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Frequency shifts heralding ground-state squeezing and entanglement of two coupled harmonic oscillators

Safoura Mirkhalaf1, Helmut Ritsch2, and Karol Gietka2,*

  • 1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warszawa, Poland
  • 2Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria

  • *Contact author: karol.gietka@uibk.ac.at
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Phys. Rev. A 114, 022426 – Published 12 August, 2026

DOI: https://doi.org/10.1103/sfy4-nx52

Abstract

It is often argued that two linearly coupled quantum harmonic oscillators, even when cooled to their ground state, display no inherently quantum features beyond quantized energy levels. Here, we challenge this view by showing that their classical observables encode genuinely quantum features. In particular, we demonstrate that the characteristic frequency shifts of the normal modes observed in coupled oscillators signal nonclassical correlations and ground-state entanglement at zero temperature, corresponding to two-mode squeezing between the uncoupled modes. From a complementary perspective, these two effects, frequency shifts and squeezing, represent the same underlying phenomenon but expressed in different mode bases. What appears as a spectral renormalization in one description manifests itself as entanglement in the other. Frequency shifts therefore constitute an entanglement witness accessible via standard spectroscopy. When the underlying squeezing is not directly measurable, it can be still exploited to enhance the signal-to-noise ratio in precision frequency measurements of individual oscillators without requiring squeezed quantum noise. This uncovers an alternative route to quantum-enhanced sensing within systems traditionally regarded as classical, offering insight into how signatures of quantumness persists across the quantum-to-classical boundary.

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Outline

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Phys. Rev. A 114, 022426– Published 12 August, 2026
  • Received 4 March 2026
  • Revised 22 July 2026
  • Accepted 24 July 2026
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