geometry; mathematical methods; quantum information; Statistical and Nonlinear Physics; Statistics and Probability; Modeling and Simulation; Mathematical Physics; Physics and Astronomy (all); Quantum Physics
Abstract :
[en] Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many respects, the 'most classical' available. For any spin s, the spin coherent states form a 2-sphere in the projective Hilbert space of the system. We address several questions regarding that sphere, in particular its possible intersections with complex lines. We also find that, like Dali's iconic clocks, it extends in all possible directions in . Given a generic spin state, we introduce an adapted spin coherent basis, and its dual, and comment on their possible uses. We give a simple expression for the Majorana constellation of the linear combination of two coherent states, and use Mason's theorem to give a lower bound on the number of distinct stars of a linear combination of two arbitrary spin-s states. Finally, we plot the image of the spin coherent sphere, assuming light in propagates along Fubini-Study geodesics. We argue that, apart from their intrinsic geometric interest, such questions translate into statements experimentalists might find useful.
Disciplines :
Physics
Author, co-author :
Chryssomalakos, Chryssomalis ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico
Guzmán-González, E. ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico
Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX, Mexico
Language :
English
Title :
Geometry of spin coherent states
Publication date :
21 March 2018
Journal title :
Journal of Physics. A, Mathematical and Theoretical
The authors wish to thank J Martin and L L Sánchez-Soto for bringing to their attention several relevant references ([6–8, 37, 45] and [12, 13, 15] respectively). They are particulalrly indebted to Frédéric Holweck for communicating to them the references [1, 11, 19, 26, 32], complete with an explanation of their relevance. They also acknowledge partial financial support from the UNAM-DGAPA-PAPIIT project IG 100316.
Commentary :
Added an explanatory comment on eq. (68) and several new references. 16 pages, 5 figures
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