Topology of quadrupolar Berry phase of a Qutrit

We examine Berry phase pertaining to purely quadrupolar state (\(\langle \psi | \vec{S} | \psi \rangle = 0\)) of a spin-\(1\) system. Using the Majorana stellar representation of these states, we provide a visualization for the topological (zero or \(\pi\)) nature of such quadrupolar Berry phase. We...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Singh, Rajeev, Karn, Navneet Kumar, Bhowmick, Rahul, Das, Sourin
Format: Article
Language:English
Subjects:
Great circles
Subspaces
Topology
Online Access:Get full text
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Summary:We examine Berry phase pertaining to purely quadrupolar state (\(\langle \psi | \vec{S} | \psi \rangle = 0\)) of a spin-\(1\) system. Using the Majorana stellar representation of these states, we provide a visualization for the topological (zero or \(\pi\)) nature of such quadrupolar Berry phase. We demonstrates that the \(\pi\) Berry phase of quadrupolar state is induced by the Majorana stars collectively tracing out a closed path (a great circle) by exchanging their respective positions on the Bloch sphere. We also analyse the problem from the perspective of dynamics where a state from the quadrupolar subspace is subjected to a static magnetic field. We show that time evolution generated by such Hamiltonian restricts the states to the quadrupolar subspace itself thereby producing a geometric phase (of the Aharonov-Anandan type) quantized to zero or \(\pi\). A global unitary transformation which maps the quadrupolar subspace to the subspace of purely real states proves a natural way of understanding the topological character of this subspace and its connection to the anti-unitary symmetries.
ISSN:2331-8422