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Physical Review A

Atom-modulated dynamic optical hysteresis in driven-dissipative systems

Jianning Li, H. Z. Shen, Wei Wang, X. X. Yi

Published Jul 12, 2021• 5 citations
Publisher

Abstract

We introduce a two-level atom into a cavity as an ancilla to control the hysteresis of the system where the cavity is described by a driven-dissipative nonlinear Kerr model. We find that the dynamic optical hysteresis can be modulated by changing the atom-cavity coupling strength, and the nonlinearity induced by atom-cavity coupling weakens the Kerr nonlinearity in the weak coupling regime. This leads to the change in the critical point corresponding to the decrease in the hysteresis area. The physics behind the modulation is closely related to the effect of the atom-cavity coupling on the discontinuity of the first nonzero Liouvillian eigenvalue. A relative deviation of the metastable state and target steady state is defined to characterize the relation between the hysteresis and adiabaticity of the system. Taking only two Liouvillian eigenvectors into account in the composite system, we derive an expression for the dependence of the hysteresis area on the sweeping speed and discuss its feature in the slow sweeping limit.

DOI
10.1103/physreva.104.013709

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We introduce a two-level atom into a cavity as an ancilla to control the hysteresis of the system where the cavity is described by a driven-dissipative nonlinear Kerr model. We find that the dynamic optical hysteresis can be modulated by changing the atom-cavity coupling strength, and the nonlinearity induced by atom-cavity coupling weakens the Kerr nonlinearity in the weak coupling regime. This leads to the change in the critical point corresponding to the decrease in the hysteresis area. The physics behind the modulation is closely related to the effect of the atom-cavity coupling on the discontinuity of the first nonzero Liouvillian eigenvalue. A relative deviation of the metastable state and target steady state is defined to characterize the relation between the hysteresis and adiabaticity of the system. Taking only two Liouvillian eigenvectors into account in the composite system, we derive an expression for the dependence of the hysteresis area on the sweeping speed and discuss its feature in the slow sweeping limit.
In this paper, we study the optical-hysteresis regime in a driven-dissipative Bose-Hubbard dimer under a symmetric configuration and analyze the classical optical bistability with the Gross-Pitaevskii mean-field approach. We find that the critical point of the optical-hysteresis regime can be determined by the classical optical-bistability transformation predicted with a steady state equation, and the critical tunneling rate is given by analyzing the bistable threshold points. In addition, we apply the same approach to a single nonlinear microcavity coupled with an atom and the critical atom-cavity coupling strength of the optical-hysteresis regime is also obtained. Finally, in order to illustrate that the critical point could be determined by the classical optical-bistability transformation, we analyze the Liouvillian gap and find it opens at the critical point of the optical-hysteresis regime. This work clarifies the relation between optical hysteresis and classical optical bistability, which provides theoretical references for the modulation of optical hysteresis in experiment.
We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states; in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a nonadiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in the presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.
We present dual hysteretic behavior of a three-level ladder system exhibiting optical bistability in a double-cavity configuration in the mean-field limit. The two fields coupling the atomic system experience competing cooperative effects along the two transitions. We observe a hump-like feature in the bistable curve arising due to cavity-induced inversion, which transforms into a negative-hysteresis loop. Apart from negative- and positive-hysteresis regions, the system offers a variety of controllable nonlinear dynamical features, ranging from switching, periodic self-pulsing to chaos.
We study the quantum dynamics of many-body arrays of two-level atoms in a driven cavity subject to collective decay and interactions mediated by the cavity field. We work in the bad cavity limit accessible, for example, using long-lived electronic clock states of alkaline-earth atoms, for which the bare atomic linewidth is much less than the cavity linewidth. In the absence of interactions, our system reduces to previously studied models of collective fluorescence. We show that while interactions do not qualitatively change the steady-state properties they lead to a drastic change in the dynamical properties. We find that, for some intervals of driving strengths, the system shows two very distinct types of transient behaviors that depend on the initial state of the system. In particular, there is a parameter regime where the system features oscillatory dynamics with a period of oscillation that becomes much shorter than the duration of the overall transient dynamics as the atom number increases. We use both mean-field and exact numerical calculations of the quantum system to investigate the dynamics.