Stochastic Hopf bifurcations in vacuum optical tweezers

Stephen H. Simpson, Yoshihiko Arita, Kishan Dholakia, Pavel Zemánek

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1 Citation (Scopus)


The forces acting on an isotropic microsphere in optical tweezers are effectively conservative. However, reductions in the symmetry of the particle or trapping field can break this condition. Here we theoretically analyze the motion of a particle in a linearly nonconservative optical vacuum trap, concentrating on the case where symmetry is broken by optical birefringence, causing nonconservative coupling between rotational and translational degrees of freedom. Neglecting thermal fluctuations, we first show that the underlying deterministic motion can exhibit a Hopf bifurcation in which the trapping point destabilizes and limit cycles emerge whose amplitude grows with decreasing viscosity. When fluctuations are included, the bifurcation of the underlying deterministic system is expressed as a transition in the statistical description of the motion. For high viscosities, the probability distribution is normal, with a kurtosis of three, and persistent probability currents swirl around the stable trapping point. As the bifurcation is approached, the distribution and currents spread out in phase space. Following the bifurcation, the probability distribution function hollows out, reflecting the underlying limit cycle, and the kurtosis halves abruptly. The system is seen to be a noisy self-sustained oscillator featuring a highly uneven limit cycle. A variety of applications, from autonomous stochastic resonance to synchronization, is discussed.

Original languageEnglish
Article number043518
JournalPhysical Review A
Issue number4
Publication statusPublished - 2021 Oct

Bibliographical note

Funding Information:
We acknowledge the support from the Engineering and Physical Sciences Research Council (Grant No. EP/P030017/1), the European Regional Development Fund (Grant No. CZ.02.1.01/0.0/0.0/15_003/0000476), the Czech Science Foundation (Grant No. GA19-17765S), and the Czech Academy of Sciences (Praemium Academiae, Grant No. RVO:68081731).

Funding Information:
Engineering and Physical Sciences Research Council European Regional Development Fund Grantov? Agentura ?esk? Republiky Akademie V?d ?esk? Republiky

Publisher Copyright:
©2021 American Physical Society

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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