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Journal of the Physical Society of Japan

Two-Photon Echo and Excited State Photon Echo Methods to Determine the Transverse Relaxation Constants of Excitonic Molecules

T. Takagahara

Published Nov 1, 1981• 2 citations
Publisher

Abstract

Nonlinear optical methods to determine the transverse relaxation constants of excitonic molecules making use of two-photon echo and a new type of excited state photon echo are proposed. The two-photon echo is a seventh order nonlinear effect at the lowest and one needs three pulses to observe it, while the excited state photon echo is a fifth order nonlinear effect and requires four pulses. In these nonlinear optical methods we can satisfy the phase matching condition rather easily due to the large dispersion of excitonic polaritons. We can determine directly the transverse relaxation constants associated with the excitonic molecule from the correlation trace of the two-photon echo and the excited state photon echo.

DOI
10.1143/jpsj.50.3718

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arXiv:1803.10651•Physics of the Solid State•Aug 1, 2018•28 citations
Nonlinear optical methods to determine the transverse relaxation constants of excitonic molecules making use of two-photon echo and a new type of excited state photon echo are proposed. The two-photon echo is a seventh order nonlinear effect at the lowest and one needs three pulses to observe it, while the excited state photon echo is a fifth order nonlinear effect and requires four pulses. In these nonlinear optical methods we can satisfy the phase matching condition rather easily due to the large dispersion of excitonic polaritons. We can determine directly the transverse relaxation constants associated with the excitonic molecule from the correlation trace of the two-photon echo and the excited state photon echo.
Theoretical considerations of a method to measure the dephasing relaxation constant ${\ensuremath{\Gamma}}_{M}$ of excitonic molecules are presented. The proposed method is based on the principle of the two-photon free-induction decay and makes use of an appropriate combination of polarizations of the incident light beams to eliminate the contribution from the excitonic polariton. It is demonstrated that the correlation trace of the signal is sensitive to the value of ${\ensuremath{\Gamma}}_{M}$ and that a determination of ${\ensuremath{\Gamma}}_{M}$ from the experiments is quite feasible.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
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.
The dispersion characteristics of the nonlinear susceptibility χ ( n ) ( n =3, 5, 7) describing a new type of optical mixing have been calculated for their application to the study of ultra-fast relaxation dynamics in resonant media. The process is that two incident light waves at frequencies ω 1 and ω 2 produce new light waves at ω 1 - m ε and ω 1 + n ε ( ε =ω 2 -ω 1 ; m , n =1, 2, 3, …) under the conditions of two-photon resonance (2ω 1 , 2ω 2 ≃optical transition frequency) and Rayleigh-type resonance (|ω 1 -ω 2 |≃relaxation rate). Results of analysis based on an inhomogeneously broadened three-level model revealed that Rayleigh-type dispersions involving the longitudinal and transverse relaxation rates appear in χ ( n ) ( n ≧5) and χ ( n ) ( n ≧7), respectively. Their analogy with two-photon resonant photon echo and various precautions in applying them to actual situations are also discussed.
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
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.