The quantum numbers of monopoles in in the presence of massless fermions have been analyzed using a uniform flux background in coupled to fermions. An analogous study in is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on with a total flux of in the continuum. The degenerate ground states are classified based on their transformation properties under rotations of that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society2025
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SU(2) geometric phase induced by a periodically driven Raman process in an ultracold dilute Bose gas
We propose a practical protocol to generate and observe a non-Abelian geometric phase using a periodically driven Raman process in the hyperfine ground-state manifold of atoms in a dilute ultracold gas. Our analysis is based upon recent developments and application of Floquet theory to periodically driven quantum systems. The simulation results show the non-Abelian gauge transformation and the noncommuting property of the SU(2) transformation operators. Based on these results, we propose a possible experimental implementation with an ultracold dilute Bose gas.
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- Award ID(s):
- 1708008
- PAR ID:
- 10475338
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review A
- Volume:
- 101
- Issue:
- 1
- ISSN:
- 2469-9926
- Subject(s) / Keyword(s):
- Bose-Einstein Condensation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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