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physica status solidi (b)

Photon Echoes and the Structure of Wannier Excitons

Izo I. Abram

Published May 1, 1990• 2 citations
Publisher

Abstract

Abstract The coherent polarization of a Wannier exciton system, induced by a short incident resonant light pulse, is calculated within a formalism that takes into account explicitly the internal structure of excitions. By examining the phase‐space filling interactions among excitons, it is shown that the hydrogenic structure of excitions causes significant deviations in their coherent optical response when compared with the response of the traditional two‐level model of optical coherence. This suggests that photon echo experiments, which measure directly the coherent polarization, may provide information on the structure of Wannier excitons.

DOI
10.1002/pssb.2221590103

Related papers

Theory of optical coherence for Wannier excitons: Application to photon echoes

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The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.

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Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver rich information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a CdTe/(Cd, Mg)Te quantum well. The echoes of the trion and donor-bound exciton are linearly polarized at the angle 2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cosφ.

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Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle $φ$ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D$^0$X. We find that polarimetry of the photon echo on the trion and D$^0$X is substantially different from the exciton: The echoes of the trion and D$^0$X are linearly polarized at the angle $2φ$ with respect to the first pulse polarization and their amplitudes are weakly dependent on $φ$. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as $\cosφ$.

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Excitonic nonlinearities in the weak-excitation limit condition are examined with time-integrated and time-resolved four-wave mixing (FWM). Below an excitation of 3\ifmmode\times\else\texttimes\fi{}${10}^{9}$ excitons/${\mathrm{cm}}^{2}$, coherent third-order processes prevail. Echo-type signals are observed in parallel and perpendicular polarization configurations. The coherent process induced by the two-photon coherence of the two-exciton state is attributable to signals in the perpendicular configuration. The polarization dependences of a temporal profile and the intensity of FWM signals are well explained with third-order perturbational analysis that takes into account the two-exciton states and inhomogeneity.

Physical review. B, Condensed matter•Mar 15, 1994•73 citations
Abstract The coherent polarization of a Wannier exciton system, induced by a short incident resonant light pulse, is calculated within a formalism that takes into account explicitly the internal structure of excitions. By examining the phase‐space filling interactions among excitons, it is shown that the hydrogenic structure of excitions causes significant deviations in their coherent optical response when compared with the response of the traditional two‐level model of optical coherence. This suggests that photon echo experiments, which measure directly the coherent polarization, may provide information on the structure of Wannier excitons.
The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver rich information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a CdTe/(Cd, Mg)Te quantum well. The echoes of the trion and donor-bound exciton are linearly polarized at the angle 2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cosφ.
In this article the third-order response of an excitonically coupled dimer is studied. The three-pulse photon echo signals were calculated by extracting polarization components from the total polarization in the corresponding phase-matched directions. The total nonlinear response was obtained by numeric propagation of the density matrix, with the exciton-vibrational coupling modeled via Redfield relaxation theory. The full two-dimensional three-pulse photon echo signals and the peak shift were analyzed in terms of the density-matrix dynamics of coherence dephasing and population relaxation. The location of the two-exciton state was found to be essential for proper modeling of the three-pulse photon echo. In particular, an oscillation in the three-pulse photon echo peak shift is found if the two-exciton state is displaced. The oscillations can be related to the dynamics of the one-exciton coherences.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φφφ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D0^00X. We find that polarimetry of the photon echo on the trion and D0^00X is substantially different from the exciton: The echoes of the trion and D0^00X are linearly polarized at the angle 2φ2φ2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φφφ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cos⁡φ\cosφcosφ.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
Excitonic nonlinearities in the weak-excitation limit condition are examined with time-integrated and time-resolved four-wave mixing (FWM). Below an excitation of 3\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 excitons/cm2{\mathrm{cm}}^{2}cm2, coherent third-order processes prevail. Echo-type signals are observed in parallel and perpendicular polarization configurations. The coherent process induced by the two-photon coherence of the two-exciton state is attributable to signals in the perpendicular configuration. The polarization dependences of a temporal profile and the intensity of FWM signals are well explained with third-order perturbational analysis that takes into account the two-exciton states and inhomogeneity.