Quantum Oscillators Find a Shared Beat
When clocks share a wall, heart cells pulse in a dish, or fireflies flash in a summer field, separate rhythms can somehow become one. Physicists call this phenomenon synchronization. It is familiar in the everyday world but becomes slippery in the quantum world, where an oscillator’s phase can be smeared out by environmental fluctuations and disturbed by measurements. Now, in a trapped-ion experiment, Jiarui Liu at the University of California, Berkeley, and his colleagues have observed synchronization between two quantum oscillators [1]. Their demonstration is important not just because it realizes a long-sought quantum version of a textbook nonlinear system, but also because the shared rhythm is hidden: Each oscillator alone shows no phase preference, and the beat emerges only when the two are measured together.
The classical picture of synchronization predates quantum mechanics. A key component is a self-sustained oscillator, a system that keeps repeating the same motion on its own. Such a system continually replaces the energy it loses through damping, while also preventing its motion from growing uncontrollably. Its amplitude is fixed, but its phase remains free, allowing an interaction with another oscillator to lock the two rhythms together.
The so-called Van der Pol oscillator is the paradigmatic model for this behavior. In the quantum version, the ingredients become controlled processes that add and remove quanta of vibrational motion known as phonons [2]. In particular, a one-phonon gain process adds a quantum of vibration, while a two-phonon loss process prevents runaway growth. Theoretical studies have explored such systems for more than a decade [3], and recent experimental advances have focused on a single quantum Van der Pol oscillator [4]. But what had remained missing was the ability to scale up this system into a collection of synchronized quantum clocks.
Liu and his colleagues have experimentally realized the first step toward such a network: two self-sustained nonlinear Van der Pol oscillators synchronizing with each other (Fig. 1). Within a radio-frequency electromagnetic trap, the researchers created an ordered arrangement of two calcium ions: one calcium-40 and the other calcium-44. In many trapped-ion experiments, the ions’ electronic states serve as the relevant quantum oscillators, but here that role was played by two shared vibrational modes of the ion pair. In one mode, the ions moved together; in the other, they moved in opposite directions.
One of the experiment’s innovative features was its use of dissipation. Dissipation is often treated as the enemy of quantum coherent dynamics, leaking information to the environment and washing out delicate states. Here, it was the primary tool in the experiment. To synchronize the oscillators, Liu and his colleagues engineered dissipation by tailoring phonon gain and loss processes together with a collective dissipative channel. This setup favored a fixed relative phase between the vibrational modes and produced synchronization that remained robust to frequency detuning and to the dominant experimental imperfections.
The most striking part of the experiment was how synchronization was detected. The researchers repeatedly probed the trapped ions and reconstructed the Wigner function, a phase-space map of the oscillators’ quantum state in position and momentum space. When either oscillator was examined individually, its Wigner function appeared as a donut-shaped ring in position–momentum space. This ring indicates a stable oscillation amplitude, much like a clock whose hand points in a random direction. However, when the team reconstructed the joint state of both oscillators, a preferred relative phase emerged. In-phase synchronization appeared as a diagonal feature in the joint map, antiphase synchronization as an antidiagonal feature, and quarter-cycle synchronization as a circular pattern. The synchronization was therefore invisible in either oscillator alone and existed only in the correlations between the two oscillators.
Liu and his colleagues note that their trapped-ion platform could be scaled up to large oscillator networks, which might exhibit topologically protected synchronization and other novel phenomena [5]. These effects are difficult or impossible to simulate on a classical computer and could be explored at scale using such a platform.
The long-term dream of physicists is to use these phase-locked quantum states to build quantum sensors and clocks that can achieve a measurement precision beyond that of conventional devices. From a fundamental point of view, researchers ultimately aim to determine whether long-range quantum fluctuations can drive self-organization in large quantum systems. And if so, whether this process can lead to collective, self-sustained oscillations that have no classical counterparts and that cannot be reduced to the behavior of only a few interacting components. Such advances would expand our understanding of how complex organization can emerge from the fundamental laws of quantum physics.
References
- J. Liu et al., “Observation of synchronization between two quantum van der Pol oscillators in trapped ions,” Phys. Rev. X 16, 021062 (2026).
- T. E. Lee and H. R. Sadeghpour, “Quantum synchronization of quantum van der Pol oscillators with trapped ions,” Phys. Rev. Lett. 111, 234101 (2013).
- S. Walter et al., “Quantum synchronization of two Van der Pol oscillators,” Ann. Phys. (Berl., Ger.) 527, 131 (2015).
- Y. Li et al., “Experimental realization and synchronization of a quantum van der Pol oscillator,” Sci. Adv. 11, eady5649 (2025).
- C. W. Wächtler and G. Platero, “Topological synchronization of quantum van der Pol oscillators,” Phys. Rev. Res. 5, 023021 (2023).