Quantum-limited optical time transfer for future geosynchronous links.

The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity1-3, dark-matter searches4 and gravitational-wave detection5. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry6,7, advanced satellite navigation8, clock-based geodesy2,9,10 and thousandfold improvements in intercontinental time dissemination11,12. Thus far, only optical clocks have pushed towards quantum-limited performance13. By contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches14-24. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 µW, distant sites are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links in which photons are few and amplification costly: at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits.

The time-programmable frequency comb and its use in quantum-limited ranging.

Two decades after its invention, the classic self-referenced frequency comb laser is an unrivalled ruler for frequency, time and distance metrology owing to the rigid spacing of its optical output1,2. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision3-5. Many of these applications, however, are limited by the trade-offs inherent in the rigidity of the comb output and operate far from quantum-limited sensitivity. Here we demonstrate an agile programmable frequency comb where the pulse time and phase are digitally controlled with ±2-attosecond accuracy. This agility enables quantum-limited sensitivity in sensing applications as the programmable comb can be configured to coherently track weak returning pulse trains at the shot-noise limit. To highlight its capabilities, we use this programmable comb in a ranging system, reducing the required power to reach a given precision by about 5,000-fold compared with a conventional dual-comb system. This enables ranging at a mean photon per pulse number of 1/77 while retaining the full accuracy and precision of a rigid frequency comb. Beyond ranging and imaging6-12, applications in time and frequency metrology1,2,5,13-23, comb-based spectroscopy24-32, pump-probe experiments33 and compressive sensing34,35 should benefit from coherent control of the comb-pulse time and phase.

An optical-frequency synthesizer using integrated photonics.

Optical-frequency synthesizers, which generate frequency-stable light from a single microwave-frequency reference, are revolutionizing ultrafast science and metrology, but their size, power requirement and cost need to be reduced if they are to be more widely used. Integrated-photonics microchips can be used in high-coherence applications, such as data transmission 1 , highly optimized physical sensors 2 and harnessing quantum states 3 , to lower cost and increase efficiency and portability. Here we describe a method for synthesizing the absolute frequency of a lightwave signal, using integrated photonics to create a phase-coherent microwave-to-optical link. We use a heterogeneously integrated III-V/silicon tunable laser, which is guided by nonlinear frequency combs fabricated on separate silicon chips and pumped by off-chip lasers. The laser frequency output of our optical-frequency synthesizer can be programmed by a microwave clock across 4 terahertz near 1,550 nanometres (the telecommunications C-band) with 1 hertz resolution. Our measurements verify that the output of the synthesizer is exceptionally stable across this region (synthesis error of 7.7 × 10-15 or below). Any application of an optical-frequency source could benefit from the high-precision optical synthesis presented here. Leveraging high-volume semiconductor processing built around advanced materials could allow such low-cost, low-power and compact integrated-photonics devices to be widely used.

Optical timing jitter due to atmospheric turbulence: comparison of frequency comb measurements to predictions from micrometeorological sensors.

During propagation through atmospheric turbulence, variations in the refractive index of air cause fluctuations in the time-of-flight of laser light. These timing jitter fluctuations are a major noise source for precision laser ranging, optical time transfer, and long-baseline interferometry. While there exist models that estimate the turbulence-induced timing jitter power spectra using parameters obtainable from conventional micrometeorological instruments, a direct and independent comparison of these models to measured timing jitter data has not been done. Here we perform this comparison, measuring turbulence-induced optical pulse timing jitter over a horizontal, near-ground path using frequency comb lasers while independently characterizing the turbulence along the path using a suite of micrometeorological sensors. We compare the power spectra of measured optical pulse timing jitter to predictions based on the measured micrometeorological data and standard turbulence theory. To further quantitatively compare the frequency comb data to the micrometeorological measurements, we extract and compare the refractive index structure parameter, Cn2, from both systems and find agreement to within a factor of 5 for wind speed >1 m/s, and further improvement is possible as wind speed increases. These results validate the use of conventional micrometeorological instruments in predicting optical timing jitter statistics over co-located laser beam paths.

Obtaining more energetic modelocked pulses from a SESAM-based fiber laser.

A major design goal for femtosecond fiber lasers is to increase the output power but not at the cost of increasing the noise level or narrowing the bandwidth. Here, we perform a computational study to optimize the cavity design of a femtosecond fiber laser that is passively modelocked with a semiconductor saturable absorbing mirror (SESAM). We use dynamical methods that are more than a thousand times faster than standard evolutionary methods. We show that we can obtain higher pulse energies and hence higher output powers by simultaneously increasing the output coupling ratio, the gain, and the anomalous group delay dispersion. We can obtain output pulses that are from 5 to 15 times the energy of the pulse in the current experimental design with no penalty in the noise level or bandwidth.

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10

We demonstrate carrier-phase optical two-way time-frequency transfer (carrier-phase OTWTFT) through the two-way exchange of frequency comb pulses. Carrier-phase OTWTFT achieves frequency comparisons with a residual instability of 1.2×10^{-17} at 1 s across a turbulent 4-km free space link, surpassing previous OTWTFT by 10-20 times and enabling future high-precision optical clock networks. Furthermore, by exploiting the carrier phase, this approach is able to continuously track changes in the relative optical phase of distant optical oscillators to 9 mrad (7 as) at 1 s averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.

Wake mode sidebands and instability in mode-locked lasers with slow saturable absorbers.

Passively mode-locked lasers with semiconductor saturable absorption mirrors are attractive comb sources due to their simplicity, excellent self-starting properties, and their environmental robustness. These lasers, however, can have an increased noise level and wake mode instabilities. Here, we investigate the wake mode dynamics in detail using a combination of evolutionary and dynamical methods. We describe the mode-locked pulse generation from noise when a stable pulse exists and the evolution of the wake mode instability when no stable pulse exists. We then calculate the dynamical spectrum of the mode-locked pulse, and we show that it has six discrete eigenmodes, two of which correspond to wake modes. The wake modes are unstable when the wake mode eigenvalues have a positive real part. We also show that even when the laser is stable, the wake modes lead to experimentally observed sidebands.

Broadband Phase Spectroscopy over Turbulent Air Paths.

Broadband atmospheric phase spectra are acquired with a phase-sensitive dual-frequency-comb spectrometer by implementing adaptive compensation for the strong decoherence from atmospheric turbulence. The compensation is possible due to the pistonlike behavior of turbulence across a single spatial-mode path combined with the intrinsic frequency stability and high sampling speed associated with dual-comb spectroscopy. The atmospheric phase spectrum is measured across 2 km of air at each of the 70,000 comb teeth spanning 233 cm(-1) across hundreds of near-infrared rovibrational resonances of CO(2), CH(4), and H(2)O with submilliradian uncertainty, corresponding to a 10(-13) refractive index sensitivity. Trace gas concentrations extracted directly from the phase spectrum reach 0.7 ppm uncertainty, demonstrated here for CO(2). While conventional broadband spectroscopy only measures intensity absorption, this approach enables measurement of the full complex susceptibility even in practical open path sensing.

Comb-calibrated frequency-modulated continuous-wave ladar for absolute distance measurements.

We demonstrate a comb-calibrated frequency-modulated continuous-wave laser detection and ranging (FMCW ladar) system for absolute distance measurements. The FMCW ladar uses a compact external cavity laser that is swept quasi-sinusoidally over 1 THz at a 1 kHz rate. The system simultaneously records the heterodyne FMCW ladar signal and the instantaneous laser frequency at sweep rates up to 3400 THz/s, as measured against a free-running frequency comb (femtosecond fiber laser). Demodulation of the ladar signal against the instantaneous laser frequency yields the range to the target with 1 ms update rates, bandwidth-limited 130 µm resolution and a ~100 nm accuracy that is directly linked to the counted repetition rate of the comb. The precision is <100 nm at the 1 ms update rate and reaches ~6 nm for a 100 ms average.

Frequency comb velocity-modulation spectroscopy.

We have demonstrated a new technique that provides massively parallel comb spectroscopy sensitive specifically to ions through the combination of cavity-enhanced direct frequency comb spectroscopy with velocity-modulation spectroscopy. Using this novel system, we have measured electronic transitions of HfF⁺ and achieved a fractional absorption sensitivity of 3×10⁻7 recorded over 1500 simultaneous channels spanning 150 cm⁻¹ around 800 nm with an absolute frequency accuracy of 30 MHz (0.001 cm⁻¹). A fully sampled spectrum consisting of interleaved measurements is acquired in 30 min.

Femtosecond time synchronization of optical clocks off of a flying quadcopter.

Future optical clock networks will require free-space optical time-frequency transfer between flying clocks. However, simple one-way or standard two-way time transfer between flying clocks will completely break down because of the time-of-flight variations and Doppler shifts associated with the strongly time-varying link distances. Here, we demonstrate an advanced, frequency comb-based optical two-way time-frequency transfer (O-TWTFT) that can successfully synchronize the optical timescales at two sites connected via a time-varying turbulent air path. The link between the two sites is established using either a quadcopter-mounted retroreflector or a swept delay line at speeds up to 24 ms-1. Despite 50-ps breakdown in time-of-flight reciprocity, the sites' timescales are synchronized to < 1 fs in time deviation. The corresponding sites' frequencies agree to ~ 10-18 despite 10-7 Doppler shifts. This work demonstrates comb-based O-TWTFT can enable free-space optical networks between airborne or satellite-borne optical clocks for precision navigation, timing and probes of fundamental science.

Tight real-time synchronization of a microwave clock to an optical clock across a turbulent air path.

The ability to distribute the precise time and frequency from an optical clock to remote platforms could enable future precise navigation and sensing systems. Here we demonstrate tight, real-time synchronization of a remote microwave clock to a master optical clock over a turbulent 4-km open air path via optical two-way time-frequency transfer. Once synchronized, the 10-GHz frequency signals generated at each site agree to 10-14 at one second and below 10-17 at 1000 seconds. In addition, the two clock times are synchronized to ±13 fs over an 8-hour period. The ability to phase-synchronize 10-GHz signals across platforms supports future distributed coherent sensing, while the ability to time-synchronize multiple microwave-based clocks to a high-performance master optical clock supports future precision navigation/timing systems.

Synchronization of Clocks Through 12 km of Strongly Turbulent Air Over a City.

We demonstrate real-time, femtosecond-level clock synchronization across a low-lying, strongly turbulent, 12-km horizontal air path by optical two-way time transfer. For this long horizontal free-space path, the integrated turbulence extends well into the strong turbulence regime corresponding to multiple scattering with a Rytov variance up to 7 and with the number of signal interruptions exceeding 100 per second. Nevertheless, optical two-way time transfer is used to synchronize a remote clock to a master clock with femtosecond-level agreement and with a relative time deviation dropping as low as a few hundred attoseconds. Synchronization is shown for a remote clock based on either an optical or microwave oscillator and using either tip-tilt or adaptive-optics free-space optical terminals. The performance is unaltered from optical two-way time transfer in weak turbulence across short links. These results confirm that the two-way reciprocity of the free-space time-of-flight is maintained both under strong turbulence and with the use of adaptive optics. The demonstrated robustness of optical two-way time transfer against strong turbulence and its compatibility with adaptive optics is encouraging for future femtosecond clock synchronization over very long distance ground-to-air free-space paths.