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Intrinsic Bi-Stability Due to Local Dipole–Dipole Interactions in Two-Level Systems and in Excited Crystalline Atomic Dimers

Y. Ben-Aryeh

Published Dec 23, 2025• 0 citations

Abstract

Intrinsic optical bi-stability in dense two-level systems is developed for the bad cavity limit where electromagnetic modes are adiabatically eliminated. Each atom interacts via dipole–dipole forces with its nearby spatial distribution of atoms. The theory is developed into two parts, corresponding to the short sample, with dimensions shorter than the wavelength, and the long sample. In both cases, the local field corrections modify the Maxwell–Bloch equations, so that cubic or quartic equations are obtained for the inversion of population as a function of the external light intensity, thus leading to intrinsic bi-stability. The effects of noise sources on intrinsic bi-stability were treated, and I found that while the observability of bi-stability was not obtained experimentally for a simple two-level system, there were many observations of bi-stability obtained through the ‘up-conversion’ of rare earth excited crystals. I show the differences between these two systems.

DOI: 10.3390/solids7010002

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Intrinsic optical bi-stability in dense two-level systems is developed for the bad cavity limit where electromagnetic modes are adiabatically eliminated. Each atom interacts via dipole–dipole forces with its nearby spatial distribution of atoms. The theory is developed into two parts, corresponding to the short sample, with dimensions shorter than the wavelength, and the long sample. In both cases, the local field corrections modify the Maxwell–Bloch equations, so that cubic or quartic equations are obtained for the inversion of population as a function of the external light intensity, thus leading to intrinsic bi-stability. The effects of noise sources on intrinsic bi-stability were treated, and I found that while the observability of bi-stability was not obtained experimentally for a simple two-level system, there were many observations of bi-stability obtained through the ‘up-conversion’ of rare earth excited crystals. I show the differences between these two systems.

We use a fully quantum, many-body treatment to show mirrorless optical bistability in terms of the spacial properties of interacting two-level systems. The bistability effects are related to the coherent dipole-dipole interactions which introduce an inversion-dependent renormalization of the frequency (or relaxation). Conditions of stability and instability are discussed for a thin sample of two-level atoms with a width smaller than a wavelength. For a long sample of two-level atoms, we find that the two phases of high transmissivity and low transmissivity may coexist spacially in the material.

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.

Transient processes are analyzed based on modified Bloch equations describing the interaction of optical radiation with dense resonant media with allowance for dipole-dipole interaction between atoms (the local-field effect). An analytical solution to the equation for the population difference of resonant atomic levels, taking into account the up-conversion processes, is obtained for a rectangular pulse in the quasi-stationary approximation. Computer simulation is performed for the kinetics of the population difference of resonant atomic levels in the field of a long sine-shaped pulse. It is shown that the time dynamics of the population difference of resonant atomic levels manifests characteristic features inherent in the intrinsic optical bistability effect under adiabatically slow variation of the acting field.

In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.

Transient processes are analyzed based on modified Bloch equations describing the interaction of optical radiation with dense resonant media with allowance for dipole-dipole interaction between atoms (the local-field effect). An analytical solution to the equation for the population difference of resonant atomic levels, taking into account the up-conversion processes, is obtained for a rectangular pulse in the quasi-stationary approximation. Computer simulation is performed for the kinetics of the population difference of resonant atomic levels in the field of a long sine-shaped pulse. It is shown that the time dynamics of the population difference of resonant atomic levels manifests characteristic features inherent in the intrinsic optical bistability effect under an adiabatically slow variation of the acting field.