Broadening power

The broadening of homogeneous line profiles by intense laser fields can also be regarded from another viewpoint compared to Sect. 3.6.2. When a two-level system is exposed to a radiation field E = E co cot, the population probability of the upper level b) is, according to (2.95) and (2.119), 

If the upper level b) can decay by spontaneous processes with a relaxation constant y, its mean population probability is 

Since the induced absorption rate within the spectral interval y is, according to (2.41) and (2.77) 

If both levels a) and b) decay with the relaxation constants ya and y, respectively, the line profile of the homogeneously broadened transition a) 

If a strong pump wave is tuned to the center coo = ab of the transition and the absorption profile is probed by a tunable weak probe wave, the absorption profile looks different due to the population modulation with the 

The broadening of homogeneous line profiles by intense laser fields can also be regarded from another viewpoint compared to the previous section. 

This shows that the saturation decreases the absorption coefficient a(co) by the factor (1 + Sa ). At the line center, this factor has its maximum value (1 + So), while it decreases for increasing (co — coq) to 1, see (3.72). The saturation is therefore strongest at the line center, and approaches zero for (co — coo) oo (Fig. 3.24). This is the reason why the line broadens. For a more detailed discussion of saturation broadening, see Vol. 2, Chap. 2 and [3.38-3.40]. 

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One effect of saturation, and the dependence of e on /, is to decrease the maximum absorption intensity of a spectral line. The central part of the line is flattened and the intensity of the wings is increased. The result is that the line is broadened, and the effect is known as power, or saturation, broadening. Typically, microwave power of the order of 1 mW cm may produce such broadening. Minimizing the power of the source and reducing the absorption path length t can limit the effects of power broadening. 

Of the four types of broadening that have been discussed, that due to the natural line width is, under normal conditions, much the smallest and it is the removal, or the decrease, of the effects of only Doppler, pressure and power broadening that can be achieved. 

Fig. 18.2 Chart recorder trace of the 91D2-91,3G4 resonances. The resonances are power broadened by a factor of 2-3 for purposes of display. Sweep rate 0.4 MHz/s, lock-in time...

An example for one of the first applications of the coupled-channel equations y with quantized fields for photodissociation problems is shown in Figure 12.1, where, the dissociation of the IBr molecule by a two-photon (visible + IR) process wasJS studied [388], The results of the calculations, shown in Figure 12.2, demonstrate 3 how the strong IR photon broadens the transition ( power broadening ) allowing th system to be dissociated even if the first photon is tuned substantially away from, 7 resonance. This illustrates how multiphoton transitions induced by strong fields [392] are less restricted insofar as they need not be very close to an intermediate T resonance, the situation described in Section 3.3. 

S = 0 and P r) reaches unity at the reduced time xp = n/(2Qn) — nj[2.F S>S F0 < 1, then rp 1, and the time taken to attain complete population transfer nth level is very long. The same applies to the use of optimal pulses in popula rotational states [116] and to the use of adiabatic passage, discussed in Section 9 Further, it was found [455] that increasing F0, which shortens xp, results in complq loss of selectivity. Basically, in this case the power broadening increases so piu that all n-photon resonances overlap., i ... 

The power broadening curves allow one to determine the saturation intensity ... 

Figure 3. Power broadening of P(99)15-7 Nat line, fitted with the theory (8J (rate equation approximation, Gaussian beams). S = 1 corresponds to an Ar laser intensity of 54 mW/mm. ...

Our experience tells us that power broadening by the laser pulses combined with light assisted atomic collisions play the important role in the decoherence processes. For high densities and high optical powers we may find T2 as low as 5 ms. A fair guess for ft is an exponential decay over a typical time scale of 2 ms (the time between the central parts of the entangling and verifying pulses). This yields ft exp(—2/5) 0.67. This is not far from the observed... 

Fig. 8.3. Autoionising resonances coupled to a power-broadened continuum. The pure profile of the power-broadened line was also determined experimentally, and is shown by the broken curve (after A. Safinya and T.F. Gallagher [401]).

Two especially important variants of REMPI (Johnson, et al., 1975) spectroscopy are ionization-dip (Cooper, et al., 1981) and Zero Electron Kinetic Energy (ZEKE) (Miiller-Dethlefs and Schlag, 1991 Merkt, 1997 Signorell and Merkt, 1999) photoelectron spectroscopy. Ionization-dip REMPI spectroscopy is especially useful when one wants to record free<—bound spectra from a single, selectable v, J level. Without such v, J selection, most of the oscillatory structure in a free<—bound spectrum will be washed out. One potential problem with some ionization-dip schemes is that, if the ionization transition originates from the initial level of the free<—bound transition being studied, there is a possibility that the observed linewidths will be distorted by power broadening (especially when the free final state is a weakly predissociated state with linewidth < lcm-1). 

Figure 6.13 OODR differential power broadening in BaO. The PUMP laser is tuned to the A1 E+ <— X1 E+ (1,0) R(50) line the PROBE is scanned in the region near P(51) of C1 E+ <— A1E" "(3,1). The main line (P3) and two of four extra lines (P2 and P4) are shown. The unassigned collisional satellite line marked with an arrow has area equal to that of the P4 extra line [from Gottscho and Field (1978).]...

An extremely sensitive MODR scheme, microwave optical polarization spectroscopy (MOPS), was introduced by Ernst and Torring (1982). The most important features of MOPS are that it requires respectively 100 and 10 times lower laser and microwave intensities than MODR and results in 10 times narrower lines. This means that it will be possible to take full advantage of differential power broadening effects (Section 6.5.1) and to utilize low-power, frequency-doubled dye lasers and low-power, broadly tunable microwave sources (backward wave oscillators) in order to gain access to and systematically study perturbations. 

How about some other examples of homogeneously broadened lines The application of high radio frequency power to a transition not only causes saturation (if is sufficiently long) but also causes power broadening for the entire system. When a strongly coupled system, coupled by dipolar interactions, permits spin diffusion and the establishment of a common spin temperature, the attempt to burn a hole in the line will also result in a collapse of the entire line. Dipolar interactions, spin diffusion, and spin temperatures are discussed later in this chapter, as well as in III.C.l. and in IV.D. 

The result of this power broadening or saturation is to reduce the absorption in the line centre compared with the absorption in the wings of the line. This in turn leads to loss of analytical signal intensity and an apparent broadening of the absorption line profile. The resulting effect on the line shape function can be described by an equation due to Karplus and Schwinger, for low powers and incomplete saturation (ref 3, p. 50) ... 

By setting v = Vq in Equation 1.39 it can be seen that the effect of the power broadening is to reduce the value of S and hence ao at the line centre. The influence on ao is not great although the Q of the cavity does amplify the effect. Relatively little attention appears to have been given to this amplification in the literature, and so in the next section we derive expressions for the conditions under which it may occur. 

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