Phase-relaxation time

Because of the finite linewidth Aco of the transition 1) 2) (for example, the Doppler width in a gaseous sample), the frequencies con = (E — E2)/h of the atomic transitions of our N dipoles are distributed within the interval Aco. This causes the phases of the N oscillating dipoles to develop in time at different rates after the end of the 7r/2-pulse aX t > r. After a time t > T2, which is large compared to the phase relaxation time T2, the phases are again randomly distributed (Fig. 7.20c,d). 

These experiments give information on the polarizability of excited molecules (from the amplitude of the oscillation), on the transverse phase relaxation times T2 (which depend on the cross sections of phase-perturbing collisions, Vol.l, Sect. 3.3), and on the population decay time T. For more details see [911, 913]. 

Fig. 2 Typical correlation traces of transient degenerate four-wave mixing calculated by analytical equations for idealized light sources t (A) coherent short pulses with zero pulse width (tp 0), and (B) incoherent long pulses with zero correlation time (Tq 0). Here, x is the delay time, and Tj and T2 denote the longitudinal (energy) and transverse (phase) relaxation times, respectively.

The narrowing of correlation trace in the four-wave mixing for a chirped pluse has been pointed out, and used to investigate the coherence property of light pulses.We have examined the possibility of high time-resolution measurement of phase relaxation time T2 with a chirped coherent pulse in the same configuration as described in Sec. 2 by means of computer simulation, which will be summarized below. Recently, a similar attempt has also been reported by other workers. 

By applying an input signal to excite an exciton to the (1,1,1) energy level of the input-QD, the linewidth of the (2,1,1) energy level of the input QD is broadened due to the decrease in the phase-relaxation time of the exciton induced by carrier-carrier... 

One more trend in laser control is based on the use of the property of coherence of the laser light. To effect coherent laser control, it is necessary that not only the light, but also the atom (or molecule) should be in a coherent state during the interaction. For atoms in a beam or in a low-pressure gas, the phase relaxation time of their wave functions depends on spontaneous decay or on collisions and can be comparatively long (from 10 to 10 s). It was for precisely this reason that the main experiments on coherent interaction were conducted with atoms. These experiments led in the final analysis to the discovery of new effects, such as coherent population trapping (Arimondo 1996), electromagnetically induced transparency (Harris 1997), and the slow-light effect (Hau et al. 1999 Kash et al. 1999). 

The situation with molecules is much more involved for several reasons. First, for polyatomic molecules, the intramolecular relaxation processes that occur on a subpicosecond timescale are essential. It was for exactly this reason that the first successful experiments were conducted on the noncoherent laser control of polyatomic molecules with intermolecular selectivity. Second, the phase relaxation time in a condensed medium is also on a subpicosecond scale because of the interaction between the quantum system and its surroundings. Therefore, it was only the creation of relatively simple and inexpensive femtosecond lasers that made it possible to set about realizing the ideas of the coherent laser control of unimolecular processes (Tannor and Rice 1985 Brumer and Shapiro 1986 Judson and Rabitz 1992), particularly the... 

Fig. 2.4 Resonant excitation of (a) an ideal, relaxation-free two-level system and (b) a two-level system with a popnlation relaxation time Ti and a phase relaxation time T2.

The evolution of the off-diagonal matrix elements is described by equations that also follow from the Schrodinger equation after the appropriate averaging and introduction of the phase relaxation time T2, that is, the time of the decay of the particle polarization ... 

In this case, the populations of states 1 and 2 oscillate at the Rabi frequency, as shown in Fig. 2.6. The only difference is that the oscillations decay exponentially during the phase relaxation time T2- If condition (2.62) is satisfied, the interaction of the two-level system with the laser-light field is said to be coherent. 

PDA was, in 1981, predicted to give ultrafast switching of the order of 0.1 ps. In this connection, the exciton lifetime (Tj) was evaluated by DFWM using PTS thin single crystals. values of 1.8 0.5 ps were obtained in the near resonant region at 652 nm Tj in the nonresonant region between 700 and 720 nm is shorter than the used pulse width of 300 fs. The phase relaxation time (Tj) of cast films of a soluble PDA, 3BCMU, was measured by DFWM, and Tj was found to be 30 fs at 648 nm and 90 fs at 582 nm. ... 

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