Relaxation of Coherently Excited Systems

The time-dependent Schrodinger equation (2.57) is written in the density-matrix formalism as 

In order to separate the different contributions of induced absorption or emission and of relaxation processes, we write the Hamiltonian as the sum 

The decay of the off-diagonal elements pab, pba describes the decay of the coherence, i.e., of the phase relations between the atomic dipoles. 

The dephasing rate is represented by the phase-relaxation constants and the decay of the nondiagonal elements is governed by 

In general, the phase relaxation is faster than the population relaxation defined by the relaxation time T, which means that the nondiagonal elements decay faster than the diagonal elements (Chap. 12). 

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The previous sections indicate that the full quantum dynamical treatment of IVR in an intermediate size molecule even under conditions of coherent excitation shows phenomena reminiscent of relaxation and equilibration. This suggests that, in general, at very high excitations in large polyatomic molecules with densities of states easily exceeding the order of 10 cm (or about 10 molecular states in an energy interval corresponding to 1 J moP ), a statistical master equation treatment may be possible [38, 122]. Such an approach has been justified by quantum simulations in model systems as well as analytical considerations... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

The events taking place in the RCs within the timescale of ps and sub-ps ranges usually involve vibrational relaxation, internal conversion, and photo-induced electron and energy transfers. It is important to note that in order to observe such ultrafast processes, ultrashort pulse laser spectroscopic techniques are often employed. In such cases, from the uncertainty principle AEAt Ti/2, one can see that a number of states can be coherently (or simultaneously) excited. In this case, the observed time-resolved spectra contain the information of the dynamics of both populations and coherences (or phases) of the system. Due to the dynamical contribution of coherences, the quantum beat is often observed in the fs time-resolved experiments. 

In Ref. [4] we have studied an intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two state electronic system with relaxation treated as diffusion on electronic potential energy surfaces with respect to the generalized coordinate a. We solved numerically equations for the density matrix of a molecular system under the action of chirped pulses of carrier frequency a> with temporal variation of phase [Pg.131]

While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. 

The procedure that we propose to enhance the concentration of a particulap enantiomer when starting with a racemic mixture, that is, to purify the mixture) is as follows [259], The mixture of statistical (racemic) mixture of L and irradiated with a specific sequence of three coherent laser pulses, as described below. These pulses excite a coherent superposition of symmetric and antisymmetric vibrational states of G. After each pulse the excited system is allowed to relax bg t to the ground electronic state by spontaneous emission or by any other nonradiativ process. By allowing the system to go through many irradiation and relaxatio cycles, we show below that the concentration of the selected enantiomer L or can be enhanced, depending on tire laser characteristics. We call this scenario lat distillation of chiral enantiomers. 

The first optical laser, the ruby laser, was built in 1960 by Theodore Maiman. Since that time lasers have had a profound impact on many areas of science and indeed on our everyday lives. The monochromaticity, coherence, high-intensity, and widely variable pulse-duration properties of lasers have led to dramatic improvements in optical measurements of all kinds and have proven especially valuable in spectroscopic studies in chemistry and physics. Because of their robustness and high power outputs, solid-state lasers are the workhorse devices in most of these applications, either as primary sources or, via nonlinear crystals or dye media, as frequency-shifted sources. In this experiment the 1064-mn near-infrared output from a solid-state Nd YAG laser will be frequency doubled to 532 nm to serve as a fast optical pump of a raby crystal. Ruby consists of a dilute solution of chromium 3 ions in a sapphire (AI2O3) lattice and is representative of many metal ion-doped solids that are useful as solid-state lasers, phosphors, and other luminescing materials. The radiative and nonradiative relaxation processes in such systems are important in determining their emission efficiencies, and these decay paths for the electronically excited Cr ion will be examined in this experiment. 

Additional features arise from spontaneous transfers of coherence particularly, but not exclusively, when the population relaxations are very fast. The coherence equations, which are effectively the Redfield relations without interchanges of population with coherence, must be solved during each time interval and probabilities worked out for the appearance of coherences other than those that are driven by the excitation pulses. This procedure is particularly important for vibrational systems, where there are often a significant number of transitions having nearly the same frequency. For example, the coherence pj,. oscillates... 

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