Subfemtowatt Laser Phase Tracking.

Low power optical phase tracking is an enabling capability for intersatellite laser interferometry, as minimum trackable power places significant constraints on mission design. Through the combination of laser stabilization and control-loop parameter optimization, we have demonstrated continuous tracking of a subfemtowatt optical field with a mean time between slips of more than 1000 s. Comparison with analytical models and numerical simulations verified that the observed experimental performance was limited by photon shot noise and unsuppressed laser frequency fluctuations. Furthermore, with two stabilized lasers, we have demonstrated 100 min of continuous phase tracking of Gravity Recovery and Climate Experiment (GRACE)-like signal dynamics with an optical carrier ranging in power between 1-7 fW with zero cycle slips. These results indicate the feasibility of future interspacecraft laser links operating with significantly reduced received optical power.

Absolute frequency readout derived from ULE cavity for next generation geodesy missions: erratum.

We found a calculation error affecting the scaling of results presented in Figure 7 of our article "Absolute frequency readout derived from ULE cavity for next generation geodesy missions" [Opt. Express2926014 (2021)10.1364/OE.434483] . The corrected Figure 7 is published here.

Enhancing the precision limits of interferometric satellite geodesy missions.

Satellite geodesy uses the measurement of the motion of one or more satellites to infer precise information about the Earth's gravitational field. In this work, we consider the achievable precision limits on such measurements by examining approximate models for the three main noise sources in the measurement process of the current Gravitational Recovery and Climate Experiment (GRACE) Follow-On mission: laser phase noise, accelerometer noise and quantum noise. We show that, through time-delay interferometry, it is possible to remove the laser phase noise from the measurement, allowing for almost three orders of magnitude improvement in the signal-to-noise ratio. Several differential mass satellite formations are presented which can further enhance the signal-to-noise ratio through the removal of accelerometer noise. Finally, techniques from quantum optics have been studied, and found to have great promise for reducing quantum noise in other alternative mission configurations. We model the spectral noise performance using an intuitive 1D model and verify that our proposals have the potential to greatly enhance the performance of near-future satellite geodesy missions.

Improved cross-talk suppression for digitally enhanced interferometry using Golay complementary pairs.

We demonstrate digitally enhanced interferometry with better than 100 dB mean cross-talk suppression with Golay complementary pairs using a combination of numerical simulations and experiments. These results exceed previously reported cross-talk suppression using conventional maximal length sequences by more than 48 dB.

Detection statistics for coherent RMCW LiDAR.

This paper presents an analytical model and experimental validation for the detection performance and false-alarm rates for phase-encoded random modulation continuous-wave (RMCW) LiDAR. Derivation of the model focuses on propagating the effects of relevant noise sources through the system to determine an analytical expression for the detection rate, expressed by the probability of detection. The model demonstrates that probability of detection depends only on three factors: i) the mean signal-to-noise ratio (SNR) of the measurement; ii) the measurement integration time; and iii) speckle-induced intensity noise. The predicted analytical relationship between measurement SNR and probability of detection was validated by numerical simulations and experimental demonstrations in both a controlled fiber channel and under fully-developed speckle conditions in an uncontrolled free-space channel.

Absolute frequency readout derived from ULE cavity for next generation geodesy missions.

The next generation of Gravity Recovery and Climate Experiment (GRACE)-like dual-satellite geodesy missions proposals will rely on inter-spacecraft laser interferometry as the primary instrument to recover geodesy signals. Laser frequency stability is one of the main limits of this measurement and is important at two distinct timescales: short timescales over 10-1000 seconds to measure the local gravity below the satellites, and at the month to year timescales, where the subsequent gravity measurements are compared to indicate loss or gain of mass (or water and ice) over that period. This paper demonstrates a simple phase modulation scheme to directly measure laser frequency change over long timescales by comparing an on-board Ultra-Stable Oscillator (USO) clocked frequency reference to the Free Spectral Range (FSR) of the on-board optical cavity. By recording the fractional frequency variations the scale correction factor may be computed for a laser locked to a known longitudinal mode of the optical cavity. The experimental results demonstrate a fractional absolute laser frequency stability at the 10 ppb level (10-8) at time scales greater than 10 000 seconds, likely sufficient for next generation mission requirements.

High stability laser locking to an optical cavity using tilt locking.

This paper describes, to our knowledge, the first demonstration of high performance tilt locking, a method of stabilizing laser frequency to an optical reference cavity using a spatial-mode readout technique. The experiment utilized a traveling wave cavity with a finesse of approximately 10,000, housed in a thermally controlled vacuum chamber. The tilt locking method in a double pass configuration has promising performance in the 100 µHz-1 Hz band, including surpassing the Gravity Recovery and Climate Experiment (GRACE) Follow-On laser ranging interferometer requirement. Tilt locking offers a number of benefits such as high sensitivity, low cost, and simple implementation and therefore should be considered for future applications requiring high performance laser locking, such as future laser-based satellite geodesy missions and the Laser Interferometer Space Antenna.

Mitigation of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave LiDAR.

We present a detailed analysis of techniques to mitigate the effects of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave (RAMCW) LiDAR. The analysis focuses specifically on a technique which uses coherent dual-quadrature detection to enable a sum of squares calculation to remove the input signal's dependence on carrier phase and frequency. This increases the correlation bandwidth of the matched-template filter to the bandwidth of the acquisition system, whilst also supporting the simultaneous measurement of relative radial velocity with unambiguous direction-of-travel. A combination of simulations and experiments demonstrate the sum of squares technique's ability to measure distance with consistently high SNR, more than 15 dB better than alternative techniques whilst operating in the presence of otherwise catastrophic phase noise and large frequency offsets. In principle, the technique is able to mitigate any sources of phase noise and frequency offsets common to the two orthogonal outputs of a coherent dual-quadrature receiver including laser frequency noise, speckle-induced phase noise, and Doppler frequency shifts due to accelerations.

Arm-Locking with the GRACE Follow-On Laser Ranging Instrument.

Arm-locking is a technique for stabilizing the frequency of a laser in an inter-spacecraft interferometer by using the spacecraft separation as the frequency reference. A candidate technique for future space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA), arm-locking has been extensive studied in this context through analytic models, time-domain simulations, and hardware-in-the-loop laboratory demonstrations. In this paper we show the Laser Ranging Instrument flying aboard the upcoming Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission provides an appropriate platform for an on-orbit demonstration of the arm-locking technique. We describe an arm-locking controller design for the GRACE-FO system and a series of time-domain simulations that demonstrate its feasibility. We conclude that it is possible to achieve laser frequency noise suppression of roughly two orders of magnitude around a Fourier frequency of 1Hz with conservative margins on the system's stability. We further demonstrate that 'pulling' of the master laser frequency due to fluctuating Doppler shifts and lock acquisition transients is less than 100MHz over several GRACE-FO orbits. These findings motivate further study of the implementation of such a demonstration.

Weak-light phase tracking with a low cycle slip rate.

The Gravity Recovery and Climate Experiment Follow-On mission will use a phase-locked loop to track changes in the phase of an optical signal that has been transmitted hundreds of kilometers between two spacecraft. Beam diffraction significantly reduces the received signal power, making it difficult to track, as the phase-locked loop is more susceptible to cycle slips. The lowest reported weak-light phase locking is at 40 fW with a cycle slip rate of 1 cycle per second. By selecting a phase-locked loop bandwidth that minimized the signal variance due to shot noise and laser phase fluctuations, a 30 fW signal has been tracked with a cycle slip rate less than 0.01 cycles per second. This is tracking at a power 25% lower with a 100-fold improvement in the cycle slip rate. This capability will enable a new class of missions, opening up new opportunities for space-based interferometry.

Laser ranging and communications for LISA.

The Laser Interferometer Space Antenna (LISA) will use Time Delay Interferometry (TDI) to suppress the otherwise dominant laser frequency noise. The technique uses sub-sample interpolation of the recorded optical phase measurements to form a family of interferometric combinations immune to frequency noise. This paper reports on the development of a Pseudo-Random Noise laser ranging system used to measure the sub-sample interpolation time shifts required for TDI operation. The system also includes an optical communication capability that meets the 20 kbps LISA requirement. An experimental demonstration of an integrated LISA phase measurement and ranging system achieved a ≈ 0.19 m rms absolute range error with a 0.5Hz signal bandwidth, surpassing the 1 m rms LISA specification. The range measurement is limited by mutual interference between the ranging signals exchanged between spacecraft and the interaction of the ranging code with the phase measurement.

Experimental demonstration of time-delay interferometry for the laser interferometer space antenna.

We report on the first demonstration of time-delay interferometry (TDI) for LISA, the Laser Interferometer Space Antenna. TDI was implemented in a laboratory experiment designed to mimic the noise couplings that will occur in LISA. TDI suppressed laser frequency noise by approximately 10(9) and clock phase noise by 6×10(4), recovering the intrinsic displacement noise floor of our laboratory test bed. This removal of laser frequency noise and clock phase noise in postprocessing marks the first experimental validation of the LISA measurement scheme.

Technical limitations to homodyne detection at audio frequencies.

Homodyne detection relies on the beat between a relatively strong local oscillator (LO) field at the carrier frequency and a signal beam with sidebands centered around the carrier frequency. This type of signal detection, or signal readout, is widely used in quantum optics applications and is expected to be used in advanced interferometric gravitational wave detectors. We investigate experimentally the limitations to making such measurements in a laboratory environment at audio frequencies. We find that beam jitter noise, electronic noise of the photodetectors, and the LO intensity noise can limit the homodyne detection in this frequency band, and we discuss potential solutions.

Harmonic entanglement with second-order nonlinearity.

We investigate the second-order nonlinear interaction as a means to generate entanglement between fields of differing wavelengths and show that perfect entanglement can, in principle, be produced between the fundamental and second-harmonic fields in these processes. Neither pure second-harmonic generation nor parametric oscillation optimally produce entanglement; such optimal entanglement is rather produced by an intermediate process.

Nonlinear phase matching locking via optical readout.

For optimal Chi((2)) nonlinear interaction the phase matching condition must be satisfied. For type I and type II phase matched materials, this is generally achieved by controlling the temperature of the nonlinear media. We describe a technique to readout the phase-matching condition interferometrically, and experimentally demonstrate feedback control in a degenerate optical parametric amplifier (OPA) which is resonant at both the fundamental and harmonic frequencies. The interferometric readout technique is based on using the cavity resonances at the fundamental and harmonic frequencies to enable the readout of the phase mismatch. We achieve relatively fast temperature feedback using the photothermal effect, by modulating the amplitude of the OPA pump beam.

Squeezing in the audio gravitational-wave detection band.

We demonstrate the generation of broadband continuous-wave optical squeezing from 280 Hz-100 kHz using a below-threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise, and detuning fluctuations, present in optical parametric amplifiers, have negligible effect on squeezing produced by a below-threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational-wave detectors.

Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection.

Interferometric gravitational wave detectors are expected to be limited by shot noise at some frequencies. We experimentally demonstrate that a power recycled Michelson with squeezed light injected into the dark port can overcome this limit. An improvement in the signal-to-noise ratio of 2.3 dB is measured and locked stably for long periods of time. The configuration, control, and signal readout of our experiment are compatible with current gravitational wave detector designs. We consider the application of our system to long baseline interferometer designs such as LIGO.