Quantum beats and level crossing

A good example of the use of the electric resonance technique is the measurement of the Na nd fine structure intervals and tensor polarizabilities.38 These transitions were observed using selective field ionization, although they appear to be unlikely prospects for field ionization detection because of the small separations of the levels, 20 MHz. The nd3/2 states were selectively excited from the 3p1/2 state in a small static electric field and the = 0 transitions to the nd5/2 states induced by a 

When the fine structure frequencies fall below 100 MHz they can also be measured by quantum beat spectroscopy. The basic principle of quantum beat spectroscopy is straightforward. Using a polarized pulsed laser, a coherent superposition of the two fine structure states is excited in a time short compared to the inverse of the fine structure interval. After excitation, the wavefunctions of the two fine structure levels evolve at different rates due to their different energies. For example if the nd3/2 and nd5/2 mf = 3/2 states are coherently excited from the 3p3/2 state at time t = 0, the nd wavefunction at a later time t can be written as40 

Here Wn is the average energy of the two fine structure levels. The real numerical coefficients a and b, where a2+b2=1, depend on the polarizations used in the excitation scheme, but are constant in time. Thus the relative amounts of d5/2 and d3/2 states do not change with time but simply decay together at the radiative decay rate T. However, the relative amounts of m character oscillate at the fine structure frequency, and this oscillation is manifested in any property which depends upon m, such as the fluorescence polarized in a particular direction, or the field ionization signal due to a particular value of m. This fact becomes more apparent 

The first measurements of Na nd fine structure intervals using quantum beats were the measurements of Haroche et al41 in which they detected the polarized time resolved nd-3p fluorescence subsequent to polarized laser excitation for n=9 and 10. Specifically, they excited Na atoms in a glass cell with two counterpropa-gating dye laser beams tuned to the 3s1/2— 3p3/2 and 3p3/2— ndj transitions. The two laser beams had orthogonal linear polarization vectors et and e2 as shown in Fig. 16.9. 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by 

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Kelly, R.L (1966) Theory of quantum-beat and level-crossing experiments utilizing electronic excitation. Phys. Rev., 147, 376. 

The electronic structure of a molecule may be correlated to chemical reaction rates, and in this manner Hammett s concept of O can, in principle, be correlated to a nuclear quadmpole coupling or hyperfine interaction constant. The analogy between ESEEM and quantum beats or level-crossing spectroscopy opens up the opportunity to measure the effective zero-field NQI parameters for quadmpolar nuclei in the reactive center (ligands or metal ion) of proteins and supramolecular assemblies. As one might expect, however, one is constrained to a system in which... 

Variations of coherent spectroscopy, such as level-crossing, quantum beat, and pulsed-field... 

Either two or more molecular levels of a molecule are excited coherently by a spectrally broad, short laser pulse (level-crossing and quantum-beat spectroscopy) or a whole ensemble of many atoms or molecules is coherently excited simultaneously into identical levels (photon-echo spectroscopy). This coherent excitation alters the spatial distribution or the time dependence of the total, emitted, or absorbed radiation amplitude, when compared with incoherent excitation. Whereas methods of incoherent spectroscopy measure only the total intensity, which is proportional to the population density and therefore to the square ir of the wave function iff, the coherent techniques, on the other hand, yield additional information on the amplitudes and phases of ir. 

Quantum beats can be observed not only in emission but also in the transmitted intensity of a laser beam passing through a coherently prepared absorbing sample. This has first been demonstrated by Lange et al. [872, 873]. The method is based on time-resolved polarization spectroscopy (Sect. 2.4) and uses the pump-and-probe technique discussed in Sect. 6.4. A polarized pump pulse orientates atoms in a cell placed between two crossed polarizers (Fig. 7.12) and generates a coherent superposition of levels involved in the pump transition. This results in an oscillatory time dependence of the transition dipole moment with an oscillation period AF = 1/Av... 

These coherence effects allow Doppler-free spectroscopy of ground states and excited states in atoms or molecules. While level crossing spectroscopy can be performed with both cw and pulsed lasers, the quantum beat technique... 

A short pump pulse excites coherently different upper levels. The time evolution of the superposition of states following the coherent excitation causes time-dependent changes of the complex susceptibility x of the sample. Similar to the quantum beats in the fluorescence intensity the susceptibility x(t) is found to contain oscillating nonisotropic contributions which can be readily detected by placing the sample between crossed polarizers and transmitting a probe pulse with variable delay (see also Sect.10.3 on polarization spectroscopy). Even a cw broadband dye laser can be used for probing if the probe intensity transmitted by the polarizer is monitored with sufficient time resolution. 

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