Correlated spin states in the phase space representation

Yoshinori Takahashi, Fumiaki Shibata

J. Kutzner

H. D. Liu, Libin Fu

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.

Caio Fernando e Silva, Alex E. Bernardini

Following the information-based approach to Dirac spinors under a constant magnetic field, the phase-space representation of symmetric and antisymmetric localized Dirac cat states is obtained. The intrinsic entanglement profile implied by the Dirac Hamiltonian is then investigated so as to shed a light on quantum states as carriers of qubits correlated by phase-space variables. Corresponding to the superposition of Gaussian states, cat states exhibit nontrivial elementary information dynamics which include the interplay between intrinsic entanglement and quantum superposition as reported by the corresponding Dirac archetypes. Despite the involved time evolution as nonstationary states, the Wigner function constrains the elementary information quantifiers according to a robust framework which can be consistently used for quantifying the time-dependent $\text{SU}(2)\ensuremath{\bigotimes}\text{SU}(2)$ (spin projection and intrinsic parity) correlation profile of phase-space localized Dirac spinor states. Our results show that the Dirac Wigner functions for cat states---described in terms of generalized Laguerre polynomials---exhibit an almost maximized timely persistent mutual information profile which is engendered by either classical- or quantumlike spin-parity correlations, depending on the magnetic field intensity.

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

Lorenzo M. Narducci, C. M. Bowden, V. Bluemel +2 more

We consider the evaluation of multitime-correlation functions for quantum statistical systems characterized by dynamical variables of the angular-momentum type (such as, for example, paramagnetic or nuclear spins or collections of two-level atoms), and show how the atomic coherent-state representation of Arecchi et al. can be used to express the multitime averages in terms of phase-space integrals. Our calculation suggests a convenient classical-quantum correspondence rule for angular-momentum degrees of freedom.