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In a mesoscopic Josephson
junction, the quantum mechanical nature of charge has to be taken into
account. According to the quantum prescription, the Coulomb energy $\frac{Q^{2}}{2C}$ leads to a term
in the Hamiltonian. Therefore, the
quantum behavior of a superconducting junction is described by the Schrödinger
equation
where the Josephson coupling energy plays a role of a periodic potential.
Presently, we are working mostly on noise spectroscopy applications to
detect higher order moments of noise and counting statistics using Coulomb
blockaded junctions in the regime E_J/E_C << 1.
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 Energy
levels $\lambda =\frac{E}{E_{c}}$ of the Mathieu equation as a function of
E_J/E_C. Labels a_n and b_n denote the sine- and cosine-type solutions. The
functions corresponding to an even value of $n$ are $\pi $-periodic and
those with odd index are 2$\pi $-periodic. The energy bands (shaded regions)
of the Schrödinger equation appear between a_{0}- a_{1}, b_{1}-b_{2},
a_{2}-a_{3}, etc. |
