Permutational symmetry for identical multilevel systems: A second-quantized approach

Abstract

We develop a framework that provides a straightforward approach to fully exploit the permutational symmetry of identical multilevel systems. By taking into account the permutational symmetry, we outline a simple scheme that allows us 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 multilevel systems interacting with a common subsystem under the action of collective dissipation terms.