Journal Article

FZJ-2020-02018

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems

Leiner, D. ; Zeier, R. (Corresponding author)FZJ* ; Glaser, S. J.

2020
IOP Publ. Bristol

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Please use a persistent id in citations: http://hdl.handle.net/2128/26306  doi:10.1088/1751-8121/ab93ff

Abstract: We study the representation and visualization of finite-dimensional, coupled quantum systems. To establish a generalized Wigner representation, multi-spin operators are decomposed into a symmetry-adapted tensor basis and 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. The approach based on explicit projection operator is currently only applicable for up to four spins 1/2. The resulting generalized Wigner representation 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) not necessarily equal to 1/2 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.

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Contributing Institute(s):

1. Quantum Control (PGI-8)

Research Program(s):

1. 142 - Controlling Spin-Based Phenomena (POF3-142) (POF3-142)
2. 522 - Controlling Spin-Based Phenomena (POF3-522) (POF3-522)
3. PASQuanS - Programmable Atomic Large-Scale Quantum Simulation (817482) (817482)

Appears in the scientific report 2020

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; National-Konsortium ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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