Freiburg 2019 – wissenschaftliches Programm
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FM: Fall Meeting
FM 20: Entanglement: Many-Body States II
FM 20.2: Talk
Montag, 23. September 2019, 16:45–17:00, 2004
Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems — David Leiner1, •Robert Zeier1,2,3, and Steffen J. Glaser1,4 — 1Technische Universität München, Department Chemie, Lichtenbergstrasse 4, 85747 Garching, Germany — 2Adlzreiterstrasse 23, 80337 München, Germany — 3Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8), 54245 Jülich, Germany — 4Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
We study the representation and visualization of finite-dimensional, coupled quantum systems. In order to establish a generalized Wigner representation, multi-spin operators are decomposed into a symmetry-adapted tensor basis and they are mapped to multiple spherical plots that are each assembled from linear combinations of spherical harmonics. We explicitly determine the corresponding symmetry-adapted tensor basis for up to six coupled spins 1/2 (qubits) using a first step that relies on a Clebsch-Gordan decomposition and a second step which is implemented with two different approaches based on explicit projection operators and coefficients of fractional parentage. Our approach is illustrated with various examples for the cases of four to six coupled spins 1/2. We also treat the case of two coupled spins with arbitrary spin numbers (qudits) and highlight a quantum system of a spin 1/2 coupled to a spin 1 (qutrit). Our work offers a much more detailed understanding of the symmetries appearing in coupled quantum systems. http://arxiv.org/abs/1809.09006