Coherent states general properties

It is instructive to compute the time correlation function in the simple case that the ground and excited state potentials are harmonic but differ in their equilibrium position and frequency. This is particularly simple if the initial vibrational state is the ground state (or, in general, a coherent state (52)) so that its wave function is a Gaussian. We shall also use the Condon approximation where the transition dipole is taken to be a constant, independent of the nuclear separation, but explicit analytical results are possible even without this approximation. A quick derivation which uses the properties of coherent states (52) is as follows. The initial state on the upper approximation is, in the Condon approximation, a coherent state, i /,(0)) = a). The value of the parameter a is determined by the initial conditions which, if we start from a stationary state, are that there is no mean momentum and that the mean displacement (x) is the difference in the equilibrium position of the two potentials. In general, using m and o> to denote the mass and the vibrational frequency... 

An essential property of such a coherently coupled three-level system is the existence of a dark state D) as an eigenstate of the system. This state generally occurs if both laser fields have the same resonance detuning with respect to the corresponding transition, that is, if the two-photon demning is zero. The state is dark in the sense that it is decoupled from the excited state e) and thus not influenced by its radiative decay. The dark state can be understood as a coherent superposition of state a) and state b),... 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

In the adiabatic limit, t is considered to be a parameter, and is called an adiabatic state. One of the interesting properties of this limit is that a population can be inverted by evolving the system adiabatically. This process is called adiabatic passage. Population transfer induced by a laser is generally called coherent population transfer. For a two-level system, the complete population inversion is produced by a n -pulse or by adiabatic rapid passage. 

Control of the type discussed above, in which quantum interference effects are used to constructively or destructively alter product properties, is called coherent control (CC). Photodissociation of a superposition state, the scenario described above, will be seen to be just one particular implementation of a general principle of coherent control Coherently driving a state with phase coherence through multiple, coherent,... 

The present book is an attempt to rectify this omission. Ideally, as we have just argued, we should present a coherent account of the whole field of chemistry in which the results of structural studies appeared in their rightful place among those of the many other means of determining chemical constitution. This, however, would be a formidable task, and, indeed, an unnecessary one when there already exist so many works on chemistry, valency theory and other aspects of the solid state. We shall therefore presuppose the reader to have some knowledge of general chemical principles, and we shall confine ourselves to a discussion of those properties of solids, directly related to crystal structure, which are not normally considered in detail in chemical works. 

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