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Quadrature Squeezing Enhances Wigner Negativity in a Mechanical Duffing Oscillator

Christian A. Rosiek1,2,*,§, Massimiliano Rossi1,2,¶, Albert Schliesser1,2,†, and Anders S. Sørensen1,2,‡

  • *Contact author: chanro@dtu.dk
  • †Contact author: albert.schliesser@nbi.ku.dk
  • ‡Contact author: anders.sorensen@nbi.ku.dk
  • §Present address: DTU Electro, Department of Electrical and Photonics Engineering, Technical University of Denmark, Ørsteds Plads 343, 2800 Kongens Lyngby, Denmark.
  • Present address: Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, The Netherlands.
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PRX Quantum 5, 030312 – Published 19 July, 2024

DOI: https://doi.org/10.1103/PRXQuantum.5.030312

Abstract

Generating macroscopic nonclassical quantum states is a long-standing challenge in physics. Anharmonic dynamics is an essential ingredient to generate these states, but for large mechanical systems, the effect of the anharmonicity tends to become negligible compared with the effect of decoherence. As a possible solution to this challenge, we propose using a motional squeezed state as a resource to effectively increase the anharmonicity. We analyze the production of negativity in the Wigner distribution of a quantum anharmonic resonator initially in a squeezed state. We find that initial squeezing increases the rate at which negativity is generated. We also analyze the effect of two common sources of decoherence—namely, energy damping and dephasing—and find that the detrimental effects of energy damping are suppressed by strong squeezing. In the limit of large squeezing, which is needed for state-of-the-art systems, we find good approximations for the Wigner function. Our analysis is significant for current experiments attempting to prepare macroscopic mechanical systems in genuine quantum states. We provide an overview of several experimental platforms featuring nonlinear behaviors and low levels of decoherence. In particular, we discuss the feasibility of our proposal with carbon nanotubes and levitated nanoparticles.

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Popular Summary

While quantum mechanics predicts the physics of the smallest objects with remarkable accuracy, there has long been a drive to investigate the quantum behavior of larger and larger physical systems. More massive quantum objects can provide experimental input on novel physics such as quantum gravity and can serve as key components in quantum technology. One way to demonstrate nonclassical behavior is through negative values in the Wigner quasiprobability distribution because classical phase-space distributions cannot assume negative values. However, observing Wigner negativity in large objects is challenging because large objects interact strongly with their surroundings. The ensuing decoherence quickly destroys Wigner negativity.

We show that quadrature squeezing, a quantum operation that by itself cannot produce Wigner negativity, enhances the generation of Wigner negativity by the system nonlinearity and decreases the relative decoherence. To this end, we investigate a nonlinear quantum system, a Duffing oscillator, that has undergone squeezing. We develop a formalism that describes evolution of highly squeezed states in a nonlinear potential using phase-space methods and that incorporates both nonlinear evolution and decoherence effects. We also investigate the effect of two forms of decoherence common in mechanical systems: linear damping and dephasing. We find that squeezing can be used to increase the relative strength of nonlinearity with respect to decoherence, enabling negativity in a broader range of systems.

Our results show that squeezing may allow systems with even weak nonlinearities to generate states with negative Wigner function, opening new avenues to investigate quantum mechanics.

Article Text

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PRX Quantum 5, 030312– Published 19 July, 2024
  • Received 21 December 2023
  • Accepted 3 June 2024
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