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 (8)

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• Performance boost of a collective qutrit refrigerator
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• Second quantization of open quantum systems in Liouville space
• Singly-excited resonant open quantum system Tavis-Cummings model with quantum circuit mapping
• Practical guide to the statistical mechanics of molecular polaritons
• Engineering tunable decoherence-free subspaces with collective atom-cavity interactions