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
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Quantum phase transitionsMany-body systemsSymmetric quDitsCoherent statesParityPairwise entanglementSpin squeezing
Calixto, M., Mayorgas, A. & Guerrero, J. 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. Quantum Inf Process 20, 304 (2021). [https://doi.org/10.1007/s11128-021-03218-6]
SponsorshipSpanish Government PGC2018-097831-B-I00; Junta de Andalucia SOMM17/6105/UGR UHU-1262561 FQM-381; Spanish Government European Commission FIS2017-84440-C2-2-P; Spanish MIU FPU19/06376
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 (multi-component Schrödinger 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.