Alternative approach to time-delay interferometry with optical frequency comb

TL;DR

This paper introduces an alternative OFC-based metrology method for spaceborne gravitational-wave detectors that derives the time derivative of the interspacecraft pseudorange from carrier-carrier beatnotes, allowing full noise suppression without altering the traditional TDI framework. The approach leverages coherence between the OFC-generated onboard clock and the laser carrier to couple laser and clock noises into the beatnotes in a controllable way, enabling a self-consistent estimation of the pseudorange derivative and its integration into TDI. An experimental demonstration with two OMS setups shows clock synchronization better than $0.47\,\mathrm{ns}$ and stochastic jitter suppression near the LISA performance level ($15\,\mathrm{pm}/\sqrt{\mathrm{Hz}}$), with OFC mode numbers $n_1$ and $n_2$ resolved and validated against an external reference. The study underlines the importance of precise OFC mode-number identification (potentially via TDIR-like postprocessing) and offers a practical path to exploiting OFCs for robust laser/clock noise cancellation in future space-based GW detectors.

Abstract

Spaceborne gravitational wave observatories, exemplified by the Laser Interferometer Space Antenna (LISA) mission, are designed to remove laser noise and clock noise from interferometric phase measurements in postprocessing. The planned observatories will utilize electro-optic modulators (EOMs) to encode the onboard clock timing onto the beam phase. Recent research has demonstrated the advantage of introducing an optical frequency comb (OFC) in the metrology system with the modified framework of time-delay interferometry (TDI): the removal of the EOM and the simultaneous suppression of the stochastic jitter of the laser and the clock in the observation band. In this paper, we explore an alternative approach with the OFC-based metrology system. We report that after proper treatment, it is possible to use the measured carrier-carrier heterodyne frequencies to monitor the time derivative of the pseudoranges, which represent the physical light travel time and the clock difference. This approach does not require changing the existing TDI framework, as previous OFC based efforts did. We also present the experimental demonstration of our scheme using two separate systems to model two spacecraft. Using this novel approach, we synchronize the two independent phase measurement systems with an accuracy better than 0.47 ns, while the stochastic jitter in the observation band is suppressed down to the setup sensitivity around the LISA performance levels at 15 pm/sqrt(Hz).

Figures (6)

• Figure 1: Conceptual diagram of a possible spacecraft payload equipped with an OFC, labeled by $i$ while having two remote spacecraft $j$ and $k$. The system on the left, considered the primary, is labeled after the spacecraft, while the system on the right, considered the secondary, is labeled with the primed index. The primary and secondary lasers are drawn in red and blue, respectively. Optical interference occurs at each beam splitter. Only the interspacecraft and reference interferometers are depicted, neglecting the test-mass interferometers. A spacecraft onboard clock can be generated by the OFC locked to the primary laser $i$. SC: spacecraft; OB: optical bench; BS: beam splitter; OFC: optical frequency comb.
• Figure 2: The experimental setup is composed of two optical metrology systems (OMSs), which mimic two spacecraft. The OFC setup and the free-space custom iodine setup are depicted on the bottom and top right inlays. The red and blue lasers are primary and secondary, as established in \ref{['fig:payload']}. The OFC is locked to the primary laser, $i$, which is stabilized with the custom iodine setup. The phase of the heterodyne beatnote between the primary laser from OMS 1 and the secondary laser from OMS 2 is individually extracted by the phasemeters driven by the independent OFC-generated clock signals in the OMSs. BS: beam splitter, ADC: analog-to-digital converter, PR: photo receiver, LPF: low-pass filter, BPF: band-pass filter, PBS: polarizing beam splitter, EOM: electro-optic modulator, AOM: acousto-optic modulator, SHG: second harmonic generator, EDFA: Er-doped fiber amplifier, HNLF: highly nonlinear fiber.
• Figure 3: Clock difference as measured via the carrier-carrier beatnote: bottom plot shows $\hat{\dot{q}}^{\tau_1,(1)}_2$ in \ref{['eq:bardotq2_tau1']}; top shows $\delta\hat{\tau}_2^{\tau_1,(0)}$ in light green and $\delta\hat{\tau}_2^{\tau_1,(1)}$ in \ref{['eq:deltauj_taui']} in dark green. In the top panel, the total and detrended timer deviations are shown in solid with the left axis and dashed with the right axis, respectively.
• Figure 4: Experimental results of the noise-free combinations via our OFC-based synchronization scheme. The tone at 1.0 is intentionally injected for the calibration of laser noise suppression performance. Pink: the input optical beatnote phase noise as measured by phasemeter 1; Blue: the signal combination without synchronization; Green: the expected in-band clock jitter after the optical-to-electrical downconversion; Yellow, orange, and red: the noise-free signal combination $\Delta^{\tau_1}_a$ in \ref{['eq:Delta_taui_a']} with iteration orders of 0, 1, and 2, respectively. Black: the LISA performance level, $15pm\per\sqrt{\mathrm{\Hz}}\cdot\sqrt{1 + \left(\frac{2m\Hz}{f}\right)^4}$.
• Figure 5: Noise budget of the signal combination $\Delta^{\tau_1,(2)}_a$. Red and black are identical to those in \ref{['fig:suppression_asd']}. Green is the total noise, composed of the OFC noise including peripheral RF electronics (blue), the phasemeter signal chain noise (grey), the phasemeter clock chain noise (cyan), the residual laser noise (pink), the numerical rounding error (magenta), and the aliased noise (orange).