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A reservoir for inverse power law decoherence of a qubit
The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a
continuous distribution of bosons, characterized by a special form of the
spectral density, is evaluated analytically. The special reservoir is designed
to induce anomalous decoherence, resulting in an inverse power law relaxation,
of power 3/2, over an evaluated long time scale. If compared to the
exponential-like relaxation obtained from the original Jaynes-Cummings model
for Lorentzian-type spectral density functions, decoherence is strongly
suppressed. The special reservoir exhibits an upper band edge frequency
coinciding with the qubit transition frequency. Known theoretical models of
photonic band gap media suitable for the realization of the designed reservoir
are proposed.Comment: 5 pages, 2 figure
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