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Quantum synchronization effects induced by strong nonlinearities

Yuan Shen1, Wai-Keong Mok2,3, Changsuk Noh4, Ai Qun Liu1,*, Leong-Chuan Kwek2,5,6,7,†, Weijun Fan1,‡, and Andy Chia2

  • 1School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2.1, 50 Nanyang Avenue, Singapore 639798, Singapore
  • 2Centre for Quantum Technologies, National University of Singapore, Singapore
  • 3California Institute of Technology, Pasadena, California 91125, USA
  • 4Department of Physics, Kyungpook National University, Daegu, South Korea
  • 5MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore
  • 6National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
  • 7Quantum Science and Engineering Centre (QSec), Nanyang Technological University, Singapore

  • *eaqliu@ntu.edu.sg
  • †kwekleongchuan@nus.edu.sg
  • ‡ewjfan@ntu.edu.sg
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Phys. Rev. A 107, 053713 – Published 23 May, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.053713

Abstract

A paradigm for quantum synchronization is the quantum analog of the Stuart-Landau oscillator, which corresponds to a van der Pol oscillator in the limit of weak (i.e., vanishingly small) nonlinearity. Due to this limitation, the quantum Stuart-Landau oscillator fails to capture interesting nonlinearity-induced phenomena such as relaxation oscillations. To overcome this deficiency, we propose an alternative model that approximates the Duffing–van der Pol oscillator to finitely large nonlinearities while remaining numerically tractable. This allows us to uncover interesting phenomena in the deep-quantum strongly nonlinear regime with no classical analog, such as the persistence of amplitude death on resonance. We also report nonlinearity-induced position correlations in reactively coupled quantum oscillators. Such coupled oscillations become more and more correlated with increasing nonlinearity before reaching some maximum. Again, this behavior is absent classically. We also show how strong nonlinearity can enlarge the synchronization bandwidth in both single and coupled oscillators. This effect can be harnessed to induce mutual synchronization between two oscillators initially in amplitude death.

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Phys. Rev. A 107, 053713– Published 23 May, 2023
  • Received 19 January 2023
  • Revised 17 March 2023
  • Accepted 5 May 2023
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