Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models

• URL: http://arxiv.org/abs/2104.10581v1
• Date: Wed, 21 Apr 2021 15:19:43 GMT
• Title: Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models
• Authors: Manuel Calixto, Alberto Mayorgas and Julio Guerrero
• Abstract summary: Collective spin operators for symmetric multi-quDit systems generate a U$(D)$ symmetry. We explore generalizations to arbitrary $D$ of SU(2)-spin coherent states and their adaptation to parity. We evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Collective spin operators for symmetric multi-quDit (namely, identical $D$-level atom) systems generate a U$(D)$ symmetry. We explore generalizations to arbitrary $D$ of SU(2)-spin coherent states and their adaptation to parity (multicomponent Schr\"odinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric $N$-quDit states, expressed in the last two cases in terms of collective U$(D)$-spin operator expectation values. Then we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin-Meshkov-Glick models of $3$-level identical atoms. We also propose an extension of the concept of SU(2) spin squeezing to SU$(D)$ and relate it to pairwise $D$-level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting $D$-level atom models.

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