**Optical atomic clocks are the most accurate tools available for measuring time and frequency. It is on them that the maintenance of international atomic time (TAI) and by extension, coordinated universal time (UTC) is based. The synchronization of two of these clocks makes it possible to probe the spatio-temporal variation of the fundamental constants, but the maneuver lacks precision due to the disturbances generated by the measurements. Physicists at the University of Oxford have found a way around this difficulty via quantum entanglement.**

The accuracy of an atomic clock is that it relies on the resonant frequency of atoms — the frequency of electromagnetic radiation emitted by an electron as it transitions from one energy level to another — which is by definition immutable. Atomic vibrations are indeed the most stable periodic events that scientists can observe. Their frequency is measured very precisely by means of lasers. Thus, the 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.

Even more precise, optical atomic clocks, developed in the 2000s, are based on atoms whose energy transitions take place at optical frequencies (aluminum, strontium, mercury, etc.). The second should also be redefined according to these clocks when they reach maturity. Methods to reliably and accurately compare different optical clocks around the world must first be demonstrated. The task is particularly difficult, because their measurement causes disturbances. Researchers have therefore undertaken to intertwine two optical atomic clocks to only have to perform a single measurement.

## Measurement uncertainty reduced by a factor of two

As a reminder, the quantum entanglement (or entanglement) of two systems implies that any change in one instantly affects the other. This intrinsic link is therefore likely to facilitate the synchronization of the clocks. ” *Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can exceed the standard quantum limit to reach the ultimate precision allowed by quantum theory – the Heisenberg limit* “, explain the researchers in *Nature*.

Local entanglement experiments, at microscopic distances, had already demonstrated that the approach made it possible to reduce measurement uncertainties and thus increase the precision of optical atomic clocks. In 2020, scientists at MIT developed a clock measuring the oscillations of entangled atoms (about 350 ytterbium atoms). A first laser was used to quantum entangle the atoms, then a second laser was used to measure their average frequency. They thus achieved the same precision as a non-entangled atom clock, but four times faster!

In this new experiment, the team used not one, but two atomic clocks, each made using a single strontium ion (^{88}sr^{+}), two meters apart. Using a laser, they excited the strontium ions so that they emit blue light. This was then directed via an optical fiber into an analyzer of Bell states — which designate the states of maximum quantum entanglement of two particles; the two ions were therefore entangled via a photonic bond.

From then on, the measurement of one clock immediately provided access to the measurement of the other. For frequency comparisons between ions, the researchers report an uncertainty of about 7% (compared to 28% in the case where the clocks are not entangled). ” *We find that entanglement reduces the measurement uncertainty by nearly √2, the predicted value for the Heisenberg limit* write the researchers. According to the laws of quantum physics, it is impossible to measure the clock frequency with perfect precision, but this experiment shows that it is possible to come close.

## Extreme precision that could help solve many mysteries of physics

Current optical clocks are generally limited by the phase shift of the probe laser. In this experiment, entanglement reduced measurement uncertainty by a factor of 2 compared to conventional correlation spectroscopy techniques, the researchers point out.

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

If this experiment can be repeated with clocks farther apart, for example in two separate laboratories, or with more clocks, it could really advance dark matter or gravitational wave studies. Indeed, a displacement of dark matter between the two entangled clocks, or small changes in the force of gravity, would immediately induce a difference between their “tick-tock” frequencies.