Permutational symmetry for identical multi-level systems: a second quantized approach

Abstract

We develop a framework that provides a straightforward approach to fully exploit the permutational symmetry of identical multi-level systems. By taking into account the permutational symmetry, we outline a simple scheme that allows to map the dynamics of $N$ identical $d$-level systems to the dynamics of $d$ bosonic modes with $N$ particles, achieving an exponential reduction on the dimensionality of the problem in a simple and straightforward way. In particular, we consider the Lindblad dynamics of several identical multi-level systems interacting with a common subsystem under the action of collective dissipation terms.

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Cited by in corpus (1)

• Generalization of the Tavis-Cummings model for multi-level anharmonic systems: insights on the second excitation manifold