Linewidth saturation broadening

A high-resolution spectrum of the clock transition is shown in Fig. 2. The clock-laser power was reduced to 30 nW to avoid saturation broadening. The fit with a lorentzian curve results in a linewidth of 170 Hz (FWHM), corresponding to a fractional resolution bv/v of 1.3 10-13. A spectral window of 200 Hz width contains 50% of all excitations. According to our present experimental control of the ion temperature, electromagnetic fields and vacuum conditions, no significant Doppler, Zeeman, Stark or collisional broadening of the absorption spectrum of the ion is expected beyond the level of 1 Hz. The linewidth is determined by the frequency instability of the laser and the lineshape is not exactly lorentzian... 

Lamb peaks (inverse Lamb dips) at the line centers of the absorbing transitions (Sect. 2.3). The line profiles of these peaks are determined by the pressure in the absorption cell, by saturation broadening, and by transit-time broadening (Vol. 1, Sect. 3.4). Center frequency coq, linewidth Aco, and line profile Pl(co) are measured as a function of the pressure p (Fig. 8.2). The slope of the straight line Aco p) yields the line-broadening coefficient [977], while the measurement of coo p) gives the collision-induced line shift. 

Note I [Ws/m2] is the spectral intensity.) Saturation broadening plays only a minor role. The absorption coefficient is determined only by those atoms within the natural linewidth. 

The halfwidth = ho) of the saturation-broadened line increases with the saturation parameter So at the line center coo If the induced transition rate at coo equals the total relaxation rate R, the saturation parameter 5o = [B 2p coo)VR becomes 5o = 1, which increases the linewidth by a factor /2, compared to the unsaturated linewidth Scuq for weak radiation fields (p 0). 

A possible arrangement for saturation spectroscopy in a molecular beam is depicted in Fig. 9.18. The laser beam crosses the molecular beam perpendicularly and is reflected by the mirror Ml. The incident and the reflected beam can only be absorbed by the same molecules within the transverse velocity group = 0ibyA if the laser frequency (o = o)o y matches the molecular absorption frequency coo within the homogeneous linewidth y. When tuning the laser frequency col one observes narrow Lamb dips (Fig. 9.19) with a saturation-broadened width y at the center of broader profiles with a reduced Doppler-width cAcod, from the collimation ratio c 1 of the molecular beam (Sect. 9.1). 

Calculate the minimum beam diameter that is necessary to bring about the transit-time broadening in Example 3.2c below the natural linewidth. Is saturation broadening important, if the absorption cross section is a = 10 ° cm ... 

Dab Eo/h) is proportional to the intensity of the electromagnetic wave, the linewidth increases with increasing intensity (saturation broadening. Sect. 3.5). Note, that a(t)P -t- 6(0P < 1 for t > 0, because the levels a and b can decay into other levels. 

On the other hand, Schaefer ( ) has shown from selective saturation experiments of amorphous cis polyisoprene, crystalline trans polyisoprene, as well as carbon black filled cis polyisoprene, that the resonant lines are homogeneous. The linewidths in these cases are thus not caused by inhomogeneous broadening resulting from equivalent nuclei being subject to differing local magnetic fields. The results for these systems are thus contrary in part to what has been found here. 

By comparison, a saturated methine carbon (C-H) has a CSA of only 25 ppm because the mobility of electrons around the carbon nucleus is much less in an sp3-hybridized carbon and depends much less on the orientation of the C-H bond with respect to B0. In solution-state NMR we only see the isotropic chemical shift, < iso, and the fixed-position chemical shifts and the CSA value are obtained from solid-state NMR measurements. Although CSA does not affect chemical shifts in solution, it does contribute to NMR relaxation and can be exploited to sharpen peaks of large molecules such as proteins in solution. For large molecules, such as proteins, nucleic acids, and polymers, or in viscous solutions, molecular tumbling is slow and CSA broadens NMR lines due to incomplete averaging of the three principle chemical shift values on the NMR timescale. Like isotropic chemical shifts, CSA in parts per million is independent of magnetic field strength B0 but is proportional to B0 when expressed in hertz. Because linewidths are measured in... 

The line broadening due to light-shift and saturation is shown in Fig.4 where the experimental linewidth of the 2Si/z - 10Bo/z transition in deuterium is reported versus the light intensity transmitted through the excitation cavity. 

A numerical calculation of the line profiles due to the combined effect of the natural lifetime, the light-shift and the saturation has been performed taking into account all possible trajectories of atoms inside the metastable beam. Actually, the study of experimental linewidths shows there are some other stray effects responsible for the broadening of the lines. He have considered their contribution by making a convolution of the line profile with a gaussian curve. 

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