Quantized Fields Pulses

S - The continuum component (e ]E, n-) is therefore driven by the bound state times the radiative coupling term. Driven equations of the type written here are implicitly 5%sed in all practical computational schemes developed for weak-field molecular hotodissociation problems [14, 26], 

Over the years a number of computational methods have been developed to solved the problem of the interaction of a pulse of radiation with molecular and atomic-systems [398 410], To keep the treatment as simple as possible, we only consider 11 solving the problem in the adiabatic approximation, introduced in Chapter 9, jfikjg classical fields., v fyS 

Replacing the electric field amplitude by a time-dependent pulse envelope 5, we can write the time-dependent Schrodinger equation, in the approximations fh led to Eqs. (12.44) and (12.45), as two coupled equations of the form tf  

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It predicts the adiabatic plateaus of Fig. 17, which can be interpreted as a topological quantization of the number of exchanged photons. The dips are due to nonadiabatic Landau-Zener transitions when the pulse overlap is in the neighborhood of the intersections. With a configuration of counterpropagating laser fields, perpendicular to an atomic beam, this translates into the possibility of deflection of the beam by the quantized transfer of a momentum kh(ffli +... 

Following an initial 90° excitation pulse the transverse magnetization is locked in the xy plane by an rf field which is shifted in phase by 90° with respect to the first pulse (Fig. 7.2.4), In a frame rotating with the rf carrier frequency about the laboratory z-axis, the quantization axis of the locked magnetization is in the direction of the field. Any on-resonance magnetization component off-axis from the lock field precesses about the lock field with frequency coi = —yBi, and the magnetization reduced towards zero in the rotating frame. 

A related RF technique to NMR is nuclear quad-rupole resonance (NQR). In NQR, transitions between nuclear quadrupole levels of nuclei in a solid material are induced by the applied radiation. The electric field gradients in the solid orient the quad-rupolar nuclei I>1/2) and give rise to quantized energy levels that yield transitions in the MHz range. FT-NQR spectroscopy measures these splittings and the relaxation times by free induction decay or various pulse echo experiments. FT-NQR spectroscopy provides information about the local environment around the quadrupolar nucleus in a crystal. 

The material system is promoted by the pump pulse to the excited electronic state from which it can (spontaneously) emit photons. Since the SE is a quantum process, it is described in the formalism of the quantization of the radiation field [1, 20]. The pump process, on the other hand, can be considered semiclassically. We thus start with the master equation (9.10) with N= 1,... 

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