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  • Featured in Physics
  • Open Access

Observation of Synchronization between Two Quantum van der Pol Oscillators in Trapped Ions

Jiarui Liu1,2,3,*, Qiming Wu1,2,3,*,†, Joel E. Moore1,2,3, Hartmut Haeffner1,2,3,‡, and Christopher W. Wächtler4,1,§

  • *These authors contributed equally to this work.
  • †Contact author: qiming.wu@berkeley.edu
  • ‡Contact author: hhaeffner@berkeley.edu
  • §Contact author: cwwaechtler@icmm.csic.es
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Phys. Rev. X 16, 021062 – Published 29 June, 2026

DOI: https://doi.org/10.1103/w1bm-wjl4

Abstract

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

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Quantum Oscillators Find a Shared Beat

Published 29 June, 2026

The synchronization of two quantum oscillators reveals a collective rhythm encoded solely in their correlations.

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Popular Summary

Synchronization is a widespread classical phenomenon of spontaneous collective behavior, yet understanding how such dynamics manifest in microscopic systems governed by quantum mechanics remains a complex theoretical and experimental challenge. We demonstrate synchronization between two quantum van der Pol oscillators by carefully engineering dissipative processes that generate quantum limit-cycle dynamics within a mixed-isotope trapped-ion quantum simulator. We establish that the resulting synchronized state is encoded in a fixed relative phase between the two interacting limit-cycle oscillators. This hidden relative phase, revealed exclusively through the joint readout of both oscillators, directly highlights a distinction from the classical limit where synchronization is easily observed via individual measurements. We expect that this versatile platform will facilitate the exploration of more complex synchronized quantum networks and stimulate the development of advanced applications in quantum metrology and sensing.

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Phys. Rev. X 16, 021062– Published 29 June, 2026
  • Received 17 November 2025
  • Accepted 27 April 2026
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