Topology of quadrupolar Berry phase of a Qutrit
- URL: http://arxiv.org/abs/2301.09476v1
- Date: Mon, 23 Jan 2023 15:20:53 GMT
- Title: Topology of quadrupolar Berry phase of a Qutrit
- Authors: Rajeev Singh, Navneet Kumar Karn, Rahul Bhowmick, and Sourin Das
- Abstract summary: We show that the Berry phase of quadrupolar state is induced by the Majorana stars collectively tracing out a closed path.
We show that time evolution generated by such Hamiltonian restricts the states to the quadrupolar subspace itself.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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