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Physical review. B, Condensed matter

General conditions for intrinsic optical bistability at the atomic and molecular scale: An effective spin-Hamiltonian approach

O. Guillot-Noël, Laurent Binet, Didier Gourier

Published May 28, 2002• 24 citations
Publisher

Abstract

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 ${\mathrm{Yb}}^{3+}$ pairs in ${\mathrm{CsCdBr}}_{3}$ matrix.

DOI
10.1103/physrevb.65.245101

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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.
\nA general model for intrinsic optical bistability is presented for\natomic or molecular systems which can be decomposed into two weakly\ninteracting subsystems. It is shown that optical bistability should\noccur when the interaction between the two subsystems fluctuates\nfaster than the characteristic time of the interaction. The validity\nof the model is demonstrated in the case of magnetic bistability of\nconduction electrons. It is extended in the infrared or visible\nrange with pairs of rare earth ions and rare earth-transition metal\nions systems.\n
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 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.
Intrinsic (mirrorless) optical bistability (MOB) has been predicted independently by a number of authors1. Recent experiments have demonstrated at least one major aspect of this phenomenon, i.e., MOB due to increasing absorption2. Other categories of MOB which have been predicted from theoretical models are caused by: interatomic correlation in a many-body quantum model, the anharmonic contribution in a classical Duffing oscillator, the local field correction in the macroscopic Maxwell-Bloch formulation, and coherent dipole-dipole interaction in a microscopic semiclassical model of a finite number of damped, two-level atoms driven by an external field3. All of these models share a single common characteristic which causes MOB in some region of the parameter space of each model. The characteristic is simply: an interaction-dependent nonlinearity which causes a renormalization of the resonance frequency. In each case, the sign and magnitude of the incident field detuning from the unrenormalized resonance is a crucial parameter.
We use a quantum-electrodynamical, many-body treatment to show mirrorless optical bistability in terms of the spatial properties of coherent dipole-dipole interactions among interacting two-level atoms. The general theory is applied to two special cases: (1) a thin sample of two-level atoms, with a width smaller than a resonance wavelength and (2) a long sample of two-level atoms, with dimensions very large relative to a resonance wavelength. While for the thin sample we are able to use a mean-field approximation with validity, for the long sample we are compelled to take into account retardation and propagation. In both cases bistability is found to be related to a renormalization of the frequency (or relaxation rate) that is inversion dependent. For the long sample the frequency renormalization is significant for high atomic densities and for large oscillator strengths.
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.