The coherence spike observed in the transmitted probe intensity decay curve in pump–probe experiments is analyzed with a model which depends explicitly upon the population decay and dephasing rate constants. Using this model and simple pulse shape functions a series of decay curves are calculated throughout the range of wide to narrow pulse widths relative to the dephasing time. These calculations suggest that the coherence spike may be used to obtain information about the phase coherence in the electronic or vibrational transition being investigated, when the pulse width is comparable to or smaller than the dephasing time. Methods of extracting T2 from the coherence spike are also discussed.
The coherence spike observed in the transmitted probe intensity decay curve in pump–probe experiments is analyzed with a model which depends explicitly upon the population decay and dephasing rate constants. Using this model and simple pulse shape functions a series of decay curves are calculated throughout the range of wide to narrow pulse widths relative to the dephasing time. These calculations suggest that the coherence spike may be used to obtain information about the phase coherence in the electronic or vibrational transition being investigated, when the pulse width is comparable to or smaller than the dephasing time. Methods of extracting T2 from the coherence spike are also discussed.
A detailed theoretical analysis is presented of the dephasing signal measured in four-beam picosecond time-resolved stimulated-Raman-gain experiments. The analytical expressions derived are successful in simulating observations on the CS2 model system under various experimental conditions. It is established that the tail of the curve for sufficiently long delay times is uniquely determined by the vibrational Raman term that yields the vibrational dephasing time T2. It is also found that the rotational dephasing time cannot be fundamentally determined from the rotational Raman peak centered around zero delay. Furthermore, it is shown that the coherence properties of the stimulating laser fields, as distinguished from their pure pulse-envelope properties, are crucially important in determining the time resolution of the experiments and for explaining several experimental phenomena observed under mismatched excitation-pulse conditions. In this respect, the domain model for mode-locked pulses has proved to be useful. It is found that the time resolution of the dephasing measurements is determined by the combined pulse-coherence time of the driving fields and not by the cross-correlation width of the pulse envelopes.
Pump-probe spectroscopy is the most common time-resolved technique for investigation of electronic dynamics, and the results provide the incoherent population decay time T1. Here we use a modified pump-probe experiment to investigate coherent dynamics, and we demonstrate this with a measurement of the inhomogeneous dephasing time T2∗ for phosphorus impurities in silicon. The pulse sequence produces the same information as previous coherent all-optical (photon-echo-based) techniques but is simpler. The probe signal strength is first order in the pulse area but its effect on the target state is only second order, meaning that it does not demolish the quantum information. We propose simple extensions to the technique to measure the homogeneous dephasing time T2, or to perform tomography of the target qubit.
The microscopic information content of coherent transient Raman measurements is analyzed. It is shown that for short pulses and optically thin samples the Kaiser–Laubereau pulse sequence is the Raman analog of the optical free induction decay, and that the experimental observable contains the same dynamical information as the isotropic, spontaneous Raman line shape. Under these conditions, the experiment therefore cannot be used to selectively measure the homogeneous dephasing time of a system with an inhomogeneously broadened line. The results of our analysis are at variance with the earlier results of Kaiser and Laubereau and the more recent predictions of Oxtoby. However, these experiments, under certain circumstances, may be used to obtain a nonselective line narrowing, as found by Zinth, Polland, Laubereau, and Kaiser. We also consider the situation in which the sample is optically dense, in which case laser depletion must be taken into account. The distinction between saturation of the vibrational transition and depletion of the pump pulse is discussed, and selectivity is shown to arise from the former phenomenon, rather than from the latter. This result is at variance with the predictions of George and Harris. An alternative pulse sequence, the Raman echo, is suggested as a tool to achieve selectivity. A unified theory of the Raman echo is developed, which is valid for a bath with arbitrary time scale and which interpolates between the limits of homogeneous and inhomogeneous line broadening.
One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.
In some pump–probe optical correlation experiments, the measured signal versus delay between pulses generally consists of two components: the convolution of the pulse autocorrelation with the sample impulse response, and a coherent artifact. The latter can obscure the first component near zero delay where fast time scale processes will be manifest. We present a mathematical description of the relative shapes and sizes of the two components, so that a fitting process can separate them. This can yield both the dephasing and relaxation times of saturable absorbers such as semiconductors. The method is particularly appropriate when the orientational dephasing and relaxation times are of the same time scale as the laser pulse width.
In the femtosecond pump-probe pulse experiments, the pump pulse with duration comparable to or shorter than a typical vibrational period creates a nonstationary wave pocket. In this paper, we use the density-matrix method to treat the dynamic behavior of the system (embedded in a heat bath) in the femtosecond pump-probe pulse experiment. The expression for the coherence of the system due to the pumping laser is derived, and the generalized master equations for the dynamical behavior of the system after the pumping pulse is over are also obtained. Some numerical calculations are performed for a two-level system to demonstrate the time-dependent behaviors of memory kernel, rate constant, and population.