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arXiv:1708.01345 · Physical Review A

Optical and atomic stochastic resonances in the driven dissipative Jaynes-Cummings model

Qingyang Qiu, Shengdan Tao, Cunjin Liu, Shengguo Guan, Min Xie, Bixuan Fan

Published Dec 6, 2017• 5 citations
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Abstract

In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.

DOI
10.1103/physreva.96.063808

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In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.
In this work we investigate the regime of amplitude bistability in the driven dissipative Jaynes-Cummings (JC) model. We study the semiclassical equation dynamics in contrast to entangled cavity-photon and qubit quantum trajectories, discussing our results in the context of an out-of-equilibrium first order quantum dissipative phase transition for a single JC resonator. Finally, we compare the switching process between metastable states for the two system degrees of freedom by examining a single realization of the random qubit vector in the Bloch sphere next to the intracavity amplitude quasi distributions at given time instants.
Stochastic resonance (SR) is experimentally demonstrated in an atomic optical bistable system consisting of three-level atoms in $\ensuremath{\Lambda}$-type configuration confined in an optical ring cavity. The optical bistable system with enhanced Kerr nonlinearity due to atomic coherence is driven by a periodic signal and a Gaussian white noise source with variable amplitude, and displays an improved output signal-to-noise ratio, a characteristic signature of SR. The measured results match qualitatively with the theoretical predictions of the generic model for the SR phenomenon.
Spectra of the atomic resonance fluorescence and of the cavity-transmitted light in a driven Jaynes-Cummings system are studied theoretically, where the cavity is driven by a classical field of arbitrary strength. In the regime of strong atom-cavity coupling, anomalous resonance peaks occur at $\ifmmode\pm\else\textpm\fi{}\sqrt{n}{g}^{\ensuremath{'}} (n=2,3,\dots{}),$ with the modified vacuum Rabi frequency ${g}^{\ensuremath{'}},$ both in the atomic fluorescence and the cavity transmission. These peaks as well as the observed shift of the vacuum Rabi splitting are explained in terms of the quasienergy levels induced dynamically by the strong driving field. For a stronger driving field, it is shown that the spectrum of the cavity transmission deviates from that of the atomic fluorescence. In the presence of significant damping, the spectrum of the cavity transmission approaches a singlet structure in the strong driving-field limit, and it is found additionally that a bimodal photon-number distribution, which results in a unique quintuplet spectrum of the atomic fluorescence, does not show up in the cavity transmission.
We generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasi -distribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qubit-cavity entanglement. Focusing on the effect of quantum-activated switching for both coupled degrees of freedom, we move from a region of minimal entanglement in the dispersive regime, where we derive analytical perturbative results, to the threshold behaviour of spontaneous dressed-state polarization at resonance.
We investigate a novel type of conditional dynamic that occurs in the strongly driven Jaynes-Cummings system with dissipation. Extending the work of Alsing and Carmichael [Quantum Opt. 3, 13 (1991)], we present a combined numerical and analytic study of the stochastic master equation that describes the system's conditional evolution when the cavity output is continuously observed via homodyne detection, but atomic spontaneous emission is not monitored at all. We find that quantum jumps of the atomic state are induced by its dynamical coupling to the optical field, in order retroactively to justify atypical fluctuations occurring in the homodyne photocurrent.