Spontaneous transitions between degenerate

The expression for the spontaneous transition probability, equation (4.18), refers to a transition between non-degenerate states k and i. Thus k and i are labels which should actually specify the magnetic quantum numbers, m, and m., of the levels involved. Then the total decay rate of a non-degenerate sub-level kmj to a degenerate level i would be given by the sum of the transition probabilities taken over all the possible decay channels to the lower 

However, if now tire upper level is also degenerate we expect intuitively that the different degenerate states knij will all decay at the same rate. If this were not so then there would be a preferred direction in space and the polarization of the emitted radiation would be observed to change with time. The following result must therefore hold (Problem 4.2)  

Thus equation (4.22) also gives the radiative decay rate between degenerate levels k and i. The form of this result can be made more symmetrical by introducing an additional summation over mj and dividing by the statistical weight 

In many-electron atoms, the operator in this equation should 

Let us consider an assembly of atoms in which Nj (O) atoms per unit volume are excited into the level k at time 

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The interest in quantum interference stems from the early 1970s when Agarwal [4] showed that the ordinary spontaneous decay of an excited degenerate V-type three-level atom can be modified due to interference between the two atomic transitions. The analysis of quantum interference has since been extended to other configurations of three- and multilevel atoms and many interesting effects have been predicted, which can be used to control optical properties of quantum systems, such as high-contrast resonances [5,6], electro-magnetically induced transparency [7], amplification without population inversion [8], and enhancement of the index of refraction without absorption [9]. 

For the selective enhancement of the wanted reaction channel by laser excitation of the reactants, the time span At between photon absorption and completion of the reaction is of fundamental importance. The excitation energy n hco (n = 1,2,...) pumped by photon absorption into a selected excited molecular level may be redistributed into other levels by unwanted relaxation processes before the system ends in the wanted reaction channel. It can, for instance, be radiated by spontaneous emission, or it may be redistributed by intramolecular radiationless transitions due to vibrational or spin-orbit couplings onto many other nearly degenerate molecular levels. However, these levels may not lead to the wanted reaction channel. At higher pressures collision-induced intra- or intermolecular energy transfer may also play an important role in enhancing or suppressing a specific reaction channel. 

The tetracarbonylcobalt radical has a high reactivity. It dimerizes spontaneously (146), reacts with O2 to form 02Co(CO)4 (236,237) and abstracts hydrogen atom from transition metal hydrides (147). According to NMR line-shape analysis of the degenerate hydrogen-atom transfer reaction between HCo(CO)4 and Co(CO)4 proceeds with activation parameters of AH = (23.5 2.5) kJ/mol and AS = (-68.3 4.3) J/(mol K) (147). 

Quantum-beat lasers are a particular form of correlated spontaneous emission lasers (CEL s) [43-49]. Quantum-beat is formed by creating coherence between near degenerate atomic states, either excited states or ground states. In particular, a beam of three-level atoms in Vee configuration emit photons into two modes. The atomic upper levels are initially prepared in a coherent superposition or are coupled by a coherent field [13-17]. The fluetuations of the relative phase and the relative amplitude drop to the vacuum levels. In addition to this, as a different form, correlated spontaneous emission can be formed by creating eoherenee between a pair of states between which lasing transitions occm. One such example is a two-photon CEL [13-17] with a beam of three-level atoms in cascade configuration. The top and bottom states are initially prepared in a coherent superposition state. It was predicted that the phase noise is reduced by 50% below the vacuum noise level. 

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