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Physical Review A

Dynamics of intrinsic optical bistability in two weakly interacting quantum systems

O. Guillot-Noël, Philippe Goldner, Didier Gourier

Published Dec 27, 2002• 8 citations
Publisher

Abstract

The dynamics of the intrinsic optical bistability (IOB) in an elementary quantum system is investigated in the situation where this system is composed of two weakly interacting subsystems. Numerical calculations have been performed for two ``real'' systems where IOB has been experimentally observed. The first situation corresponds to the electron-nuclear spin system of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3},$ where the transition between electron spin states exhibit a strong bistability. The other situation corresponds to optical transitions in ${\mathrm{Yb}}^{3+}$ pairs in ${\mathrm{CsCdBr}}_{3}:\mathrm{Yb}$ compound, where IOB has been experimentally observed. It is shown that, in addition to the classical hysteresis of the response of the system upon variation of the power of the external field, the observation of the so-called critical slowing down is a clear signature of IOB.

DOI
10.1103/physreva.66.063813

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The dynamics of the intrinsic optical bistability (IOB) in an elementary quantum system is investigated in the situation where this system is composed of two weakly interacting subsystems. Numerical calculations have been performed for two ``real'' systems where IOB has been experimentally observed. The first situation corresponds to the electron-nuclear spin system of \ensuremathβ\ensuremath−Ga2O3,\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3},\ensuremathβ\ensuremath−Ga2​O3​, where the transition between electron spin states exhibit a strong bistability. The other situation corresponds to optical transitions in Yb3+{\mathrm{Yb}}^{3+}Yb3+ pairs in CsCdBr3:Yb{\mathrm{CsCdBr}}_{3}:\mathrm{Yb}CsCdBr3​:Yb compound, where IOB has been experimentally observed. It is shown that, in addition to the classical hysteresis of the response of the system upon variation of the power of the external field, the observation of the so-called critical slowing down is a clear signature of IOB.
A system of coherently driven spatially distributed two-level atoms, coupled with each other via dipole–dipole interaction, exhibits intrinsic optical bistability (IOB) at solid-state densities,1 i.e., optical bistability without optical feedback. The origin of the IOB was shown to be due to inversion-dependent renormalization of the single-atom resonance frequency caused by dipole–dipole interaction among the atoms located mainly within an atomic resonance wavelength.2 For normally incident plane waves of intensity beyond threshold, a spatially dependent discontinuity in the nonlinear refractive index was shown to exist inside the medium,1 corresponding to spatial separation of the high and low absorption phases of the IOB. We present numerical results for the time-dependent solutions of the equations of motion and dynamics of the field propagation.
A model for intrinsic optical bistability is presented in the case of systems that can be described as two weakly interacting subsystems embedded in a matrix M. This model is based on an effective spin-Hamiltonian and a semiclassical density-matrix approach. It is shown that optical bistability should occur when the interaction between the two subsystems fluctuates more rapidly than the characteristic time of the interaction. The validity of the model is demonstrated in the case of bistable electron magnetic resonance, involving real spins. It is also shown that this model provides a semiquantitative explanation of intrinsic optical bistability for Yb3+{\mathrm{Yb}}^{3+}Yb3+ pairs in CsCdBr3{\mathrm{CsCdBr}}_{3}CsCdBr3​ matrix.
This paper presents theoretical investigations on the dynamics of intrinsic optical bistability (IOB) in Tm3+/Yb3+ codoped systems with an upconversion avalanche mechanism. Numerical simulations based on the rate equation model demonstrate distinct IOB hysteresis and critical slowing dynamics around the avalanche thresholds. Moreover, the unusual IOB characteristics are well interpreted by developing a simplified analytic model which gives the formulations of two critical thresholds and the necessary condition for IOB to occur. The simplified model shows that such IOB phenomena may occur only if the total quantum yields of the dipole–dipole energy transfer processes are much higher than that of the inherent decay losses involved in an upconversion avalanche. The analytic model developed in the paper may be useful for the prediction of new rare-earth-doped materials giving rise to IOB.
We theoretically investigate the nonlinear intersubband response, in particular the intrinsic optical bistability (IOB), of quantum well (QW) structures embedded into layered systems. A semiclassical approach is employed based on the plane-wave approximation, the transfer-matrix formalism, the sheet model, and the density-matrix formalism developed to calculate the two-dimensional nonlinear intersubband electron conductivity and the IOB. A variety of presented numerical results demonstrate the importance of inhomogeneity of spatial distribution of radiation intensity induced by multiple radiation reflection for the IOB in layered structures. It is shown that knowing the radiation intensity distribution in the area occupied by QWs, in part standing-wave patterns, are crucial for understanding of IOB pictures. The IOB in systems of one, two, three, five, and ten QWs is investigated. The multistability phenomenon is addressed.
We observe and characterize intrinsic optical bistability in a dilute Rydberg vapor. The bistability is characterized by sharp jumps between states of low and high Rydberg occupancy with jump-up and -down positions displaying hysteresis depending on the direction in which the control parameter is changed. We find that the shift in frequency of the jump point scales with the fourth power of the principal quantum number. Also, the width of the hysteresis window increases with increasing principal quantum number, before reaching a peak and then closing again. The experimental results are consistent with predictions from a simple theoretical model based on semiclassical Maxwell--Bloch equations including the effects of interaction-induced broadening and level shifts. These results provide insight into the dynamics of driven dissipative systems.