Pure dephasing

If we neglect pure dephasing, the general tensor element of the third order hyperpolarizability relates to those of the first order polarizability tensor according to... 

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

The interference term is thus of the form of Eq. (4), where in the present case 8s reflects the molecular as well as the environment properties. Within our occupation space formalism, it is given as a simple analytical function of system parameters, and its physical content is explicit. In the isolated molecule limit, where pure dephasing vanishes, Eq. (58) reduces to... 

As seen in Eqs. (59)—(61), dephasing processes introduce two new time scales into the dynamics, in addition to the intermediate state lifetime that determines the structure of 8s in the isolated molecule case. One is the time scale of pure dephasing, and the other is the lifetime of the final state. Equation (64) illustrates that the Tff dependence of 8s is a condensed phase effect that vanishes in the limit of no dephasing. The more careful analysis later shows that the qualitative behavior of the channel phase is dominated by the rpd/rrr and Tpd / [ ratios, that is, by the rate of dephasing as compared to the system time scales. 

Figure 17. The total signal versus the relative phase of the laser fields for the case of no pure dephasing (solid curves) and for = 30 fs (dashed curves). The pulsewidth for the two cases is varied as follows (a) 4fs (circles) and 30 fs (diamonds) and (b) 150 fs (squares) and 200 fs (triangles). (Reproduced with permission from Ref. 48, Copyright 2006 American Institute of Physics.)...

From Eqs (7.5) and (7.6) we can deduce that the pure dephasing rate is Yio( ) = 0.2ps 1 and the vibrational relaxation takes place in the timescale of 0.5 ps for the 100-cm 1 mode. More results related to vibrational relaxation have been reported by Martin group [1-5], In this chapter we choose 0.3 ps for the 100-cm-1 mode, and the vibrational relaxation rates for other modes are scaled with their vibrational frequencies. 

From the above discussion, we can see that vibrational relaxation plays a very important role in ultrafast phenomena. In this appendix we shall present a model that can describe vibrational relaxation and dephasing (especially pure dephasing). Suppose that... 

By omitting the pure dephasing processes, which is warranted at low temperatures, the dephasing constant 1) ), in Eq. (III. 19) can be expressed, in terms of the population decay constants of the states v and v , as... 

Figure 4.12 BOMEC-minimization of the gate error for a single qubit jr-gate caused by pure dephasing with a given bath spectrum (G(w), bold red line, scaled to 0.61 with respect to its maximum value, scaling of m with respect to the chosen bath resonance, that is, in units of the inverse bath correlation time). The Z-components of the obtained system modulation spectra Fj(w) are shown for...

The origin of the 105-cnT1 mode is not known with certainty, but it is tempting to associate it with intradimer motion as is done for the very similar frequency observed in the special pair of reaction centers [15], Remarkably, Vos et al. [15] and Chachisvilis et al. [19] find that damping rate is independent of temperature. The absence of pure dephasing on a picosecond time scale is unexpected and implies very weak coupling of this motion to the protein photons. 

Equation (33) assumes that IV// is large compared to 2J (i.e., no electronic and vibrational recurrences). In addition, Eq. (33) deals only with population dynamics Interferences between different Franck-Condon factors are neglected. These interferences do influence the rate, and the interplay between electronic and vibrational dynamics can be quite complex [25], Finally, as discussed by Jean et al. [22], Eq. (33) does not separate the influence of pure dephasing (T-T) and population relaxation (Ti). These two processes (defined as the site representation [22]) can have significantly different effects on the overall rate. For example, when (T () becomes small compared to Eq. (33) substantially overestimates the rate compared to... 

D. J. Tannor To understand the role of dissipation in quantum mechanics, it is useful to consider the density operator in the Wigner phase-space representation. Energy relaxation in a harmonic oscillator looks as shown in Fig. 1, whereas phase relaxation looks as shown in Fig. 2 that is, in pure dephasing the density spreads out over the energy shell (i.e., spreads in angle) while not changing its radial distribution... 

Z. Ma and D.F. Coker. Quantum initial condition sampling for linearized density matrix dynamics Vibrational pure dephasing of iodine in krypton matrices. J. Chem. Phys., 128 244108, 2008. 

In condensed phase, ybutime scale of experiment, the vibronic coherence term may disappear. 

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

The pure dephasing rate constant can be derived by using the second-order term with respect to the system variable and, for example, assuming... 

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