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Uncertainties of coherent states for a generalized supersymmetric annihilation operator
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10.1063/1.4772607
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1 Physics Department, Yeshiva University, 500 W 185th Street, New York, New York 10033, USA
J. Math. Phys. 54, 012101 (2013)
/content/aip/journal/jmp/54/1/10.1063/1.4772607
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/1/10.1063/1.4772607

## Figures

FIG. 1.

Uncertainty of the supercoherent state |Z θ⟩, describing the superposition of two basis states |Z θ⟩ = 2−1/2(|Z +⟩ + e iπ/4|Z ⟩). The uncertainty separates into two regions: (1) In 0 < θ < π/2, the uncertainty is bounded. The maximum is 0.83, at approximately z = 0.5e iπ/4, θ = π/4. (2) In π/2 < θ < π, the uncertainty diverges with z. The rate of divergence depends upon the phase of z: |z|2 for , while |z|4 for .

FIG. 2.

Graph of the parameter space of the supercoherent states. The blue-yellow surface describes the degenerate case, while the green surface corresponds to the singular matrix. The red-black circle describes the family , for which the red portions have bounded uncertainty for all eigenstates while the black portions have unbounded uncertainty for most eigenstates. All parameters k i are assumed to be real and divided by k 1, because the SUSY annihilation matrix effectively occupies a three-dimensional space.

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/content/aip/journal/jmp/54/1/10.1063/1.4772607
2013-01-04
2014-04-17

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