Representation of Berry phase by the trajectories of Majorana stars

Abstract

The Majorana's stellar representation, which represents the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, provides an intuitive way to study a physical system with high dimensional projective Hilbert space. In this Letter, we study the Berry phase by these stars and their loops on the Bloch sphere. It is shown that the Berry phase of a general spin state can be expressed by an elegant formula with the solid angles of Majorana star loops. Furthermore, these results can be naturally used to a general state with arbitrary dimensions. To demonstrate our theory, we study a two mode interacting boson system. Finally, the relation between stars' correlations and quantum entanglement is discussed.

arXiv comment12 pages, 2 figures

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Cited by in corpus (23)

• Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings
• Enhanced magnetic sensitivity with non-gaussian quantum fluctuations
• Modal Majorana sphere and hidden symmetries of structured-Gaussian beams
• Anticoherence of spin states with point group symmetries
• Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars
• Anticoherence measures for pure spin states
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Spin-1 Topological Monopoles in Parameter Space of Ultracold Atoms
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
• Link between \emph{Zitterbewegung} and topological phase transition
• Entangling power of symmetric two-qubit quantum gates
• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
• Observation of nonlinear variations in three-vertex geometric phase in two-photon polarization qutrit
• Quantum spiral spin-tensor magnetism
• Coherent-State Approach for Majorana representation
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Robust quantum metrology with random Majorana constellations
• Robust Weyl points in a 1D superlattice with transverse spin-orbit coupling
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars