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Related Experiment Video

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Published on: September 5, 2019

Scheme for Building a 't Hooft-Polyakov Monopole.

Julian Sonner¹, David Tong

¹Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 USA.

Physical Review Letters

|June 13, 2009

Summary

This study explores a quantum mechanical model of a spinning particle on a sphere with a magnetic field. It reveals how ground states mix via a non-Abelian Berry phase, linked to SU(2) monopoles.

Area of Science:

Quantum mechanics
Particle physics
Condensed matter physics

Background:

A quantum mechanical model of a spinning particle on a sphere with a magnetic field is investigated.
The system exhibits two distinct ground states.

Purpose of the Study:

To analyze the mixing of ground states through a non-Abelian Berry phase as the magnetic field varies.
To establish the connection between this Berry phase and SU(2) 't Hooft-Polyakov monopoles.
To investigate the conditions under which the monopole becomes a Bogomol'nyi-Prasad-Sommerfield monopole.

Main Methods:

Utilizing quantum mechanical modeling.
Analyzing the behavior of ground states under varying magnetic fields.
Applying concepts of non-Abelian Berry phase and monopole theory.

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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

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Published on: September 26, 2014

Main Results:

The mixing of ground states is shown to be governed by a non-Abelian Berry phase.
This Berry phase is identified as the path-ordered exponential of a smooth SU(2) 't Hooft-Polyakov monopole.
It is demonstrated that adjusting the potential on the sphere can transform the monopole into a Bogomol'nyi-Prasad-Sommerfield monopole.

Conclusions:

The study provides a theoretical framework linking quantum ground state mixing to topological properties of monopoles.
The findings offer insights into the behavior of quantum systems in the presence of magnetic fields and potentials.
The research highlights the applicability of monopole theory in understanding complex quantum phenomena.