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Generating Arbitrary Superpositions of Nonclassical Quantum Harmonic Oscillator States

S. Saner*, O. Băzăvan, D. J. Webb, G. Araneda, D. M. Lucas, C. J. Ballance, and R. Srinivas†

  • Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

  • *Contact author: sebastian.saner@physics.ox.ac.uk
  • †Contact author: raghavendra.srinivas@physics.ox.ac.uk
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Phys. Rev. X 16, 021049 – Published 3 June, 2026

DOI: https://doi.org/10.1103/k1xk-yt42

Abstract

Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.

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Popular Summary

Quantum mechanics defies classical intuition, most famously through Schrödinger’s cat, where systems exist in superpositions of opposing states. Such superpositions are central to quantum technologies. Quantum “cat” states have been realized in harmonic oscillators, but implementations were largely limited to Fock, displaced, or Gottesman-Kitaev-Preskill states. A different class of macroscopic superpositions, where an oscillator is squeezed along orthogonal axes so that its positional variance is simultaneously larger and smaller than the Heisenberg limit, was proposed previously but remained unrealized. Here, we introduce a trapped-ion hybrid spin-oscillator system enabling an experimental realization of these “siblings” of Schrödinger’s cat. By interleaving spin-dependent nonlinear interactions with midcircuit measurements, we project the oscillator into macroscopic superpositions of squeezed, trisqueezed, and quadsqueezed states. We demonstrate full control over probability amplitudes and interactions, and perform complete state tomography. These states offer resources for error correction, quantum sensing, and tests of macroscopicity.

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Phys. Rev. X 16, 021049– Published 3 June, 2026
  • Received 25 February 2025
  • Revised 27 November 2025
  • Accepted 20 January 2026
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