The following subjects are being currently studied:
We study the charge transport in one-dimensional Josephson arrays. In particular we investigate the properties of charge solitons in these systems. At low temperatures and in the regime of Coulomb energy dominating over the Josephson energy the arrays show the insulating (Coulomb blockade) behavior. At high transport voltages, once the Coulomb blockade is lifted, hysteretic I-V-curves are observed. We study the microscopic mechanisms of the Cooper pair charge transport. In the analysis we encounter amongst other things the sine-Gordon equation, Landau-Zener transitions, disorder physics, and decoherence models.
A Cooper pair pump is a superconducting device, consisting of one or more islands, which are coupled to two leads via Josephson junctions or SQUIDs. Cooper pairs can be pumped through the devise by cyclic modulation of the Josephson couplings and/or the electrostatic potential of the islands. We investigate the influence of noise on the Cooper pair pumping. While zero temperature noise has no influence on adiabatic ground state pumping (it even stabilizes adiabaticity), finite temperature noise can excite the system and therefore can change the transferred charge per pumping cycle. We have developed [1] a master equation technique in the Floquet basis, which allowed us analyzing pumping in various regimes.
[1] I. Kamleitner, A. Shnirman, Time-dependent Markovian master equation for adiabatic systems and its application to Cooper-pair pumping, Phys. Rev. B 84, 235140 (2011).