This title appears in the Scientific Report :
2020
Please use the identifier:
http://dx.doi.org/10.1088/1751-8121/ab93ff in citations.
Please use the identifier: http://hdl.handle.net/2128/26306 in citations.
Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
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 comb...
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Personal Name(s): | Leiner, David |
---|---|
Zeier, Robert (Corresponding author) / Glaser, Steffen J. | |
Contributing Institute: |
Quantum Control; PGI-8 |
Published in: | Journal of physics / A Mathematical and theoretical, 53 (2020) 49, S. 495301 |
Imprint: |
Bristol
IOP Publ.
2020
|
DOI: |
10.1088/1751-8121/ab93ff |
Document Type: |
Journal Article |
Research Program: |
Programmable Atomic Large-Scale Quantum Simulation Controlling Spin-Based Phenomena Controlling Spin-Based Phenomena |
Link: |
OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/26306 in citations.
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. |