The Laser Interferometer Space Antenna (LISA) senses gravitational waves by measuring distance fluctuations between three spacecraft (SCs). These measurements rely on precise tracking of a beat-note phase that is formed on a quadrant photodiode (QPD) at each SC by interference of a local laser with a laser sent from a distant SC. The crucial prerequisite of the phase tracking is a successful acquisition of the beat-note frequency. This paper aims to optimize the carrier-to-noise density ratio (CNR) during this process and to evaluate the resulting probability of detection (PD). The CNR is generally lowest during the beat-note acquisition process, since the pointing accuracy relies on coarse acquisition techniques. Based on analytical models, we examine which combinations of QPD segments for the signal readout yield the highest CNR, i.e., are least susceptible to pointing errors. We find from simulations that the highest CNR is ensured by taking the maximum of a combination of two segments in the vertical and horizontal directions. For pointing errors (3 sigma) of 3.9 mu rad and 4.3 mu rad, this yields an improvement of around 3.7 dB and 5.6 dB in the CNR, respectively, in comparison to a combination of all four segments. In addition, the PD for various configurations of the baselined Fourier-peak detection is analyzed. Here, we find that the PD is most sensitive to the CNR compared to the design parameters of the acquisition scheme, in particular the FFT length. Moreover, it is shown that the aforementioned improvements in the CNR can lead to a significant enhancement of the PD.

Future space observatories achieve detection of gravitational waves by interferometric measurements of a carrier phase, allowing to determine relative distance changes, in combination with an absolute distance measurement based on the transmission of pseudo-random noise chip sequences. In addition, usage of direct-sequence spread spectrum modulation enables data transmission. Hereafter, we report on the findings of a novel performance evaluation of planned receiver architectures, performing phase and distance readout sequentially, addressing the interplay between both measurements. An analytical model is presented identifying the power spectral density of the chip modulation at frequencies within the measurement bandwidth as the main driver for phase noise. This model, verified by numerical simulations, excludes binary phase-shift keying modulations for missions requiring pico-meter noise levels at the phase readout, while binary offset carrier modulation, where most of the power has been shifted outside the measurement bandwidth, exhibits superior phase measurement performance. Ranging analyses of the delay-locked loop reveal strong distortion of the pulse shape due to the preceding phase tracking introducing ranging bias variations. Numerical simulations show that these variations, however, which originate from data transitions, are compensated by the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of the modulation type.

The laser interferometer space antenna (LISA) senses gravitational waves by measuring distance fluctuations between three spacecraft (SC). These measurements rely on precise tracking of a beat note phase that is formed on a quadrant-photo-diode (QPD) at each SC by interference of a local laser with a laser sent from a distant SC. The crucial prerequisite of the phase tracking is a successful acquisition of the beat note frequency. This article aims to optimize the carrier-to-noise density ratio (CNR) during this process, and to evaluate the resulting probability of detection (PD). CNR is generally lowest during the beat note acquisition process since pointing accuracy relies on coarse acquisition techniques. Based on analytical models, we examine which combinations of QPD segments for the signal read-out yield the highest CNR, i.e., they are least susceptible to pointing errors. We find from simulations that the highest CNR is ensured by taking the maximum of a combination of two segments in vertical and horizontal direction. For pointing errors (3σ) of 3.9 μrad and 4.3 μrad this yields an improvement of around 3.7 dB and 5.6 dB in CNR, respectively, in comparison to a combination of all four segments. In addition, the PD for various configurations of the baselined Fourier peak detection is analyzed. Here we find that the PD is most sensitive to the CNR compared to the design parameters of the acquisition scheme, in particular the FFT length. Moreover, it is shown that aforementioned improvements in CNR can lead to a significant enhancement of the PD.

In the context of the Laser Interferometer Space Antenna (LISA), the laser subsystems exhibit frequency fluctuations that introduce significant levels of noise into the measurements, surpassing the gravitational wave signal by several orders of magnitude. Mitigation is achieved by means of time-shifting individual measurements in a data processing step known as time-delay interferometry (TDI). The suppression performance of TDI relies on accurate knowledge and consideration of the delays experienced by the interfering lasers. While considerable efforts have been dedicated to the accurate determination of interspacecraft ranging delays, the sources for delays onboard the spacecraft have been either neglected during TDI processing or assumed to be known. Contrary to these assumptions, analog delays of the phasemeter front end and the laser modulation are not only large but also prone to change with temperature and heterodyne frequency. This motivates our proposal for a novel method enabling a calibration of these delays on-ground and in-space, based on minimal functional additions to the receiver architecture. Specifically, we establish a set of calibration measurements and elucidate how these measurements are utilized in data processing, leading to the mitigation of the delays in the TDI Michelson variables. Following a performance analysis of the calibration measurements, the proposed calibration scheme is assessed through numerical simulations. We find that in the absence of the calibration scheme, the assumed drifts of the analog delays increase residual laser noise at high frequencies of the LISA measurement band. A single, on-ground calibration of the analog delays leads to an improvement by roughly one order of magnitude, while recalibration in space may improve performance by yet another order of magnitude. Towards lower frequencies, ranging error is always found to be the limiting factor for which countermeasures are discussed.

Time-delay interferometry (TDI) is a data processing technique for space-based gravitational-wave detectors to create laser-noise-free equal-optical-path-length interferometers virtually on the ground. It relies on the interspacecraft signal propagation delays, which are delivered by intersatellite ranging monitors. Also delays due to onboard signal propagation and processing have a nonnegligible impact on the TDI combinations. However, these onboard delays were only partially considered in previous TDI-related research; onboard optical path lengths have been neglected so far. In this paper, we study onboard optical path lengths in TDI. We derive analytical models for their coupling to the second-generation TDI Michelson combinations and verify these models numerically. Furthermore, we derive a compensation scheme for onboard optical path lengths in TDI and validate its performance via numerical simulations.

The detection of gravitational waves requires a strain sensitivity at unprecedented precision. The planned space observatory LISA overcomes this extreme challenge by heterodyne laser interferometry at picometer-precision based on the exploitation of carrier phase measurements between spacecraft separated by millions of kilometers. In addition, data transmission and absolute ranging, necessary to mitigate effects of laser frequency fluctuations in post-processing, are achieved with direct-sequence spread spectrum signals. The foreseen receivers shall typically operate in a sequential phase-locked loop and delay-locked loop configuration for consecutive phase and distance measurement. Recent analysis observed code tracking delay variations, identified as ranging bias variations, as a result of this sequential arrangement. Hereafter, we present an analytical analysis of these ranging bias variations. Comparisons to numerical simulations reveal the compelling influence of the cross-correlation of the chip sequences on the ranging bias variations for a fixed modulation scheme and thus affirm the necessity of numerical analysis. In addition, a generic model for the quantisation error of a digital delay-locked loop is introduced that may be used for analysis and design of digital code tracking loops in various applications. Finally, comparison to a numerical simulation reveals that at small ranging bias variations, the code tracking error is fully described by the quantisation error, while at high ranging bias variations, this effect is negligible and the code tracking error is dominated by ranging bias variations.

Two-dimensional electron systems (2DES) subjected to a perpendicular magnetic field absorb electromagnetic radiation via cyclotron resonance (CR). Here we report a qualitative deviation from this well-known behavior. Our measurements in large-sized 2DES based on GaAs and HgTe reveal that the CR-enhanced photoconductivity becomes insensitive to the radiation helicity, showing almost the same signal amplitude for both CR active and inactive polarities of B, when the temperature T is lowered to that of liquid helium or below. Strikingly, the simultaneously measured CR in the transmission demonstrates a conventional strong helicity dependence for all T. In contrast similar photoconductivity measurements in graphene show no anomalies indicating an ordinary helicity-sensitivity in the whole investigated temperature range.