Ultrafast dynamics populations and coherences

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 this section, the density matrix method shall be applied to study the ultrafast dynamics of the system embedded in a heat bath. Due to the use of the ultrashort pulse in the pumping lasers the dynamic behaviors of both population and coherence have to be considered [1,19-21],... 

A main feature of ultrafast processes under consideration takes place in the time scale shorter than picoseconds. Thus, it is necessary to employ the laser with pulse-duration 10 fsec to study these ultrafast processes. From the uncertainty principle AE At h/2 it can be seen that using this pulse-duration, numerous vibronic states can be coherently pumped (or excited) and thus the probing signal in a pump-probe experiment will contain the information of the dynamics of both population and coherence (or phase). In other words, in order to obtain the information of ultrafast dynamics it is... 

From the above discussion one can see that due to <7 (At) the measurement of y(quantum beat the beat frequency is a>tt while the beat width is approximately dependent on its dephasing constant. From Eq. (4.53) it can be seen that the ultrafast dynamics of population and coherence appears in initial condition, created by the pumping laser. 

A microscopic theory for describing ultrafast radiationless transitions in particular for, photo-induced ultrafast radiationless transitions is presented. For this purpose, one example system that well represents the ultrafast radiationless transaction problem is considered. More specifically, bacterial photosynthetic reaction centers (RCs) are investigated for their ultrafast electronic-excitation energy transfer (EET) processes and ultrafast electron transfer (ET) processes. Several applications of the density matrix method are presented for emphasizing that the density matrix method can not only treat the dynamics due to the radiationless transitions but also deal with the population and coherence dynamics. Several rate constants of the radiationless transitions and the analytic estimation methods of those rate... 

Both population and coherence experiments provide information on the dynamics and interactions of condensed matter systems. In addition, time domain vibrational experiments can extract spectroscopic information that is hidden in a conventional measurement of the infrared or Raman spectra. This book will provide the reader with a picture of the state of the art and a perspective on future developments in the field of ultrafast infrared and Raman spectroscopy. 

Abstract The density matrix method is a powerful theoretical technique to describe the ultrafast processes and to analyze the femtosecond time-resolved spectra in the pump-probe experiment. The dynamics of population and coherence of the system can be described by the evolution of density matrix elements. In this chapter, the applications of density matrix method on internal conversion and vibrational relaxation processes will be presented. As an example, the ultfafast internal conversion process of Jt jt nn transition of pyrazine will be presented,... 

Pump-probe experiment is an efficient approach to detect the ultrafast processes of molecules, clusters, and dense media. The dynamics of population and coherence of the system can be theoretically described using density matrix method. In this chapter, for ultrafast processes, we choose to investigate the effect of conical intersection (Cl) on internal conversion (IC) and the theory and numerical calculations of intramolecular vibrational relaxation (IVR). Since the 1970s, the theories of vibrational relaxation have been widely studied [1-7], Until recently, the quantum chemical calculations of anharmonic coefficients of potential-energy surfaces (PESs) have become available [8-10]. In this chapter, we shall use the water dimer (H20)2 and aniline as examples to demonstrate how to apply the adiabatic approximation to calculate the rates of vibrational relaxation. 

The Cl of the adiabatic PESs is a common phenomenon in molecules [11-13], The singular nonadiabatic coupling (NAC) associated with Cl is the origin of ultrafast non-Born-Oppenheimer transitions. For a number of years, the effects of Cl on IC (or other nonadiabatic processes) have been much discussed and numerous PESs with CIs have been obtained [11, 12] for qualitative discussion. Actual numerical calculations of IC rates are still missing. In this chapter, we shall calculate IC rate with 2-dependent nonadiabatic coupling for the pyrazine molecule as an example to show how to deal with the IC process with the effect of CL Recently, Suzuki et al. have researched the nn state lifetimes for pyrazine in the fs time-resolved pump-probe experiments [13]. The population and coherence dynamics are often involved in such fs photophysical processes. The density matrix method is ideal to describe these types of ultrafast processes and fs time-resolved pump-probe experiments [14-19]. 

Ultrafast vibrational spectroscopy offers a variety of techniques for unraveling the microsopic dynamics of hydrogen bonds occurring in the femto- to picosecond time domain. In particular, different vibrational couplings can be separated in nonlinear experiments by measuring vibrational dynamics in real-time. Both coherent vibrational polarizations and processes of population and energy relaxation have been studied for a number of hydrogen bonded systems in liquids [1],... 

It should be noted that the ultrafast PIET is usually studied by the pump-probe experiment using ultrashort laser pulses. The probe signals usually include the dynamic information of both coherence and population and to obtain the PIET rate, a theoretical analysis of these signals is required. This has been accomplished for the studies of ultrafast PIET in bacterial photosynthetic reaction centers [22]. 

All the powerful methods of magnetic resonance, from solid-state nuclear magnetic resonance (NMR) to medical magnetic resonance imaging, depend on measuring the time evolution of a spin system following the application of one or more radio frequency pulses. In the visible and ultraviolet, ultrafast optical pulse sequences have been used for many years to measure both population dynamics and coherence phenomena. At low... 

Fig. 8 shows time-dependent state populations as obtained from quantum dynamical (MCTDH) calculations. While the full (here, 24 dimensional) model exhibits an ultrafast XT decay, no net decay is observed for the reduced 3-mode model truncated at the lowest level of the effective mode hierarchy. The dynamics is strongly diabatic if confined to the high-frequency subspace (Heff ) and involves repeated coherent crossings [51]. The dynamical interplay between the high-frequency and low-frequency modes is apparently a central feature of the process. To account for these effects, a treatment at the level of is necessary, i.e., a six-mode model including the low-frequency modes. At the level of the dynamics is found to be essentially exact. 

Recent rapid developments in ultrashort pulse laser [1-5] make it possible to probe not only the dynamics of population of the system but also the coherence (or phase) of the system. To treat these problems, the density matrix method is an ideal approach. The main purpose of this paper is to briefly describe the application of the density matrix method in molecular terms and show how to apply it to study the photochemistry and photophysics [6-9]. Ultrafast radiationless transactions taking place in bacterial photosynthetic reaction centers (RCs) are very important examples to which the proposed theoretical approach can be applied. 

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