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arXiv:2005.07582 · Chaos An Interdisciplinary Journal of Nonlinear Science

Chaotic spin-photonic quantum states in an open periodically modulated cavity

Igor Yusipov, S. Denisov, Mikhail Ivanchenko

Published Jan 1, 2021• 3 citations
arXivHTMLPDF

Abstract

When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed "chaotic." Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here, we consider quantum chaotic states emerging in a leaky cavity when the intracavity photonic mode is coherently pumped with the pumping intensity varying periodically in time. We show that a single spin when placed inside the cavity and coupled to the mode can moderate transitions between regular and chaotic regimes-that are identified by using quantum Lyapunov exponents or features of photon emission statistics-and thus can be used to control the degree of chaos.

DOI
10.1063/5.0030260

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When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed "chaotic." Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here, we consider quantum chaotic states emerging in a leaky cavity when the intracavity photonic mode is coherently pumped with the pumping intensity varying periodically in time. We show that a single spin when placed inside the cavity and coupled to the mode can moderate transitions between regular and chaotic regimes-that are identified by using quantum Lyapunov exponents or features of photon emission statistics-and thus can be used to control the degree of chaos.
Open quantum systems can exhibit complex states, for which classification and quantification are still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intracavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I. I. Yusipov et al., Chaos 29, 063130 (2019)], we identify "chaotic" and "regular" regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector so that chaotic and regular states can be discriminated without disturbing the intracavity dynamics.
Open quantum systems can exhibit complex states, for which classification and quantification are still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intracavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I. I. Yusipov et al., Chaos 29, 063130 (2019)], we identify “chaotic” and “regular” regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can\nbe retrieved by monitoring photon emission with a single-photon detector so that chaotic and regular states can be discriminated without disturbing the intracavity dynamics.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to photons statistics are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1) -- equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. We take into account parametric pumping. Corresponding equations of motion are received without the rotation-wave approximation. It was demonstrated the scenario of transition to chaos, realized by doubling frequencies mechanism with growing of 'atom + field' coupling constant. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values of order of the atomic frequency, the calculation of the maximal Lyapunov coefficient for the dynamics of many two- level atoms interacting with photon cavity mode as function of 'atoms + field' interaction constant is performed. An influence of possible parametric instabilities of nonlinear media and effects of dissipation for atoms are discussed.
Quantum systems, when interacting with their environments, can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum versions of chaotic attractors. Here we propose an approach to open cavity dynamics based on the unraveling of the corresponding master equation into an ensemble of quantum trajectories. By using the concept of ``quantum Lyapunov exponents'' [I. I. Yusipov et al., arxiv: 1806.09295], we demonstrate that `chaotic' and `regular' regimes of the intra-cavity dynamics can be identified. The chaotic regimes are marked by the emergence of power-law intermediate asymptotics in the distribution of photon waiting times. The photon counting statistics can be retrieved by monitoring photon emission in experiment. Therefore, chaotic regimes can be identified without additional measurements (and thus disturbance) of the intra-cavity dynamics.
We consider a coupled atom-photon system described by the Tavis-Cummings dimer (two coupled cavities) in an open environment, to investigate the quantum signature of dissipative chaos. The appropriate classical limit of this model allows us to obtain a phase diagram identifying different dynamical phases, especially the onset of chaos. Both classically and quantum mechanically, we demonstrate the emergence of a steady state in the chaotic regime and analyze its properties. The interplay between quantum fluctuation and chaos leads to enhanced mixing dynamics and dephasing, resulting in the formation of an incoherent photonic fluid. The steady state exhibits an intriguing phenomenon of subsystem thermalization even outside the chaotic regime; however, the effective temperature increases with the degree of chaos. Moreover, the statistical properties of the steady state show a close connection with the random matrix theory, which, in contrast, is absent in the Liouvillian spectrum for this system. Finally, we discuss the experimental relevance of our findings, which can be tested in cavity and circuit quantum electrodynamics (QED) setups.
Chaos is central to secure communication and physical random-number generation. Conventional cavity-optomechanical implementations, however, usually rely on weak single-photon optomechanical coupling and low-frequency mechanical modes, so access to deterministic chaotic dynamics often requires large driving power and careful suppression of thermal noise. Here we theoretically study a hybrid molecular optomechanical system formed by coupling a plasmonic nanocavity to a whispering-gallery-mode (WGM) microcavity. The plasmonic nanocavity provides terahertz-scale single-photon optomechanical coupling to a molecular vibration, while the WGM resonator offers a low-loss photonic channel that mitigates the short plasmon lifetime. By integrating the semiclassical equations of motion and evaluating the largest Lyapunov exponent, we map the nonlinear dynamical regimes in the parameter spaces of WGM detuning, plasmon--WGM coupling, and plasmon--vibration optomechanical coupling. We show that increasing the plasmon--vibration coupling drives the system from self-sustained oscillations to chaos through a period-doubling cascade. At moderate coupling strengths, isolated chaos windows can be opened or closed by tuning the WGM detuning and the inter-cavity coupling. These results identify molecular optomechanics as a controllable room-temperature platform for on-chip chaotic light generation and random-signal applications.