Route to Chaos in Optomechanics

Bakemeier, L.; Alvermann, Andreas; Fehske, Holger

doi:10.1103/physrevlett.114.013601

Cited by 133 publications

(117 citation statements)

References 38 publications

(62 reference statements)

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“…In particular, one can strong driving the cavity so that the OMS enters into a regime of self-induced oscillations [9][10][11][12], where the backaction-induced mechanical gain overcomes mechanical loss. Further increasing the strength of the driving laser, chaotic motion emerges both in the optical and mechanical modes requiring no external feedback or modulation [13][14][15][16]. It is useful for generating random numbers [18] and implementing secret information processing [19][20][21].…”

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confidence: 99%

PT-Symmetry-Breaking Chaos in Optomechanics

et al. 2015

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We demonstrate a PT -symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in PT -symmetry-breaking phase (PT BP). Moreover, this chaos is switchable by tuning the system parameters so that a PT -symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser triggered chaos and its potential applications in secret communication.PACS numbers: 07.10.Cm Cavity optomechanics is a rapidly developing research field exploring the radiation-pressure interaction between the electromagnetic and mechanical systems [1]. Thanks to this nonlinear interaction, the optomechanical system (OMS) provides an alternative platform for implementing many interesting quantum [2][3][4][5][6][7][8] and classical [9-17] nonlinearity phenomena. In particular, one can strong driving the cavity so that the OMS enters into a regime of self-induced oscillations [9][10][11][12], where the backaction-induced mechanical gain overcomes mechanical loss. Further increasing the strength of the driving laser, chaotic motion emerges both in the optical and mechanical modes requiring no external feedback or modulation [13][14][15][16]. It is useful for generating random numbers [18] and implementing secret information processing [19][20][21]. However, to apply chaos into the secret communication scheme requiring low-power optical interconnects, the chaos threshold should be reduced dramatically [22,23].The notion of parity-time (PT ) symmetry, initially proposed in quantum mechanics [24], attracts recently enormous attention in the field of optics [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. It is known [24] that PT symmetric Hamiltonians can exhibit a real eigenvalue spectrum in spite of the fact that they can be non-Hermitian. These systems have the interesting property to undergo an abrupt phase-transition where the system loses its PT-symmetry. At the exceptional point (EP) pairs of eigenvalues collide and become complex. Typically, the transition between PT symmetric phase (real spectrum) to spontaneously broken PT symmetry (complex spectrum) occurs as a parameter in the Hamiltonian (which somehow controls the degree of non-Hermiticity) is varied [25][26][27]. This phase transition has been demonstrated in synthetic waveguides and microcavities, and can induce unique optical phenomena including loss-induced transparency [28], power oscillations violating left-right symmetry [29], low-power optical diodes [35] and single-mode laser [36,37]. A natural question is whether it could influence the chaos dynamics (especially the chaos threshold) significantly. Moreover, the crossover b...

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PT-Symmetry-Breaking Chaos in Optomechanics

et al. 2015

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“…Moreover, as predicted in ref. 9 for sufficiently high laser power, the system can eventually enter into a chaotic regime, which may be exploited for chaos-based secure data communication or sensing, among other applications. In this regard, integrated OM systems may present advantages with respect to coupled lasers10 or hybrid optoelectric oscillators11 in terms of the ease of integration, scalability and engineering of the nonlinearities12.…”

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Nonlinear dynamics and chaos in an optomechanical beam

et al. 2017

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Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two- and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two- and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.

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“…Self-sustained oscillations occur for amplitudes A where the power balance between gains from the radiation pressure (P rad = P |α| 2 Imβ avg) and losses due to friction (P fric =Γ |β| In case (a), the two innermost orbits have amplitudes A1 ≈ 1.2 and A2 ≈ 2.7. In cases (b), (c) the innermost orbit shows a few period doubling bifurcations that occur on the route to chaos [11], in case (d) it is chaotic. Now introduce the five dimensionless parameters [5,6] …”

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“…In a previous paper [11] we observed that the classical dynamical patterns, which are characterized by the multistability of self-sustained oscillations, change in a characteristic way if one moves into the quantum regime. Previously stable orbits become unstable, the system oscillates at a new amplitude, and especially the classical chaotic dynamics is almost immediately replaced by simple periodic oscillations.…”

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“…-The interaction of light with mechanical objects [1,2] enjoys continued interest due to the successful construction and manipulation of optomechanical devices over a wide range of system sizes and parameter combinations (see the recent reviews [3,4] and references cited therein). With these devices both classical non-linear dynamics such as self-sustained oscillations [5][6][7][8] and chaos [9][10][11] as well as quantum mechanical mechanisms such as cooling into the groundstate [12,13] and quantum non-demolition measurements [14][15][16] can be studied in a unified experimental setup.…”

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Optomechanical multistability in the quantum regime

Schulz

Alvermann

Bakemeier

et al. 2016

EPL

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-Classical optomechanical systems feature self-sustained oscillations, where multiple periodic orbits at different amplitudes coexist. We study how this multistability is realized in the quantum regime, where new dynamical patterns appear because quantum trajectories can move between different classical orbits. We explain the resulting quantum dynamics from the phase space point of view, and provide a quantitative description in terms of autocorrelation functions. In this way we can identify clear dynamical signatures of the crossover from classical to quantum mechanics in experimentally accessible quantities. Finally, we discuss a possible interpretation of our results in the sense that quantum mechanics protects optomechanical systems against the chaotic dynamics realized in the classical limit.Introduction. -The interaction of light with mechanical objects [1, 2] enjoys continued interest due to the successful construction and manipulation of optomechanical devices over a wide range of system sizes and parameter combinations (see the recent reviews [3,4] and references cited therein). With these devices both classical non-linear dynamics such as self-sustained oscillations [5][6][7][8] and chaos [9-11] as well as quantum mechanical mechanisms such as cooling into the groundstate [12,13] and quantum non-demolition measurements [14][15][16] can be studied in a unified experimental setup.This raises the question whether it might be possible to detect the crossover from classical to quantum mechanics directly in the dynamical behaviour of optomechanical systems. In a previous paper [11] we observed that the classical dynamical patterns, which are characterized by the multistability of self-sustained oscillations, change in a characteristic way if one moves into the quantum regime. Previously stable orbits become unstable, the system oscillates at a new amplitude, and especially the classical chaotic dynamics is almost immediately replaced by simple periodic oscillations. In this paper we explain this behaviour from the point of view of classical and quantum phase space dynamics. Most importantly, we will show that the dynamical patterns do not change at random but that clearly identifiable and new signatures can be observed.

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Route to Chaos in Optomechanics

Cited by 133 publications

References 38 publications

PT-Symmetry-Breaking Chaos in Optomechanics

PT-Symmetry-Breaking Chaos in Optomechanics

Nonlinear dynamics and chaos in an optomechanical beam

Optomechanical multistability in the quantum regime

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