Stark near-field

Stark PRH, Halleck AE, Larson DN (2007) Breaking the diffraction barrier outside of the optical near-field with bright, collimated light from nanometric apertures. Proc Natl Acad Sci USA 104 18902-18906... 

Sensitive and accurate measurements of atomic and molecular Rydberg levels have been performed [6.87-6.89] with thermionic diodes. With a special arrangement of the electrodes, a nearly field-free excitation zone can be realized that allows the measurement of Rydberg states up to the principal quantum numbers n = 300 [6.89] without noticeable Stark shifts. 

Even at high n s one needs to follow the system for many orbital periods if one is to mimic the experimental results. The difficulty is compounded if one measures the time in units of periods of the core motion. This suggests that the time evolution be characterized using the stationary states of the Hamiltonian rather than propagating the initial state. We have done so, but our experience is that in the presence of DC fields of experimental magnitude (which means that Stark manifolds of adjacent n values overlap), and certainly so in the presence of other ions that break the cylindrical symmetry and hence mix the m/ values, the size of the basis required for convergence is near the limit of current computers. In our experience, truncating the quan-... 

One of the first properties to be explored was the sensitivity of Rydberg atoms to external electric fields, the Stark effect. While ground state atoms are nearly immune to electric fields, relatively modest electric fields not only perturb the Rydberg energy levels, but even ionize Rydberg atoms, as was shown in early... 

Fabre et a/.28 used a projection operator technique to describe the Stark shifts at fields below where low states of large quantum defects join the manifold. A less formal explanation is as follows. If, for example, the s and p states are excluded, as in Fig. 6.13 below 800 V/cm, effectively only the nearly degenerate (22 states are coupled by the electric field. The only differences among the m = 0,1, and 2 manifolds occur in the angular parts of the matrix element, i.e.1... 

Since Vd(r) is only nonzero near r = 0 the matrix element of Eq. (6.51) reflects the amplitude of the wavefunction of the continuum wave at r 0. Specifically, the squared matrix element is proportional to C, the density of states defined earlier and plotted in Fig. 6.18. From the plots of Fig. 6.18 it is apparent that the ionization rate into a continuum substantially above threshold is energy independent. However, as shown in Fig. 6.18, there is often a peak in the density of continuum states just at the threshold for ionization, substantially increasing the ionization rate for a degenerate blue state of larger This phenomenon has been observed experimentally by Littman et al.32 who observed a local increase in the ionization rate of the Na (12,6,3,2) Stark state where it crosses the 14,0,11,2 state, at a field of 15.6 kV/cm, as shown by Fig. 6.19. In this field the energy of the... 

As shown by Fig. 8.14, in most Stark spectra above the classical ionization limit there is never one isolated resonance but, more often, an irregular jumble of them. For example, in Fig. 8.15 we show the observed22 and calculated23 Na spectra near the ionization limit in a field E = 3.59 kV/cm.22 The experimental spectrum of Fig. 8.15(a) was obtained by Luk et al.22 by exciting a Na beam with two simultaneous dye laser pulses from the 3s1/2 to 3p3/2 state and then to the ionization limit. Both lasers were polarized parallel to the field, and the ions... 

Fig. 10.7 Relevant energy levels of K near the n = 16 Stark manifold. The Stark manifold levels are labeled (n,k), where k is the value of (, to which the stark state adiabatically connects at zero field. Only the lowest two and highest energy manifold states are shown. The laser excitation to the 18s state is shown by the long vertical arrow. The 18s — (16,3) multiphoton rf transitions are represented by the bold arrows. Note that these transitions are evenly spaced in static field, and that transitions requiring more photons occur at progressively lower static fields. For clarity, the rf photon energy shown in the figure is approximately 5 times its actual energy (from ref. 8).

Fig. 10.19 The microwave frequency dependence of the n changing signals at low microwave power, where n changes up or down only by 1. Resonant multiphoton transitions are observed near the expected static field Stark shifted frequencies indicated. These resonances involve the absorption of four or five microwave photons. The down n changing atom production curve was obtained with the state analyzer field EA set at 50.0 V/cm, while up n changing was studied as n = 60 atom loss with EA = 45.5 V/cm. The locations of resonances for larger direct (not stepwise) changes in n are indicated along with...

As shown by Fig. 14.15, the resonances occur near zero field, and it is easy to calculate the small Stark shifts with an accuracy greater than the linewidths of the collisional resonances. As a result it is straightforward to use the locations of the collisional resonances to determine the zero field energies of the p states relative to the energies of the s and d states. Since the energies of the ns and nd states have been measured by Doppler free, two photon spectroscopy,22 these resonant collision measurements for n = 27, 28, and 29 allow the same precision to be transferred to the np states. If we write the quantum defect dp of the K np states as... 

In stark contrast, in the research field of the high temperature superconductivity (HTSC) the role of the lattice has been all but completely neglected by the majority. The conventional view is that it is a purely electronic phenomenon involving spin excitations, and is described, for instance, by the t-J model [2], There are many reasons why the lattice has been dropped from consideration almost from the beginning, such as the near absence of the isotope effect on the critical temperature, Tc, and the linear resistivity. However, the arguments against the lattice involvement are less than perfect [3],... 

We have calculated exactly the Zeeman effect for the levels IS, 3S and 3P. Indeed it is necessary to know the shift for all the hyperfine levels very well. These calculations are very classical and we just present the results in a Zeeman diagram (see Fig. 5). The most important part in the diagram is the crossing between the 38 2 (F=l, mp=-l) and 3P1/2(F=1, mj =0) levels, because the quadratic Stark effect is proportional to the square of the induced electric field and inversely proportional to the difference of energy between the two considered levels. Moreover the selection rules for the quadratic Stark effect in our case (E perpendicular to B) impose Am.F= l. So it is near this crossing that the motional Stark shift is large enough to be measured. In our calculations the Stark effect is introduced by the formalism of the density matrix [4] where the width of the levels are taken into account. The result of the calculation presented on... 

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