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Physical review. B, Condensed matter

High-excitation-emission spectra of one-dimensional Frenkel excitons

Hidekatsu Suzuura, Tetsuji Tokihiro, Yasuhiro Ohta

Published Feb 1, 1994• 13 citations
Publisher

Abstract

The emission spectra of highly excited one-dimensional Frenkel excitons are obtained from the correlation functions of a quantum spin chain. The system-size dependence of the emission intensity reflects critical exponents of the spin system that also characterize statistical properties of Frenkel excitons intermediate between bosons and fermions. Exact expressions for these spectra show blue shifts of emission peaks and fine structure due to finite-size effects.

DOI
10.1103/physrevb.49.4344

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The emission spectra of highly excited one-dimensional Frenkel excitons are obtained from the correlation functions of a quantum spin chain. The system-size dependence of the emission intensity reflects critical exponents of the spin system that also characterize statistical properties of Frenkel excitons intermediate between bosons and fermions. Exact expressions for these spectra show blue shifts of emission peaks and fine structure due to finite-size effects.
Collective spontaneous emission from a one-dimensional mesoscopic exciton system interacting via static dipole moments is investigated by virtue of the analogy to the quantum XXZ spin chain. The rigorous expression for the initial state is obtained at any degree of excitation from the ground state by a short intense laser pulse. The emission profile from the initial state with partial population inversion exhibits oscillations and very rapid decay in comparison with that from the completely inverted state. The time-resolved emission spectra are also discussed.
The spectral shape of one-dimensional systems (describing for instance the behaviour of Frenkel excitons) is approached through the exactly solvable model of the XXO Heisenberg quantum spin chain in a transverse magnetic field. Some results for finite size chains concerning 2N-point correlators are presented in detail. In particular, the finite lattice, finite temperature 2-point correlators are explicitly worked out. Moreover, results in closed form are given for 2N-point correlators in the most general situation (finite lattice and thermodynamic limit, finite temperature, finite space and/or time separations). Their relations with frequency moments of the spectral shape are pointed out and the connection with moment expansion through continued fraction representation is given.
A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wave function and it is shown how this operator evolves from purely fermionic, in the case of a small QD, to purely bosonic, in the case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively.
Superradiance of high density Frenkel excitons in an RRR-phycoerythrin single crystal is observed at room temperature for the first time. No fluorescence is observed except the emission at the sharp exciton band when the superradiance of excitons occurs, and the higher the pump density, the sharper the emission bandwidth. A redshift and a blueshift are observed at the rise time and the fall time of the emission pulse, respectively. The experimental results also imply deformed-boson properties of high density Frenkel excitons.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
Optical emission based on excitonic scattering processes becomes important in dense exciton systems in which the average distance between excitons is of the order of a few Bohr radii but still below the exciton screening threshold. The phenomena due to interactions among excited states play significant role in the emission near band edge of the material. The theory of two-exciton collisions for GaAs/AlGaAs quantum well systems is a mild attempt to understand the physics associated with the optical spectra due to excitonic scattering processes in these novel systems. The four typical processes considered give different spectral shape, peak position and temperature dependence of the emission spectra. We have used the theory of scattering together with the second order perturbation theory to derive the radiative power spontaneously emitted at an energy ħω by these processes. The results arrived at are purely qualitative in nature. The intensity of emitted light in quantum well systems varies inversely to the square of temperature, whereas in case of bulk materials it simply decreases with the temperature.