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arXiv:1905.04728 · Physical Review A

Single-photon-triggered quantum chaos

Gui‐Lei Zhu, Xin‐You Lü, Lili Zheng, Zhiming Zhan, Franco Nori, Ying Wu

Published Aug 15, 2019• 20 citations
arXivHTMLPDF

Abstract

We demonstrate how to manipulate quantum chaos with a single photon in a hybrid quantum device combining cavity QED and optomechanics. Specifically, we show that this system changes between integrable and chaotic relying on the photon state of the injected field. This onset of chaos originates from the photon-dependent chaotic threshold of the qubit-field coupling induced by the optomechanical interaction. By deriving the Loschmidt Echo, we observe clear differences in the sensitivity to perturbations in the regular versus chaotic regimes. We also present the classical analog of this chaotic behavior and find good correspondence between chaotic quantum dynamics and classical physics. Our work opens up a route to achieve quantum manipulations, which are crucial elements in engineering new types of on-chip quantum devices and quantum information science.

DOI
10.1103/physreva.100.023825

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We demonstrate how to manipulate quantum chaos with a single photon in a hybrid quantum device combining cavity QED and optomechanics. Specifically, we show that this system changes between integrable and chaotic relying on the photon state of the injected field. This onset of chaos originates from the photon-dependent chaotic threshold of the qubit-field coupling induced by the optomechanical interaction. By deriving the Loschmidt Echo, we observe clear differences in the sensitivity to perturbations in the regular versus chaotic regimes. We also present the classical analog of this chaotic behavior and find good correspondence between chaotic quantum dynamics and classical physics. Our work opens up a route to achieve quantum manipulations, which are crucial elements in engineering new types of on-chip quantum devices and quantum information science.
We predict the occurrence of single-photon-induced entanglement and quantum superposition in a hybrid quantum model, introducing an optomechanical coupling into the Rabi model. Originally, it comes from the photon-dependent quantum property of the ground state featured by the proposed hybrid model. It is associated with a single-photon-induced quantum phase transition, and is immune to the A2{A}^{2}A2 term of the spin-field interaction. Moreover, the obtained quantum superposition state is actually a squeezed cat state, which can significantly enhance precision in quantum metrology. This work offers an approach to manipulate entanglement and quantum superposition with a single photon, which might have potential applications in the engineering of new single-photon quantum devices, and also fundamentally broaden the regime of cavity QED.
Abstract Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of ‘single-photon strong coupling’, where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.
Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.
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.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing 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. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical link is provided by measurement processes. In this work, we identify gain competition in a chaotic photon gas as an operational quantum measurement that selects single motional modes from an initial superposition through stochastic, nonlinear amplification. We show that this mechanism naturally gives rise to classical chaotic behavior, most notably sensitivity to initial conditions. Our results provide a concrete physical mechanism for the quantum-classical transition in a chaotic system and demonstrate that essential aspects of quantum measurement-state projection, Born-rule-like selection, and irreversibility-can naturally emerge from intrinsic gain dynamics.