A theory is presented describing the proposed phonon perturbed photon echo experiment. This experiment is a combination of picosecond time scale stimulated Raman pumping and photon echo experiments. The theory demonstrates that the phonon perturbed photon echo can directly measure electronic excitation–phonon coupling matrix elements by observing the influence of a well defined coherent phonon wave on the photon echo signal. The theory predicts that the echo pulse area (integrated intensity) is reduced. The size of this change is related to the strength of the excitation phonon coupling. In addition, a realistic estimate is made of the size of the effect, and it is shown that the experiment is feasible with available laser equipment.
A theory is presented describing the proposed phonon perturbed photon echo experiment. This experiment is a combination of picosecond time scale stimulated Raman pumping and photon echo experiments. The theory demonstrates that the phonon perturbed photon echo can directly measure electronic excitation–phonon coupling matrix elements by observing the influence of a well defined coherent phonon wave on the photon echo signal. The theory predicts that the echo pulse area (integrated intensity) is reduced. The size of this change is related to the strength of the excitation phonon coupling. In addition, a realistic estimate is made of the size of the effect, and it is shown that the experiment is feasible with available laser equipment.
We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.
The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.
The three-pulse stimulated photon echo has been considered as one of the most fundamental transient four wave mixing processes1, where each of the three excitation pulses induces a single elementary interaction process between a laser field and an inhomogeneously broadened two-level system., resulting in a burst of the fourth wave, i.e., echo. Now if four or more optical pulses are applied to a medium, a number of photon echoes should be expected, in general. At low excitation intensities where the perturbation theory is applicable, however, the dominant nonlinear process is still the three-pulse stimulated echo and consequently each echo signal is generated only by three of the preceding pulses. It is rather a remarkable result that the echo intensity is unaffected by the presence of all the rest of the pulses other than its three generators. With this in mind, it is theoretically and experimentally shown that by applying a single optical pulse (#1) propagating along k1 followed by N pairs of counter-propagating pulses (#2j (k2j) and #3j− (k3j = −k2j); j=1,…N) in various directions, it is possible to obtain N photon echoes along the direction -k1 opposite to the first pulse #1. We will call this degenerate photon echoes, degenerate in. the sense that the echoes are spatially overlapping and temporally simultaneous. When N=l, this scheme is reduced to the ordinary backward photon echo2,3. The doubly degenerate case (N=2) is illustrated in Fig. 1. The j-th echo will be generated by the set of pulses (#1, #2j, #3j) and appear at t = t3j + t2j − t1 where t1, i2j and t3j are the arrival times of the pulses #1, #2j and #3j, respectively.
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].
The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.
The signals of both primary and stimulated femtosecond photon echoes are observed and investigated in a dye-doped polymer film at room temperature using a modernized femtosecond echo-spectrometer. It should be noted that stimulated photon echo in the solid-state sample is observed for the first time at such a high temperature. Experimentally obtained decay curves of these signals have a nonexponential character. The spectra of these echo signals are also measured. It is found that the spectrum of the primary photon echo is short-wave shifted with respect to the spectrum of excitation. This can be used for the coherent laser cooling of a sample. The spectrum of the stimulated photon echo is also shifted to the short-wave range relative to the spectrum of excitation, but its shift is much less than that of the primary photon echo. The experiment shows that the femtosecond echo signals at room temperature are excited via the phonon-side band of the absorption line.