Entangled Ions Measure Time Faster
What time is it? How precisely you can answer this question might depend on how long you are able to measure. Glance at a clock and you’ll first register the positions of the hour and minute hands. Look for longer and you’ll make out the movement of the second hand, improving your precision 60-fold. The most precise timepieces currently available are state-of-the-art optical clocks, and these also return a more precise result the longer that they are interrogated. But for many applications—in satellite navigation systems, for example, where the position of a fast-moving vehicle needs to be determined quickly—the answer must be prompt as well as precise. Now Kai Dietze at the German National Metrology Institute and colleagues have demonstrated a way to use quantum entanglement to halve the measurement time of an ion-based optical clock without compromising its precision [1].
Optical clocks are the technological successors to microwave atomic clocks, which, for nearly 60 years, have defined the International System of Units (SI) unit of time: the second. Microwave atomic clocks have been refined since they were first invented in the 1950s, but now optical clocks are reaching maturity in the sense that several systems reach or exceed the criteria required by the International Bureau of Weights and Measures for redefining the second. Optical clocks could potentially outperform microwave clocks by 4 orders of magnitude, with implications for fundamental physics and geodesy.
In a microwave atomic clock, a microwave signal flips the nuclear spins of billions of cesium atoms up or down as long as the signal is resonant with the spins’ transition frequency. Although the probability amplitudes of the spin states shift smoothly during this process, the outcome of a single measurement for an individual atom is binary, because the spin can only point either up or down. This makes the atomic clock a hallmark device of the first quantum revolution. Measuring the state of many atoms—that is, averaging over many binary outcomes in a single shot—improves the clock’s precision up to the standard quantum limit. This improvement arises because the quantum projection noise scales with the square root of the number of atoms measured, meaning that small changes of the collective spin, which indicate how close the signal is to resonance, become detectable more quickly. But when averaging over many atoms, any frequency shift (from particle motion or from electromagnetic or gravitational fields, for example) must be controlled for every atom. This control becomes increasingly challenging as fractional accuracy and precision improve, meaning the averaging process is considerably more difficult for optical clocks than it is for microwave clocks.
Fast forward to the 21st century and the dawn of the second quantum revolution. Now the full quantum state of objects such as atoms and photons has become controllable. Thanks to the laws of quantum mechanics, one can do better than just average over the atoms. By placing the atoms in an entangled state, they become “spookily” connected, and the measurement outcome on one atom determines that on the other atoms. In an ideal clock with atoms, this entanglement causes their collective quantum state to evolve times faster than that of a single atom. As a result of this speedup, the precision of such a clock benefits from an improvement by compared to one that employs unentangled atoms [2, 3]. Corresponding protocols have been implemented successfully for both microwave and optical trapped-ion clocks [4], but since those systems generally exhibited short coherence times or had uncharacterized systematic errors, they were of limited interest to metrologists.
In their recent work, Dietze and co-workers operate an optical atomic clock based on two calcium ions that transition between two precisely defined electronic states. Even with , their device achieves a state-of-the-art stability near , which they further improve by entangling the two ions (Fig. 1). The result is a clock with better stability than any comparable system [1]. One key to their success is that they place the two ions in a “decoherence-free subspace” (DFS). In this regime, magnetic-field fluctuations shift the energies of the two ions in opposite directions. Since the two ions, being separated by only a few micrometers, experience nearly identical fluctuations, the net result is a cancellation of their energy difference, which affects the decoherence of the entangled state. Using a state-of-the-art clock laser then results in coherence being limited only by the lifetime of the clock’s excited state rather than environmental noise―in this case, fluctuations of the background magnetic field.
But Dietze and colleagues study more than just the quantum-correlated (entangled), DFS-protected state. They also prepare a classically correlated (but unentangled) state that is equally protected from magnetic-field fluctuations. This protocol enables them to isolate the gain provided by the entanglement itself and to distinguish it from other features of the clock, such as its laser noise or the operation in a DFS. As expected from theory, the entangled clock averages down twice as fast as the classically correlated clock. That’s because an additional increase in measurement precision comes from the fact that the entangled state provides a higher-contrast signal than that of the classically correlated state.
As multi-ion optical clocks improve further, implementing entanglement schemes such as the one demonstrated by Dietze and colleagues will help timekeepers to average down ever faster. The implications could be significant: For example, hypothetical dark-matter fields are expected to induce tiny shifts in atomic resonance frequencies and could be detected with highly precise optical clocks [5]. Achieving such precision will also enable the resolution of tiny systematic offsets of the transition frequency and help to develop even more accurate clocks.
The success of the experiments by Dietze and colleagues lies in their combination of excellence in frequency metrology, backed by the infrastructure of a national laboratory, and expertise in quantum information processing. If their method is to be used in a future optical-frequency standard (pending the redefinition of the second expected in the next few years), the main obstacle to be overcome is in characterizing the light shift induced by the laser pulses that entangle the ions. Because of that shift, the accuracy (or systematic uncertainty) of the entangled clock is currently not on par with the unentangled one. Though short compared to the clock interrogation laser pulse, the entangling pulses shift the effective frequency by up to Hz, or part in . This shift will need to be known very precisely (or cancelled out) to reach an accuracy close to part in , the regime in which the best clocks are currently operating [6]. The researchers are optimistic that this goal is technically achievable.
Besides pairs of ions, large ensembles of neutral atoms in optical lattices and small numbers of atoms individually trapped in optical tweezers have also been entangled for improved clock precision. Spin squeezing in lattice clocks has helped achieve exceptional stability [7], but the description is more subtle than the textbook two-atom entangled state used by Dietze and colleagues. In tweezer clocks using maximally entangled states, more than two atoms have been used but not yet at the stability demonstrated here [8].
The stability could improve further when entangling more than two ions or by using another ion species with a suitable transition at a higher optical frequency. Better control of systematic uncertainties—for example, by minimizing frequency shifts due to blackbody radiation or by using more massive ions—may ultimately prove decisive for next-generation ion optical clocks.
References
- K. Dietze et al., “Entanglement-enhanced optical ion clock,” Phys. Rev. Lett. 136, 073601 (2026).
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- A. Arvanitaki et al., “Searching for dilaton dark matter with atomic clocks,” Phys. Rev. D 91, 015015 (2015).
- S. M. Brewer et al., “27Al+ quantum-logic clock with a systematic uncertainty below 10−18,” Phys. Rev. Lett. 123, 033201 (2019); “Erratum: 27Al+ quantum-logic clock with a systematic uncertainty below 10−18 [Phys. Rev. Lett. 123, 033201 (2019)],” 131, 059901 (2023).
- E. Pedrozo-Peñafiel et al., “Entanglement on an optical atomic-clock transition,” Nature 588, 414 (2020).
- A. Cao et al., “Multi-qubit gates and Schrödinger cat states in an optical clock,” Nature 634, 315 (2024).