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

Time transfer over 113 km free space laser communication channel

The space time frequency transfer plays a crucial role in applications such as space optical clock networks, navigation, satellite ranging, and space quantum communication. Here, we propose a high-precision space time frequency transfer and time synchronization scheme based on a simple intensity modulation/direct detection (IM/DD) laser communication system, which occupies a communication bandwidth of approximately 0.2%. Furthermore, utilizing an optical-frequency comb time frequency transfer system as an out-of-loop reference, experimental verification was conducted on a 113 km horizontal atmospheric link, with a long-term stability approximately 8.3 × 10-16 over a duration of 7800 seconds. Over an 11-hour period, the peak-to-peak wander is approximately 100 ps. Our work establishes the foundation of the time frequency transfer, based on the space laser communication channel, for future ground-to-space and inter-satellite links.

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 relativity^1-3, dark-matter searches⁴ and gravitational-wave detection⁵. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry^6,7, advanced satellite navigation⁸, clock-based geodesy^2,9,10 and thousandfold improvements in intercontinental time dissemination^11,12. 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 approaches^14-24. 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.

Self-Induced Phase Locking of Terahertz Frequency Combs in a Phase-Sensitive Hyperspectral Near-Field Nanoscope

Chip-scale, electrically-pumped terahertz (THz) frequency-combs (FCs) rely on nonlinear four-wave-mixing processes, and have a nontrivial phase relationship between the evenly spaced set of emitted modes. Simultaneous monitoring and manipulation of the intermode phase coherence, without any external seeding or active modulation, is a very demanding task for which there has hitherto been no technological solution. Here, a self-mixing intermode-beatnote spectroscopy system is demonstrated, based on THz quantum cascade laser FCs, in which light is back-scattered from the tip of a scanning near-field optical-microscope (SNOM) and the intracavity reinjection monitored. This enables to exploit the sensitivity of FC phase-coherence to optical feedback and, for the first time, manipulate the amplitude, linewidth and frequency of the intermode THz FC beatnote using the feedback itself. Stable phase-locked regimes are used to construct a FC-based hyperspectral, THz s-SNOM nanoscope. This nanoscope provides 160 nm spatial resolution, coherent detection of multiple phase-locked modes, and mapping of the THz optical response of nanoscale materials up to 3.5 THz, with noise-equivalent-power (NEP) ≈400 pW √Hz-1 . This technique can be applied to the entire infrared range, opening up a new approach to hyper-spectral near-field imaging with wide-scale applications in the study of plasmonics and quantum science, inter alia.

Frequency comb-to-comb stabilization over a 1.3-km free-space atmospheric optical link

Stabilizing a frequency comb to an ultra-stable optical frequency reference requires a multitude of optoelectronic peripherals that have to operate under strict ambient control. Meanwhile, the frequency comb-to-comb stabilization aims to synchronize a slave comb to a well-established master comb with a substantial saving in required equipment and efforts. Here, we report an utmost case of frequency comb-to-comb stabilization made through a 1.3 km free-space optical (FSO) link by coherent transfer of two separate comb lines along with a feedback suppression control of atmospheric phase noise. The FSO link offers a transfer stability of 1.7 × 10^-15 at 0.1 s averaging, while transporting the master comb's stability of 1.2 × 10^-15 at 1.0 s over the entire spectrum of the slave comb. Our remote comb-to-comb stabilization is intended to expedite diverse long-distance ground-to-ground or ground-to-satellite applications; as demonstrated here for broadband molecular spectroscopy over a 6 THz bandwidth as well as ultra-stable microwaves generation with phase noise of -80 dBc Hz^-1 at 1 Hz.

X-Band photonic microwaves with phase noise below -180 dBc/Hz using a free-running monolithic comb

Free-running mode-locked monolithic optical frequency combs offer a compact and simple alternative to complicated optical frequency division schemes. Ultra-low free-running noise performance of these oscillators removes the necessity of external phase stabilization, making the microwave systems uncomplicated and compact with lower power consumption while liberating the sidebands of the carrier from servo bumps typically present around hundreds of kilohertz offsets. Here we present a free-running monolithic laser-based 8 GHz photonic microwaves generation and characterization with a cryogenically cooled power splitter to demonstrate a state-of-the-art phase noise floor of less than -180 dBc/Hz below 1 MHz offset from the carrier.

Highly stable multiple-access underwater frequency transfer with terminal phase compensation

A multiple-access underwater frequency transfer scheme using terminal phase compensation is demonstrated. With this scheme, a highly stable 100 MHz frequency signal was disseminated over a 3 m underwater link for 5000 s. The timing fluctuation and fractional frequency instability were both measured and analyzed. The experimental results show that with the phase compensation technique, the total root-mean-square (RMS) timing fluctuation is about 3 ps, and the fractional frequency instabilities are on the order of 5.9×10^-13 at 1 s and 5.3×10^-15 at 1000 s. The experiment results indicate that the proposed frequency transfer technique has a potential application of disseminating an atomic clock to multiple terminals.

Atmospheric refraction corrections in ground-to-satellite optical time transfer

Free-space optical time and frequency transfer techniques can synchronize fixed ground stations at the femtosecond level, over distances of tens of kilometers. However, optical time transfer will be required to span intercontinental distances in order to truly unlock the performance of optical frequency standards and support an eventual redefinition of the SI second. Fiber dispersion and Sagnac uncertainty severely limit the performance of long-range optical time transfer over fiber networks, so satellite-based free-space time transfer is a promising solution. In pursuit of ground-to-space optical time transfer, previous work has considered a number of systematic shifts and concluded that all of them are manageable. One systematic effect that has not yet been substantially studied in the context of time transfer is the effect of excess optical path length due to atmospheric refraction. For space-borne objects, orbital motion causes atmospheric refraction to be imperfectly canceled even by two-way time and frequency transfer techniques, and so will require a temperature-, pressure-, and humidity-dependent correction. This systematic term may be as large as a few picoseconds at low elevations and remains significant at elevations up to ~35^°. It also introduces biases into previously-studied distance- and velocity-dependent corrections.

Outdoor atmospheric optical two-way time transfer with serial time code

We demonstrated an optical two-way time transfer scheme in the outdoor free-space link using a simple complex programmable logic device-based serial time coder/decoder. With this scheme, we have transferred a 100 Hz signal with time information over a 120-m outdoor atmospheric link. The time drift, time deviation, and frequency instability are all measured to estimate the quality of the transferred time signal during the transfer process. Within 11 h, the experimental result shows that the total root-mean-square time drift is about 81 ps, with the time deviation of 70 ps at 1-s averaging time and down to 10 ps above 100-s averaging time. The calculation shows that the fractional frequency instability of the transmission link is on the order of 1.4 × 10^-10 at 1 s and of 3.0 × 10^-15 at 10 000 s. The time deviation and frequency instability for the optical two-way time transfer are superior to those of the Global Positioning System (GPS)-based time transfer method, which implies the technique proposed in this paper is able to be directly used in high-precision time transfer over atmospheric links in a short distance.

Point-to-point stabilized optical frequency transfer with active optics

Timescale comparison between optical atomic clocks over ground-to-space and terrestrial free-space laser links will have enormous benefits for fundamental and applied sciences. However, atmospheric turbulence creates phase noise and beam wander that degrade the measurement precision. Here we report on phase-stabilized optical frequency transfer over a 265 m horizontal point-to-point free-space link between optical terminals with active tip-tilt mirrors to suppress beam wander, in a compact, human-portable set-up. A phase-stabilized 715 m underground optical fiber link between the two terminals is used to measure the performance of the free-space link. The active optical terminals enable continuous, cycle-slip free, coherent transmission over periods longer than an hour. In this work, we achieve residual instabilities of 2.7 × 10-6 rad2 Hz-1 at 1 Hz in phase, and 1.6 × 10-19 at 40 s of integration in fractional frequency; this performance surpasses the best optical atomic clocks, ensuring clock-limited frequency comparison over turbulent free-space links.

Laser-based underwater frequency transfer with sub-picosecond timing fluctuation using optical phase compensation

We demonstrated a sub-picosecond laser-based underwater frequency transfer with an optical phase compensation. With this transfer technique, a highly-stable 500 MHz radio-frequency (RF) signal was disseminated over a 5-m underwater link for 5000 s, and the characteristic of the timing fluctuation and instability for the transfer was analyzed and measured. The experimental results show the total root-mean-square (RMS) timing fluctuation of the transferred RF signal with compensation is about 162 fs with a fractional frequency instability on the order of 2.8 × 10^-13 at 1 s and 2.7 × 10^-16 at 1000 s. The laser-based underwater frequency transfer proposed in this paper has a potential application of transferring atomic clock in water environment as its instability is less than the currently-used commercial Cs or H-master clocks.

Analysis and experimental demonstration of underwater frequency transfer with diode green laser

We demonstrated an underwater frequency transfer technique with a green diode laser. The characteristic of the timing fluctuation and instability for the transfer technique was analyzed and simulated. With this technique, we had transferred a highly stable 100-MHz frequency signal over an underwater link with distances of 3 m, 6 m, and 9 m for 5000 s, respectively. The experimental results involving the underwater transfer of the 100-MHz radio-frequency signal shows that the rms timing fluctuations are 5.9 ps (3-m link), 6.4 ps (6-m link), and 8.4 ps (9-m link). The calculations also show that the relative Allan deviations for the 3-m, 6-m, and 9-m transmission links are 5.6 × 10^-13 at 1 s and 5.3 × 10^-15 at 1000 s, 5.8 × 10^-13 at 1 s and 1.1 × 10^-14 at 1000, and 6.8 × 10^-13 at 1 s and 1.1 × 10^-14 at 1000 s, respectively. The measured instabilities were lower than Rb and Cs atomic clocks, implying that the proposed frequency transfer scheme can potentially be used to transfer the signals of these atomic clocks over underwater links.

Development of a photoelectric phase-locked loop model to better synchronize frequency combs and microwaves

The high phase coherence between ultralow-noise microwaves and ultrahigh-stable optical frequency combs (OFCs) is of both scientific and technological relevance for telecommunication, timekeeping, astronomy, and metrology. Here, a photoelectric phase-locked loop (PLL) model with ultralow phase noise based on the optical-microwave phase detector technique has been proposed and experimentally demonstrated. A detailed mathematical model for tight, real-time phase synchronization of OFCs and microwaves is developed to investigate the feasibility and analyze the characteristics of the phase-coherent system. We fabricate a compact PLL circuit with a proportional-integral-derivative regulator for the synchronization of an OFC to a microwave reference. Once synchronized, the long-term stability of the OFC agrees to 2.4×10^-14 at a 1000 s averaging time, which is enhanced by more than 4 orders of magnitude. Besides, the OFC almost acquires the same frequency stability as the microwave source. The ability to better phase synchronize OFCs and microwaves enables a wide range of applications beyond the laboratory.

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.

Optical clock networks have many applications from precision time keeping, sensing to fundamental physics. Here the authors demonstrate robust and free-space femtosecond time synchronization of optical clocks via a moving quadcopter.

Free-space-based multiple-access frequency dissemination with optical frequency comb

We demonstrate a free-space-based multiple-access frequency dissemination with an optical frequency comb by using a passive phase conjunction correction technique. Timing fluctuations and Allan Deviations are both measured to characterize the excess frequency instability incurred during the frequency transfer process. By reproducing a 2 GHz radio-frequency signal at a middle point over a 60-m long free-space link in 5000 s, the total root-mean-square (RMS) timing fluctuation was measured to be about 224 fs with a fractional frequency instability on the order of 8 × 10^-14 at 1 s and 1 × 10^-16 at 1000 s. This free-space-based multiple-access frequency transfer with passive phase conjunction correction can be used to disseminate a stable frequency signal at an arbitrary point in a free-space link.

Research on the spectral phase correction method for the atmospheric detection in open space

During the atmospheric detection process in open space, the excessive phase noise is introduced into the signal, due to the atmospheric turbulence, which causes the intensity and phase fluctuation. In the previous study, a spectral data processing method based on the co-frequency and dual-wave has been used to reduce the influence of the scintillation noise from the atmospheric turbulence in open space, while the influence of the phase noise remains to be solved. So the wavelength modulated signal is theoretically analyzed at first. On studying the relationship between the dual-waves in one cycle to eliminate the phase fluctuation and reduce the phase fluctuation caused by the atmospheric turbulence, a new method of the spectral phase correction for the open space atmospheric detection has been proposed. An atmospheric detection experiment on the phase correction in the open space based on co-frequency and dual-wave has been carried out. The results show that the maximum fluctuation of the spectral signal processed with this method is 1.06%, while the power spectral density fluctuation is suppressed below 50Hz, and the Allan analysis result is 8.8 × 10^-8(1s). Compared with the traditional concentration inversion method using 2f-wavelength modulation and the classical light intensity elimination, the proposed phase correction method can effectively reduce the fluctuation of random noise caused by the short-term atmospheric turbulence and the laser flashing to improve the stability of the concentration measurement, which has practical engineering value.

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10^{-17} in Frequency

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.

Low-loss reciprocal optical terminals for two-way time-frequency transfer

We present the design and performance of a low-cost, reciprocal, compact free-space terminal employing tip/tilt pointing compensation that enables optical two-way time-frequency transfer over free-space links across the turbulent atmosphere. The insertion loss of the terminals is ∼1.5  dB with total link losses of 15 dB, 24 dB, and 50 dB across horizontal, turbulent 2-km, 4-km, and 12-km links, respectively. The effects of turbulence on pointing control and aperture size, and their influence on the terminal design, are discussed.

Femtosecond-level timing fluctuation suppression in atmospheric frequency transfer with passive phase conjunction correction

We demonstrate femtosecond-level timing fluctuation suppression in indoor atmospheric comb-based frequency transfer with a passive phase conjunction correction technique. Timing fluctuations and Allan deviations are both measured to characterize the excess frequency instability incurred during the frequency transfer process. By transferring a 2 GHz microwave over a 52-m long free-space link in 5000 s, the total root-mean-square (RMS) timing fluctuation was measured to be about 280 fs with a fractional frequency instability on the order of 3 × 10^-13 at 1 s and 6 × 10^-17 at 1000 s. This atmospheric comb-based frequency transfer with passive phase conjunction correction can be used to build an atomic clock-based free-space frequency transmission link because its instability is less than that of a commercial Cs or H-master clock.

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.