streams we can exactly cancel the clock noise in the combined data set, thereby enhancing the sensitivity to gravitational waves. We estimate that, in the band ($10^{-9} - 10^{-8}$) Hz, this "interferometric" pulsar timing technique can potentially improve the sensitivity to gravitational radiation by almost two orders of magnitude over that of single-telescopes. Interferometric pulsar timing experiments could be performed with neighboring pairs of antennas of the forthcoming large arraying projects.Comment: Paper submitted to Phys. Rev. Letters. It is 9 pages long, and includes 2 figure