Optical atomic clocks are the most accurate instruments for measuring time and frequency. It is on them that the maintenance of international atomic time (TAI) and, accordingly, coordinated universal time (UTC) is based. Synchronization of two of these clocks makes it possible to investigate space-time changes in fundamental constants, but the maneuver lacks precision due to interference from measurements. Physicists at Oxford University have found a way around this difficulty with quantum entanglement.

The accuracy of atomic clocks lies in the fact that they are based on the resonant frequency of atoms—the frequency of the electromagnetic radiation emitted by an electron as it moves from one energy level to another—which, by definition, does not change. Atomic vibrations are indeed the most stable periodic phenomena that scientists can observe. Their frequency is very accurately measured using lasers. Thus, a second is historically defined as the exact duration of 9,192,631,770 oscillations of the transition between the hyperfine levels of the ground state of the cesium-133 atom.

More precisely, optical atomic clocks, developed in the 2000s, are based on atoms whose energy transitions occur at optical frequencies (aluminum, strontium, mercury, etc.). The second should also be redefined to match those hours when they reach maturity. First, methods must be demonstrated to reliably and accurately compare different optical clocks around the world. The task is especially difficult, since their measurement causes interference. So the researchers decided to connect two optical atomic clocks to make just one measurement.

## Measurement error reduced by half

Recall that the quantum entanglement (or entanglement) of two systems implies that any change in one instantly affects the other. So this intercom will probably make it easier to keep the clocks in sync. “Measurements on independent systems are limited by the standard quantum limit; measurements of entangled systems can exceed the standard quantum limit to achieve the ultimate precision allowed by quantum theory, the Heisenberg limit,” the researchers explain in Nature.

Local experiments on entanglement at microscopic distances have already demonstrated that this approach can reduce measurement errors and thus improve the accuracy of optical atomic clocks. In 2020, MIT scientists developed a clock that measures the vibrations of entangled atoms (about 350 ytterbium atoms). The first laser was used to quantum entangle the atoms, then the second laser was used to measure their average frequency. Thus, they achieved the same accuracy as an unentangled atomic clock, but four times faster!

In this new experiment, the team used not one, but two atomic clocks, each made from a single strontium (88Sr+) ion two meters apart. Using a laser, they excited strontium ions so that they emit blue light. This was then sent through an optical fiber to a Bell State Analyzer, which denotes states of maximum quantum entanglement of two particles; Thus, the two ions were entangled by the photon bond.

The array consists of two systems of trapped ions, Alice and Bob, separated by 2 meters, each containing one 88Sr+ ion. Photonic communication allows you to create entanglement at a distance. © B. Nicol et al.

From that moment on, the measurement of one clock immediately opened up access to the measurement of others. For frequency comparisons between ions, the researchers report an error of about 7% (compared to 28% when the clock is not entangled). “We found that entanglement reduces measurement uncertainty by almost √2, which is the predicted value for the Heisenberg limit,” the researchers write. According to the laws of quantum physics, it is impossible to measure the clock frequency with perfect accuracy, but this experiment shows that it is possible to get close.

## Extreme precision that can help solve many of the mysteries of physics

Modern optical clocks are usually limited by the phase shift of the probing laser. The researchers note that in this experiment, entanglement reduced the measurement uncertainty by a factor of 2 compared to conventional correlation spectroscopy methods.

“This two-node network can be extended to other nodes, to other kinds of trapped particles, or, through local operations, to larger intricate systems,” they add. They note, in particular, the possibility of choosing an ion whose transition represents a reduced sensitivity to a magnetic field, a narrower linewidth, or an increased sensitivity to fundamental constants. On the other hand, using local operations to increase the number of entangled ions at each site can further reduce measurement uncertainty for frequency comparisons.

If this experiment could be repeated with more widely spaced clocks, such as in two separate labs, or with more clocks, it could really advance research on dark matter or gravitational waves. Indeed, shifting dark matter between two entangled clocks, or small changes in the strength of gravity, would immediately cause a tick-tock difference between their frequencies.