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.

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.

Estimating vehicle carbon dioxide emissions from Boulder, Colorado, using horizontal path-integrated column measurements.

We performed 7.5 weeks of path-integrated concentration measurements of CO2, CH4, H2O, and HDO over the city of Boulder, Colorado. An open-path dual-comb spectrometer simultaneously measured time-resolved data across a reference path, located near the mountains to the west of the city, and across an over-city path that intersected two-thirds of the city, including two major commuter arteries. By comparing the measured concentrations over the two paths when the wind is primarily out of the west, we observe daytime CO2 enhancements over the city. Given the warm weather and the measurement footprint, the dominant contribution to the CO2 enhancement is from city vehicle traffic. We use a Gaussian plume model combined with reported city traffic patterns to estimate city emissions of on-road CO2 as (6.2 ± 2.2) × 105 metric tons (t) CO2 yr-1 after correcting for non-traffic sources. Within the uncertainty, this value agrees with the city's bottom-up greenhouse gas inventory for the on-road vehicle sector of 4.5 × 105 t CO2 yr-1. Finally, we discuss experimental modifications that could lead to improved estimates from our path-integrated measurements.

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.

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.

Speed-dependent Voigt lineshape parameter database from dual frequency comb measurements at temperatures up to 1305 K. Part II: Argon-broadened H2O absorption, 6801-7188 cm-1.

We report argon-broadened water vapor transition parameters and their temperature dependence based on measured spectra spanning 6801-7188 cm-1 from a broad-bandwidth, high-resolution dual frequency comb spectrometer. The 25 collected spectra of 2% water vapor in argon ranged from 296 K to 1305 K with total pressure spanning 100 Torr to 600 Torr. A multispectrum fitting routine was used in conjunction with a quadratic speed-dependent Voigt profile to extract broadening and shift parameters, and a power-law temperature-dependence exponent for both. The measurements represent the first broad bandwidth, argon-broadened water vapor absorption study, and are an important step toward a foreign-gas-perturbed, high-temperature database developed using advanced lineshape profiles.

Speed-dependent Voigt lineshape parameter database from dual frequency comb measurements up to 1305 K. Part I: Pure H2O absorption, 6801-7188 cm-1.

We measure speed-dependent Voigt lineshape parameters with temperature-dependence exponents for several hundred spectroscopic features of pure water spanning 6801-7188 cm-1. The parameters are extracted from broad bandwidth, high-resolution dual frequency comb absorption spectra with multispectrum fitting techniques. The data encompass 25 spectra ranging from 296 K to 1305 K and 1 to 17 Torr of pure water vapor. We present the extracted parameters, compare them to published data, and present speed-dependence, self-shift, and self-broadening temperature-dependent parameters for the first time. Lineshape data is extracted using a quadratic speed-dependent Voigt profile and a single self-broadening power law temperature-dependence exponent over the entire temperature range. The results represent an important step toward a new high-temperature database using advanced lineshape profiles.

Intercomparison of Open-Path Trace Gas Measurements with Two Dual Frequency Comb Spectrometers.

We present the first quantitative intercomparison between two open-path dual comb spectroscopy (DCS) instruments which were operated across adjacent 2-km open-air paths over a two-week period. We used DCS to measure the atmospheric absorption spectrum in the near infrared from 6021 to 6388 cm-1 (1565 to 1661 nm), corresponding to a 367 cm-1 bandwidth, at 0.0067 cm-1 sample spacing. The measured absorption spectra agree with each other to within 5×10-4 without any external calibration of either instrument. The absorption spectra are fit to retrieve concentrations for carbon dioxide (CO2), methane (CH4), water (H2O), and deuterated water (HDO). The retrieved dry mole fractions agree to 0.14% (0.57 ppm) for CO2, 0.35% (7 ppb) for CH4, and 0.40% (36 ppm) for H2O over the two-week measurement campaign, which included 23 °C outdoor temperature variations and periods of strong atmospheric turbulence. This agreement is at least an order of magnitude better than conventional active-source open-path instrument intercomparisons and is particularly relevant to future regional flux measurements as it allows accurate comparisons of open-path DCS data across locations and time. We additionally compare the open-path DCS retrievals to a WMO-calibrated cavity ringdown point sensor located along the path with good agreement. Short-term and long-term differences between the two systems are attributed, respectively, to spatial sampling discrepancies and to inaccuracies in the current spectral database used to fit the DCS data. Finally, the two-week measurement campaign yields diurnal cycles of CO2 and CH4 that are consistent with the presence of local sources of CO2 and absence of local sources of CH4.

Open-path dual comb spectroscopy to an airborne retroreflector.

We demonstrate a new technique for spatial mapping of multiple atmospheric gas species. This system is based on high-precision dual-comb spectroscopy to a retroreflector mounted on a flying multi-copter. We measure the atmospheric absorption over long open-air paths to the multi-copter with comb-tooth resolution over 1.57 to 1.66 pm, covering absorption bands of CO2, Cm, H2O and isotopologues. When combined with GPS-based path length measurements, a fit of the absorption spectra retrieves the dry mixing ratios versus position. Under well-mixed atmospheric conditions, retrievals from both horizontal and vertical paths show stable mixing ratios as expected. This approach can support future boundary layer studies as well as plume detection and source location.

Broadband, high-resolution investigation of advanced absorption line shapes at high temperature.

Spectroscopic studies of planetary atmospheres and high-temperature processes (e.g., combustion) require absorption line-shape models that are accurate over extended temperature ranges. To date, advanced line shapes, like the speed-dependent Voigt and Rautian profiles, have not been tested above room temperature with broadband spectrometers. We investigate pure water vapor spectra from 296 to 1305 K acquired with a dual-frequency comb spectrometer spanning from 6800 to 7200 cm-1 at a point spacing of 0.0033 cm-1 and absolute frequency accuracy of <3.3 × 10-6 cm-1. Using a multispectral fitting analysis, we show that only the speed-dependent Voigt accurately models this temperature range with a single power-law temperature-scaling exponent for the broadening coefficients. Only the data from the analysis using this profile fall within theoretical predictions, suggesting that this mechanism captures the dominant narrowing physics for these high-temperature conditions.

Accurate frequency referencing for fieldable dual-comb spectroscopy.

We describe a dual-comb spectrometer that can operate independently of laboratory-based rf and optical frequency references but is nevertheless capable of ultra-high spectral resolution, high SNR, and frequency-accurate spectral measurements. The instrument is based on a "bootstrapped" frequency referencing scheme in which short-term optical phase coherence between combs is attained by referencing each to a free-running diode laser, whilst high frequency resolution and long-term accuracy is derived from a stable quartz oscillator. The sensitivity, stability and accuracy of this spectrometer were characterized using a multipass cell. We demonstrate comb-resolved spectra spanning from 140 THz (2.14 µm, 4670 cm-1) to 184 THz (1.63 µm, 6140 cm-1) in the near infrared with a frequency sampling of 200 MHz (0.0067 cm-1) and ~1 MHz frequency accuracy. High resolution spectra of water and carbon dioxide transitions at 1.77 µm, 1.96 µm and 2.06 µm show that the molecular transmission acquired with this system operating in the field-mode did not deviate from those measured when it was referenced to a maser and cavity-stabilized laser to within 5.6 × 10-4. When optimized for carbon dioxide quantification at 1.60 µm, a sensitivity of 2.8 ppm-km at 1 s integration time, improving to 0.10 ppm-km at 13 minutes of integration time was achieved.

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.

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.

Speckle phase noise in coherent laser ranging: fundamental precision limitations.

Frequency-modulated continuous-wave laser detection and ranging (FMCW LADAR) measures the range to a surface through coherent detection of the backscattered light from a frequency-swept laser source. The ultimate limit to the range precision of FMCW LADAR, or any coherent LADAR, to a diffusely scattering surface will be determined by the unavoidable speckle phase noise. Here, we demonstrate the two main manifestations of this limit. First, frequency-dependent speckle phase noise leads to a non-Gaussian range distribution having outliers that approach the system range resolution, regardless of the signal-to-noise ratio. These outliers are reduced only through improved range resolution (i.e., higher optical bandwidths). Second, if the range is measured during a continuous lateral scan across a surface, the spatial pattern of speckle phase is converted to frequency noise, which leads to additional excess range uncertainty. We explore these two effects and show that laboratory results agree with analytical expressions and numerical simulations. We also show that at 1 THz optical bandwidth, range precisions below 10 µm are achievable regardless of these effects.

Time-domain stabilization of carrier-envelope phase in femtosecond light pulses.

We report a time-domain method of stabilizing the carrier-envelope phase (CEP) of femtosecond pulses. Temporal variations of the pulse envelope and the carrier electric-field phase were separately detected with the aid of intensity cross-correlation and interferometric cross-correlation. These detected signals were used to stabilize the CEP; the resulting 50-fold improvement in the fractional stability of the carrier-envelop-offset frequency was evaluated as 1.2 × 10(-11) at 0.1 second averaging periods and 1.7 × 10(-9) at 80 seconds, corresponding to a carrier envelope phase noise of 75 microradians and 10 milliradians, respectively. This method can be realized with a low pulse energy of ~10 pJ and does not require subsequent power amplification or spectral broadening. The high efficiency and short-term stability of this method can facilitate the use of femtosecond lasers in the field of industrial surface measurements, telecommunications, and space sciences.

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.

Microwave generation with low residual phase noise from a femtosecond fiber laser with an intracavity electro-optic modulator.

Low phase-noise microwave generation has previously been demonstrated using self-referenced frequency combs to divide down a low noise optical reference. We demonstrate an approach based on a fs Er-fiber laser that avoids the complexity of self-referenced stabilization of the offset frequency. Instead, the repetition rate of the femtosecond Er-fiber laser is phase locked to two cavity-stabilized cw fiber lasers that span 3.74 THz by use of an intracavity electro-optic modulator with over 2 MHz feedback bandwidth. The fs fiber laser effectively divides the 3.74 THz difference signal to produce microwave signals at harmonics of the repetition rate. Through comparison of two identical dividers, we measure a residual phase noise on a 1.5 GHz carrier of -120 dBc/Hz at 1 Hz offset.

Time-domain spectroscopy of molecular free-induction decay in the infrared.

Time-domain spectroscopy using dual, coherent frequency combs is used to measure free-induction decay from a molecular gas sample in the near-IR with a time-domain signal-to-noise ratio of approximately 10(6) over a approximately 6 ns window at 55 fs time resolution (corresponding to the 9 THz source bandwidth) and a frequency/timing accuracy set by the frequency combs. The free-induction decay exhibits the expected periodic pulses from the rephasing of the multiply excited rovibrational levels. This demonstration represents the first high-resolution, high-accuracy, broadband measurement of optical free-induction decay, to our knowledge.

High-performance, vibration-immune, fiber-laser frequency comb.

We demonstrate an environmentally robust optical frequency comb based on a polarization-maintaining, all-fiber, figure-eight laser. The comb is phase locked to a cavity-stabilized cw laser by use of an intracavity electro-optic phase modulator yielding 1.6 MHz feedback bandwidth. This high bandwidth provides close to shot-noise-limited residual phase noise between the comb and cw reference laser of -94 dBc/Hz from 20 Hz to 200 kHz and an integrated in-loop phase noise of 32 mrad from 1 Hz to 1 MHz. Moreover, the comb remains phase locked under significant mechanical vibrations of over 1 g. This level of environmental robustness is an important step toward a fieldable fiber frequency comb.