Non-Abelian generalization of off-diagonal geometric phases

Abstract

If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.

Additional material, journal reference added

References in corpus (5)

• Noncyclic geometric changes of quantum states
• Off-diagonal generalization of the mixed state geometric phase
• Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states
• Manifestations of quantum holonomy in interferometry
• Off-diagonal quantum holonomy along density operators

Cited by in corpus (6)

• A general treatment of geometric phases and dynamical invariants
• Nodal free geometric phases: Concept and application to geometric quantum computation
• Geometric phase for nonlinear coherent and squeezed state
• Non-Abelian off-diagonal geometric phases in nano-engineered four-qubit systems
• Berry phases for interacting spins in composite environments
• Geometric phases for two-mode squeezed state