Bargmann Invariants and Geometric Phases - a Generalised Connection

Abstract

We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces. Examples of such curves are developed. Our generalisation is shown to be essential to properly understand geometric phase results in the cases of coherent states and of Gaussian states. Differential geometric aspects of null phase curves are also briefly explored.

Accepted for publication in Physical Review A

Cited by in corpus (33)

• Off-Diagonal Geometric Phases
• Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
• Geometric phases of mesoscopic spin in Bose-Einstein condensates
• Geometric phase for mixed states: a differential geometric approach
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach
• Hamilton's turns as visual tool-kit for designing of single-qubit unitary gates
• Creation and manipulation of anyons in a layered superconductor-2DEG system
• <A^2> Condensate, Bianchi Identities and Chromomagnetic Fields Degeneracy in SU(2) YM Theory
• Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions
• Quaternions in mathematical physics (1): Alphabetical bibliography
• Schrödinger-Koopman quasienergy states of quantum systems driven by a classical flow
• Floquet topological phase transitions in a kicked Haldane-Chern insulator
• Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits
• Kirkwood-Dirac classical pure states
• Null Phase Curves and Manifolds in Geometric Phase Theory
• Manifestation of a nonclassical Berry phase of an electromagnetic field in atomic Ramsey interference
• Entropy as a function of Geometric Phase
• Optimal arrangements of classical and quantum states with limited purity
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Classical Light Beams and Geometric Phases
• Experimentally testable geometric phase of sequences of Everett's relative quantum states
• Quantum Particle-Trajectories and Geometric Phase
• Geometric Phases in Kaon Decays and Baryogenesis
• Weak Measurement of Berry's Phase
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• Holonomic Quantum Computation
• Geometric phases in neutrino mixing
• Bargmann Invariants and Correlated Geometric CP-Violating Structures in Neutral Meson Systems
• Bargmann Invariants, Geometric Phases and Recursive Parametrization with Majorana Fermions
• Generalised Geometric Phase
• Estimation of multivariate traces of states given partial classical information
• Sum rule for non-adiabatic geometric phases