We propose a spin model which exhibits the main properties of the Kerr medium. The description of the model uses a recently generalized quasiprobability distribution (Wigner function) for the SU(2) group. This function is naturally defined on the sphere, which plays the role of phase space for the spin system. Our model leads to macroscopic quantum superposition states on the sphere.

Physical Review ASep 1, 199963 citations

Springer eBooks

Wigner function dynamics on the sphere

A. B. Klimov, S. M. Chumakov

Published Jan 1, 2003• 1 citation

Publisher

DOI: 10.1007/978-1-4419-8907-9_154

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The SU(2) Wigner function represents a quantum state of a spin-

J

as a real-valued function on the surface of a 2-sphere. For an ensemble of

N

spin-1/2 particles, this representation is useful when the dynamics is restricted to a single SU(2) irrep, e.g., the symmetric subspace with

J=N/2

. Physically relevant noise sources tend to be local, such as spontaneous emission, depolarizing, and incoherent optical pumping, all of which transfer the state outside of the initial irrep, and as such the SU(2) Wigner function is no longer a useful representation. In this work, we address this issue by encoding a noisy spin ensemble in an SU(3) irrep, and evaluating the SU(3) Wigner function for that irrep. We find that physical constraints enforced by the noise eliminate all but three real parameters from the input to the Wigner function, which can then be interpreted as a polar, azimuthal, and radial component. This interpretation leads us to refer to the resulting Wigner function as the solid spin Wigner function, visualized on a solid ball rather than a hollow sphere.