Yuli begins his talk explaining topological meaning of phase-slip effects. There are different interpretations of phase slips. Particularly, phase slip is manifestation of non-equilibrium dynamics in superconductors.
In I-V measurements of phase-slips, resistance changes a few orders of magnitude. For a few decades, people measured I-V-characteristics, and only recently new proposals for different characterization of phase slip appeared. For example, A. Bezryadin suggested to measure phase slips in resonators, Guichard and others have measured high frequency properties of a chain of Josephson junctions. Mooij, Harmans proposed phase-slip qubits.
Behavior of such a qubit is identical to the Cooper pair box, if charge is formally replaced by flux. There is an exact duality between charge-flux in charge systems and flux-charge in phase-slip systems. The phase-slip energy is replaced by Josephson energy (Es -> Ej) and magnetic energy is replaced by charging energy (EL -> Ec) also impedance is replaced by admittance (Z -> Y). Using the duality one can understand that so-called inverse Shapiro steps must be observed.
Yuli states that up to now no reliable theory has been developed and phenomenological behavior of Es ~ exp (-a/(GqR)) (where Gs is quantum conductance, R is the wire resistance and a is unknown parameter) is often used.
Another problem is that the real wires in real experiments are inhomogeneous, e. g. width fluctuates, therefore weak links (the places where resistance is mainly acquired) are very probable. The conditions for mainly uniform probability along the phase slip is Rlink << Rwire. Lev Ioffe raised a question about definition of the boundary condition for the Rlink. According to Yuli, the weak links are mainly determine the prosperities of the nano-wires.
For the weak links, one need to solve a scattering problem, in which the phase-slip energy is expressed as Es = 2 Delta sqrt(Sum Tp)Prod (sqrt(1-Tp)). The “best” weak link is a tunnel junction. On the other hand, the homogeneous wire can be considered as a sequence of weak links each of coherence length.
Yuli proposed a series of devices based on quantum phase slips. An interesting system is a Cooper pair box (a superconducting island) connected to a reservoir via the nano-wire. The charge in such a system is localized, in spite of absence of the tunnel junctions. Another interesting experiment can be done on making a Cooper pair single-electron transistor: an island connected to two reservoirs via two nano-wires. Also phase-slip oscillators should exhibit similar to Duffing oscillator behavior but with “multiple stability”.
M. Figelman and L. Ioffe raised a question about accounting electron-electron scattering in the Yuli’s theory. Yuli’s opinion is that the interaction is not relevant unless the size of the weak link is smaller than coherence length. This bolgger asked to clarify the situation with probable weak links in his experiments. According to Yuli, it is possible, however requires close resistances of weak links for two similar devices.
Next a short talk was presented again by Hans Mooij. He mainly discussed Bezryadin’s data on measuring nano-wires. The data show points of large number different phase-slip transitions. The main statement of Hans is that the condition for quantum phase slip can not be determined by only quantum resistance, but characterized by Zaikin’s formula, which includes exponent of Rn/Rq with an additional prefactor. By playing with the parameters of the formula he demonstrates perfect explanation and the boundary for the phase slip conditions.
Blogged by Oleg Astafiev
On the issue of the influence of electron-electron interaction \lambda in the contact region upon the theoretical result presented by Yuli: the present blogger believes that in the product over channels of \sqrt(1-Ti}, the contributions of most conductive channels will be increased according to the parameter (l/\xi)\lambda where l is the length of weak link
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