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arXiv:quant-ph/0411129 · Journal of the Physical Society of Japan

Drastic Effects of Damping Mechanisms on Third-Order Optical Nonlinearity

Kazuki Koshino, Hajime Ishihara

Published Nov 15, 2005• 0 citations
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Abstract

We have investigated the optical response of superradiant atoms, which undergoes three different damping mechanisms: radiative dissipation ($γ_r$), dephasing ($γ_d$), and nonradiative dissipation ($γ_n$). Whereas the roles of $γ_d$ and $γ_n$ are equivalent in the linear susceptibility, the third-order nonlinear susceptibility drastically depends on the ratio of $γ_d$ and $γ_n$: When $γ_d \ll γ_n$, the third-order susceptibility is essentially that of a single atom. Contrarily, in the opposite case of $γ_d \gg γ_n$, the third-order susceptibility suffers the size-enhancement effect and becomes proportional to the system size.

DOI
10.1143/jpsj.74.2921

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We have investigated the optical response of superradiant atoms, which undergoes three different damping mechanisms: radiative dissipation (γrγ_rγr​), dephasing (γdγ_dγd​), and nonradiative dissipation (γnγ_nγn​). Whereas the roles of γdγ_dγd​ and γnγ_nγn​ are equivalent in the linear susceptibility, the third-order nonlinear susceptibility drastically depends on the ratio of γdγ_dγd​ and γnγ_nγn​: When γd≪γnγ_d \ll γ_nγd​≪γn​, the third-order susceptibility is essentially that of a single atom. Contrarily, in the opposite case of γd≫γnγ_d \gg γ_nγd​≫γn​, the third-order susceptibility suffers the size-enhancement effect and becomes proportional to the system size.
The third-order optical susceptibility ${\mathrm{\ensuremath{\chi}}}^{(3)}$ is calculated for a system of N cold atoms trapped in a three-dimensional harmonic potential. The dipole-dipole interaction between atoms contributes to ${\mathrm{\ensuremath{\chi}}}^{(3)}$ reflecting quantum statistical properties of atoms. This contribution in Bose condensed systems is proportional to N2{\mathit{N}}^{2}N2 and is much larger than that in the system of Fermi atoms. \textcopyright{} 1996 The American Physical Society.
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We investigate the third-order nonlinear-optical susceptibility ${\ensuremath{\chi}}^{(3)}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\ensuremath{\chi}}^{(3)}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\ensuremath{\chi}}^{(3)}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\ensuremath{\chi}}^{(3)}$ contains terms that scale as \ensuremath{\sim}N2{N}^{2}N2 and \ensuremath{\sim}N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear \ensuremath{\sim}N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.
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It is argued that superradiant processes are those in which the radiative response of an atom to an excitation is appreciably influenced by interactions with its neighbors, rather than processes in which the output intensity is proportional to the square of the number NNN of atoms. On the basis of this criterion, optical free induction is a limiting response of an inhomogeneously broadened system in which cooperative effects become very small, but in which there is a strict N2{N}^{2}N2 dependence. In such a system, superradiance is manifest by a departure of the output from an N2{N}^{2}N2 dependence. Expressions are derived for the free induction response of an atomic system to an arbitrary excitation pulse, and are reduced to simple analytic forms in certain special cases. The free induction and superradiant responses are compared under conditions in which the inhomogeneous lifetime is shorter than the superradiance time $\frac{1}{N\ensuremath{\beta}}$, and an error in a previously published curve is corrected.