Light clocks achieve the highest precision of star-ground transmission at the quantum limit!

Communication networks, satellite navigation and experiments in fundamental physics that test general relativity are just a few of the various systems that rely on modern networks of atomic clocks. These clocks are accurate to a few 1018ths of a second: roughly equivalent to being able to measure the time between now and the Big Bang with an uncertainty of only one second. However, in order to take advantage of this precision, the time signal from the atomic clocks needs to be reliably transmitted.

Recently, a joint team of scientists from NIST, the University of Colorado and others demonstrated a technique that can be used to transmit time signals from atomic clocks between Earth and satellites without compromising the precision and accuracy of the signal - limited only by the quantum nature of light.

The results were published in the journal Nature on June 21 under the title "Quantum-limited optical time transfer for future geosynchronous links.

Atomic clocks use the frequency of light emitted by electrons as they transition between the energy states of an atom to keep time. Optical atomic clocks use intersecting laser beams to capture the atoms: these laser beams are designed so that the frequency of the laser has little effect on the frequency emitted by the electrons. The time signal of an optical atomic clock needs to be transmitted with a laser, through a fiber optic cable or through air, a process called optical time transmission. To avoid degrading the accuracy of the timing during transmission, the transmission systems need to be more stable than the clocks themselves; however, their stability can be degraded by vibrations and temperature changes near the optical fibers, or by turbulence in the air.

Previously, members of the team had demonstrated optical time transmission by pairing atomic clocks with optical frequency combs (lasers that produce very short, precise pulses of light). One of the reasons these "combs" are so useful for precise measurements is that the pulses can be generated at a very regular rate; by measuring the difference in the arrival times of the pulses from the two comb pairs at either end of the optical link, the time difference between the clocks can be calculated, revealing how close they are to being synchronized. Moreover, since the two "combs" send pulses through the link simultaneously, any degradation in time accuracy caused by vibration or air turbulence can be eliminated.

Last year, such "combs" were used to transmit a stable clock signal over a 113-kilometer link between two mountains. However, the demonstration relied on a high-powered optical frequency comb to transmit and receive the signal, using a telescope equipped with a complex optical system to correct for the distortion of the comb signal caused by turbulence on the link. In contrast, this time Caldwell et al. used combs with 200 times lower power to transmit such signals over a range of 300 km: thus enabling the use of smaller telescopes that do not require correction of the optical system.

The authors showed that this system works by sending signals between the Hawaiian volcanoes Mauna Loa and Haleakala, which are about 150 km apart. The clocks are stationed on Mauna Loa so that the accuracy and precision of the time transmission can be easily verified; and the signals are reflected from Haleakala to maximize the distance traveled.

Not only that, but the experimental team also optimized the optical time transmission to the quantum limit; a limit at which the highest possible stability and accuracy is fundamentally limited by the number of photons received from the combs.

In the quantum limit, precise time synchronization is achieved between distant clocks. caldwell et al. paired optical clocks with optical frequency combs (lasers that produce precise, regular pulses of light) to transmit reflected signals between the Mauna Loa and Haleakala volcanoes in Hawaii over a round-trip distance of 300 km. They calculated the time difference between the clocks using the arrival time difference of pulses sent from one clock combination to another with an accuracy close to the quantum limit, which is determined by the number of photons transmitted. These clocks were connected for verification of the time transmission, and the pulse rates of the two combs were adjusted to scan for possible time differences, which were then steered into synchronized pulses.

The "time-programmable frequency comb" proposed in previous experiments

To achieve this goal, Caldwell et al. used a device they had previously developed, the "time-programmable frequency comb". In research conducted prior to this innovation, the combs at each end of the link were set to pulse at different rates; at regular intervals, the pulses of each comb were aligned so that the time difference between the clocks could be measured. This allowed the time transfer system to scan the range of possible time differences between the two clocks, but because the rates were fixed, it also meant that most of the combs' pulses were out of sync, so most of the photons were not used.

The authors' time-programmable combs allowed them to precisely adjust the pulse rate so that the two combs could be synchronized after an initial scan of the possible time differences. However, despite this progress, photons are still lost when crossing the 300 km of air between the transmitter and receiver: only about one out of every 100 pulses from the combs detects a photon at the other end of the link. However, through digital filtering and careful optimization of the comb control system, the authors were able to use the few photons that were detected to achieve efficient time transmission in the presence of these losses.

One of the most promising aspects of Caldwell and colleagues' work is that it shows that the system can be used to span the distance between the ground and a geostationary satellite. Geostationary satellites orbit the Earth at an altitude that allows them to stay in the same position on Earth as it rotates. And the comb needed to successfully transmit a time signal across this distance requires only 4 milliwatts of power (a typical laser pointer emits 1 milliwatt). Thus, these findings allow fundamental physics experiments to be performed with much greater precision than existing systems.

One of the most promising aspects of Caldwell and colleagues' work is that it shows that the system can be used to span the distance between the ground and a geostationary satellite. Geostationary satellites orbit the Earth at an altitude that allows them to stay in the same position on Earth as it rotates. And the comb needed to successfully transmit a time signal across this distance requires only 4 milliwatts of power (a typical laser pointer emits 1 milliwatt). Thus, these findings allow fundamental physics experiments to be performed with much greater precision than existing systems.

Ground-to-space time transfer. The efficiency of this paper's system makes it ideal for satellite use because its low power and small telescope aperture minimizes its size and weight, thus minimizing the cost of the satellite.

More broadly, this feat represents the highest time transmission accuracy achievable in the "standard" quantum limit.

In the future, the team says, a technique called "quantum squeezing" can reduce the quantum uncertainty of one measurement by increasing the uncertainty of another, which can then be used to push the limits of achievable accuracy even further to keep pace with atomic clock technology.

The team's work now provides the most convincing demonstration to date that time signals from optical clocks can be transmitted between ground and satellite - a prospect that will have profound implications for the use of satellites in basic and applied science.

Reference links:
[1] https://www.nature.com/articles/s41586-021-03253-4
[2]https://www.nature.com/articles/s41586-022-05228-5
[3]https://www.nature.com/articles/s41586-023-06032-5
[4]https://www.nature.com/articles/d41586-023-01937-7