Time domain simulations of arm locking in LISA

Abstract

Arm locking is a proposed laser frequency stabilization technique for the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that compose LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of a Kalman-filter-based arm locking system that includes the expected limiting noise sources as well as the effects of imperfect a priori knowledge of constellation geometry on which the design is a based. We use the simulation to study aspects of the system performance that are difficult to capture in a steady-state frequency domain analysis such as frequency pulling of the master laser due to errors in estimates of heterodyne frequency. We find that our implementation meets requirements on both the noise and dynamic range of the laser frequency with acceptable tolerances and that the design is sufficiently insensitive to errors in the estimated constellation geometry that the required performance can be maintained for the longest continuous measurement intervals expected for the LISA mission.

Arm locking with the GRACE follow-on laser ranging interferometer

“…For LISA, the much larger separation in frequency between the science band and the primary Doppler modulation frequencies, coupled with the much simpler Doppler signal (no geoid signal) means that the trade between frequency pulling and low-frequency gain is not as tightly constrained. The LISA armlocking designs presented in [9] and [10] demonstrate how this trade can be addressed for LISA.…”

“…Two ways to mitigate this frequency pulling are (i), estimate and subtract the Doppler signal in a feed-forward scheme; and (ii), reduce the frequency pulling by reducing the gain of the controller below the science band, an approach colloquially referred to as 'AC coupling'. Arm-locking system designs for LISA employing both of these techniques have been successfully demonstrated analytically [9] and numerically [10]. Table I shows a comparison between LISA and GRACE-FO of the key parameters for an arm-locking system.…”

TDI and clock noise removal for the split interferometry configuration of LISA

“…Each of the three spacecrafts carries two nearly identical OB, where one is denoted with unprimed numbers (1,2,3) and the other by primed numbers (1 , 2 , 3 ), as shown in figure 1. The 'armlengths' of the triangle in terms of the light travel time t i , L i = ct i , are marked as follows: the opposed side of S/C i is denoted by L i and L i , respectively, depending on the direction of light travel (counter-clockwise or clockwise).…”

“…However, many noise sources also enter the measured data. The dominant noise source is the laser phase noise, which enters via the armlength difference (up to 1% ≈ 50 000 km) and completely swamps the gravitational wave signal, even after various laser stabilization schemes have been applied [3]. To remove the laser phase noise, a post-processing method called time-delay interferometry (TDI), first proposed by [4], has to be applied.…”

Arm locking for space-based laser interferometry gravitational wave observatories

“…None of these experiments reached the 16.6 s delay of LISA or added Doppler shifts to their experiment. Arm locking was further studied numerically and analytically by different groups [14][15][16]. Their work included for example time varying Doppler shifts, the different clocks on the three spacecraft, and the spacecraft motion while we proceeded to set up the experiments to test arm locking under these realistic conditions.…”