Ac Stark shift

Figure 4.5 Schematic drawing of system and bath, (a) Amplitude noise (AN) (red) combatted by AC-Stark shift modulation (green), (b) Phase noise (PN) (red) combatted by resonant-field modulation (green). (See color plate section for the color representation of this figure.)...

We first consider the AN regime of a two-level system coupled to a thermal bath. We will use off-resonant dynamic modulations, resulting in AC-Stark shifts (Figure 4.5(a)). The Hamiltonians then assume the following form ... 

This would accomplish the goal of DD [39,41 7, 79], Conversely, the increase of R due to a shift can be much greater than that achievable by repeated measurements, that is, the anti-Zeno effect [9,13-15]. In practice, however, AC Stark shifts are usually small for (cw) monochromatic perturbations, whence pulsed perturbations should often be used, resulting in multiple shifts as per Eq. (4.132). 

While the formalism of DD is quite different from the formalism presented here, it can be easily incorporated into the general framework of universal dynamical decoherence control by introducing impulsive PM. Let the phase of the modulation function periodically jump by an amount 4> at times r, 2t,. .. Such modulation can be achieved by a train of identical, equidistant, narrow pulses of nonres-onant radiation, which produce pulsed AC-Stark shifts of co. When (/> = tt, this modulation corresponds to DD pulses. 

Several reasons have been put forward to explain the change in the angular intensity pattern of the photoelectrons. One explanation is that intermediate neutral energy levels are ac-Stark shifted into resonance and contribute new selection rules to the photoionization process [53,54], Another possibility is that the electrons of the Kr or D2 are driven into the core Kr+ or D2 in a scattering-like process that creates interference fringes in the photoelectron angular distribution due to interference between multiple scattering channels [55],... 

As the laser intensity is increased and the vibrational energy levels of the ion are ac-Stark shifted to higher energy, they bring with them the Rydberg states of the neutral D2. As the laser intensity moves a particular vibrational level of the D2 into and through resonance with the laser light at the... 

That part of the black body spectrum coincident with the atomic transition frequencies leads to the transitions which redistribute the population. In contrast, all the energy of the black body radiation contributes to the shift of the energy levels. The energy shift is a second order ac Stark shift, and for state n the shift AWb is given by10... 

For an accurate data analysis, a detailed understanding of systematic effects is necessary. Although they are significantly reduced with the improved spectroscopy techniques described above, they still broaden the absorption line profile and shift the center frequency. In particular, the second order Doppler shift and the ac-Stark shift introduce a displacement of the line center. To correct for the second order Doppler shift, a theoretical line shape model has been developed which takes into account the geometry of the apparatus as well as parameters concerning the hydrogen atom flow. The model is described in more detail in Ref. [13]. 

It appears likely that the statistical uncertainty will eventually be reduced to around 100 kHz, so we consider sources of systematic error which may be expected to enter at this level. The uncertainty in the second-order Doppler shift (450kHz/eV) will be reduced to 100 kHz by a 5% measurement of the beam energy. The AC Stark shift of the 2S-3S transition will be around 70 kHz for the present laser intensity, and can be extrapolated to zero intensity by varying the UV power. Finally, as mentioned above, the systematic uncertainties will be quite different from those in the microwave and quench anisotropy measurements. 

Fig. 5. Diagrams contributing to the AC Stark-shifts and mixing of the I1S1/2- and 2S i/2-levels of a hydrogen-like atom under the action of two laser waves of the frequency u>l, counter-propagating in the direction nz. As seen by an atom in its rest frame moving with the velocity v = vn relative to the laboratory system, appropriate Doppler-shifted frequencies are determined as 0)1,2 = wl(1 vn-n /c) / 1 — (v/c)2...

Table 1. Estimated shifts and uncertainties of the indium frequency standard. All values are given relative to the frequency 1267 THz. For the small effects the uncertainties may be comparable to the total shift, with the exception of the blackbody AC stark shift. All Stark shifts are based on an estimated upper bound for the polarisability. The collisional shift is an estimate based on data in comparable atomic systems. The assumed conditions are T 0 = 100 pK uncompensated stray fields, leading to micromotion amplitude < A/20 = 12 nm AB = 10 fJtG P = 5 10-8 Pa TtraP = 300 K 1 K...

In the NBS work, the transition of interest for a frequency standard is the Hg+ 5d 6s Si 5d 6s 5/2 quadrupole transition at 281.5 nm shown in Fig. 1. The 5/2 level has a lifetime of 86 ms, corresponding to a natural width of 1.8 Hz. Use of the single photon quadrupole transition has an advantage over two-photon Doppler free transitions because ac Stark shifts are negligible. 

The dominant uncertainties in the measurement were the dc Stark shift of the deuterium line in the discharge tube, the ac Stark shift of the Ps line, the second-order Doppler shift of the thermal Ps and the amplified laser frequency shift relative to the cw laser. Counting statistics show up in the measurement of the Ps - tellurium frequency shifts as one extrapolates to zero laser power and zero atomic velocity. 

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