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Phase Transitions

A New Bosonization Method for Photoexcited Electronic States and Its Application to Nonlinear Optical Responses

Satoru Okumura, Tetsuo Ogawa

Published Jan 1, 2002• 0 citations
Publisher

Abstract

We derive a bosonized Hamiltonian for a semiconductor quantum well with a light field by a new bosonization method taking exactly into account the composite-particle effects of excitons. Then we apply the bosonized Hamiltonian to the four-wave-mixing (FWM) processes. The obtained Hamiltonian describes two-boson states corresponding to bound and unbound two-exciton states and guarantees exclusion of unphysical states, which cannot exist in the fermionic space due to the Pauli exclusion principle. Calculated results of the FWM signals are in good agreement with the experimental ones, and therefore, the bosonized Hamiltonian turns out to be able to describe two-exciton correlations effectively.

DOI
10.1080/01411590290034155

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We derive a bosonized Hamiltonian for a semiconductor quantum well with a light field by a new bosonization method taking exactly into account the composite-particle effects of excitons. Then we apply the bosonized Hamiltonian to the four-wave-mixing (FWM) processes. The obtained Hamiltonian describes two-boson states corresponding to bound and unbound two-exciton states and guarantees exclusion of unphysical states, which cannot exist in the fermionic space due to the Pauli exclusion principle. Calculated results of the FWM signals are in good agreement with the experimental ones, and therefore, the bosonized Hamiltonian turns out to be able to describe two-exciton correlations effectively.
We derive a bosonized Hamiltonian describing two-exciton correlation of semiconductor-photon coupled systems with a bosonization method, which takes into full account an effect of deviation of the excitons from ideal bosons. This deviation effect stems from the fact that excitons are composite particles, whose character appears clearly in the case where the excitons overlap each other. We call this effect a composite-particle effect (CPE). To our knowledges this effect was not considered completely in previous theoretical works on exciton-exciton interaction. The Hamiltonian introduced in this paper includes the results of the previous works as low-order terms of the CPE. After the introduction of a general theory of the bosonization method for arbitrary dimension and electron-hole mass ratio, we also demonstrate an application to a semiconductor bulk system coupled with a photon field in the heavy-hole limit. The bosonized Hamiltonian shows that the CPE brings about an enhancement of the exciton-exciton scattering strength and a qualitative change of the photo transition amplitude. It is also shown that the Hamiltonian describes two-exciton bound and scattering states.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
Summary form only given. Four-particle correlation mediated by the Coulomb interaction has been found to play a major role in the nonlinear optical response at the semiconductor band edge at low excitation density. The attractive interaction of the excitons with opposite spins result in the formation of bound (bi-exciton) and unbound (scattered) two-exciton states. In this paper we report on the first to our knowledge, comparison of the contributions to the coherent nonlinearity from the bound and unbound two-exciton states. The polarization-sensitive four wave mixing experiment is performed in the high-Q semiconductor microcavity, in which the incoherent effects are suppressed due to strong exciton-photon coupling. The semiconductor microcavity has a single 12-nm-thick GaAs quantum well.
A theory of degenerate four-wave mixing (DFWM) in the low density excitation limit at the semiconductor band edge is developed on the basis of the bosonic representation of the electron-hole Hamiltonian. By accounting for the exciton-exciton interactions of the lowest order we arrive at the practical few-level density matrix description of the third-order excitonic nonlinearity. The developed theory accounts phenomenologically for the phase space filling, and excitation induced dephasing effects and well reproduces the results of the recent DFWM experiments in high- and low-fineness microcavity. We show that polarization-sensitive four-wave mixing measurements enable to discriminate the contributions to the DFWM signal from the exciton-exciton interactions of different symmetry.
We propose an exact bosonization scheme for two two-fermion composites with identical internal structures, that is, a mapping of the two-exciton (four-fermion) subspace to a two-boson subspace. We obtain analytical, exact expressions of the boson-boson interactions and the boson-photon ones taking into full account that the commutation relation of the composite bosons deviates from the ideal-boson commutation due to internal motions of the composite. We can distinguish the "composite-particle effects' from the Coulomb interactions among the fermions in the interactions. With this method, origins of optical nonlinearity in a system with two 1s excitons are studied in terms of the mutual excitonic correlations and exciton-photon interactions.