C-Number Representation for Multilevel Systems and the Quantum-Classical Correspondence
We use the r-mode direct product coherent states as generating functions for r-level coherent states which are ideal for the description of collective behavior of an ensemble of N identical r-level atoms or molecules, where the r-levels are not necessarily evenly spaced. It is noted that the Lie algebra for an r-level system can be given a realization in terms of bilinear combinations of boson creation and annihilation operators. This provides a homomorphism from the algebra describing a multimode system to the algebra describing a multilevel system. This in turn provides a homomorphism from the multimode coherent states and their diagonal projectors onto the multilevel coherent states and their diagonal projectors. The action of a creation or annihilation operator on a multimode projector can be replaced by the action of a first order differential operator.
KeywordsCoherent State Master Equation Operator Algebra Density Operator Annihilation Operator
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