Archana Pai

Discrete time and frequency Wigner-Ville distribution: Moyal's formula and aliasing

In this letter, we propose a new definition of the discrete time and frequency Wigner-Ville distribution. The proposed distribution not only displays a readable representation (small aliasing) but also exhibits unitarity and is easy to compute. We compare the time-frequency representation associated with this proposed definition with other existing ones.

Interferometers for Displacement-Noise-Free Gravitational-Wave Detection

We propose a class of displacement- and laser-noise-free gravitational-wave-interferometer configurations, which does not sense nongeodesic mirror motion and laser noise, but provides a nonvanishing gravitational-wave signal. Our interferometers consist of four mirrors and two beam splitters, which form four Mach-Zehnder interferometers. By contrast to previous works, no composite mirrors with multiple reflective surfaces are required. Each mirror in our configuration is sensed redundantly, by at least two pairs of incident and reflected beams. Displacement- and laser-noise-free detection is achieved when output signals from these four interferometers are combined appropriately. Our 3-dimensional interferometer configuration has a low-frequency response proportional to f2, which is better than the f3 achievable by previous 2-dimensional configurations.

Demonstration of Displacement- and Frequency-Noise-Free Laser Interferometry Using Bidirectional Mach-Zehnder Interferometers

We have demonstrated displacement- and frequency-noise-free laser interferometry (DFI) by partially implementing a recently proposed optical configuration using bidirectional Mach-Zehnder interferometers (MZIs). This partial implementation, the minimum necessary to be called DFI, has confirmed the essential feature of DFI: the combination of two MZI signals can be carried out in a way that cancels displacement noise of the mirrors while maintaining gravitational-wave signals. The attained maximum displacement-noise suppression was 45 dB.

Best network chirplet chain: Near-optimal coherent detection of unmodeled gravitational wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts from supernova core collapses and frequency modulated signals (or chirps) from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps ‘‘in general,’’ i.e., with an arbitrary phase/frequency vs time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting or spinning sources. We expect the quasiperiodic nature of the waveform to be preserved independently of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. Improvements can be expected from the joint observation of a GW by multiple detectors and the coherent analysis of their data, namely, a larger sight horizon and the more accurate estimation of the source location and the wave polarization angles. Here, we present an extension of the BCC search to the multiple detector case. This work is based on the coherent analysis scheme proposed in the detection of inspiralling binary chirps. We revisit the derivation of the optimal statistic with a new formalism which allows the adaptation to the detection of unmodeled chirps. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full-sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.

Displacement noise free interferometory for gravitational wave detection

We have demonstrated displacement- and frequency-noise-free laser interferometry (DFI) by partially implementing a recently proposed optical configuration using bidirectional Mach-Zehnder interferometers (MZIs). This partial implementation, the minimum necessary to be called DFI, has confirmed the essential feature of DFI: the combination of two MZI signals can be carried out in a way that cancels displacement noise of the mirrors and beam splitters while maintaining gravitational-wave signals. The attained maximum displacement noise suppression was 45 dB.

An all-sky search of EXPLORER data

We have analysed three data sets, each two days long, of the EXPLORER resonant bar detector. We have searched for continuous gravitational-wave signals from spinning neutron stars. Our data analysis technique was based on the maximum likelihood detection method. We briefly describe the theoretical methods that we used in our search and we present results of the search. The main outcome of our analysis is an upper limit of 1 × 10 −22 for the dimensionless amplitude of a continuous gravitational-wave signal. The upper limit is for any source location in the sky, any polarization of the wave and for signals of frequency from 921.00 Hz to 921.76 Hz and with spin down from −2.36 × 10 −8 Hz s −1 to +2.36 × 10 −8 Hz s −1 .

The experimental plan of displacement- and frequency-noise free laser interferometer

We present the partial demonstration of displacement- and laser-noise free interferometer (DFI) and the next experimental plan to examine the complete configuration. A part of the full implementation of DFI has been demonstrated to confirm the cancellation of beamsplitter displacements. The displacements were suppressed by about two orders of magnitude. The aim of the next experiment is to operate the system and to confirm the cancellation of all displacement noises, while the gravitational wave (GW) signals survive. The optical displacements will be simulated by electro-optic modulators (EOM). To simulate the GW contribution to laser lights, we will use multiple EOMs.

Demonstration of displacement-noise-free interferometry using bi-directional Mach–Zehnder interferometers

We have demonstrated displacement- and frequency-noise-free laser interferometry (DFI) by partially implementing a recently proposed optical configuration using bi-directional Mach–Zehnder interferometers (MZIs). This partial implementation, the minimum necessary to be called DFI, has confirmed the essential feature of DFI: the combination of two MZI signals can be carried out in a way that cancels the displacement noise of the mirrors and beam splitters while maintaining gravitational-wave signals. The attained maximum displacement noise suppression was 45 dB.

Response of resonant gravitational wave detectors to damped sinusoid signals

Till date, the search for burst signals with resonant gravitational wave (GW) detectors has been done using the δ-function approximation for the signal, which was reasonable due to the very small bandwidth of these detectors. However, now with increased bandwidth (of the order of 10 or more Hz) and with the possibility of comparing results with interferometric GW detectors (broad-band), it is very important to exploit the resonant detectors’ capability to detect also signals with specific wave shapes. As a first step, we present a study of the response of resonant GW detectors to damped sinusoids with given frequency and decay time and report on the development of a filter matched to these signals. This study is a preliminary step towards the comprehension of the detector response and of the filtering for signals such as the excitation of stellar quasi-normal modes.

Optimal Source Tracking and Beaming of LISA

We revisit the directionally optimal data streams of LISA first introduced in Nayak etal. It was shown that by using appropriate choice of Time delay interferometric (TDI) combinations, a monochromatic fixed source in the barycentric frame can be optimally tracked in the LISA frame. In this work, we study the beaming properties of these optimal streams. We show that all the three streams ν+,×,0 with maximum, minimum and zero directional SNR are highly beamed. We study in detail the frequency dependence of the beaming.