At the narrowest part of a superconducting nano wire order parameter fluctuates (Quantum or Thermal) to zero and phase can slip by 2pi.
What is the physical significance of this? Mathematically the washboard potential "U=EJ(1-cos(fi)-n(fi))" gives minimum at 2n(pi) . But what is the physical phenomenon governing this slippage?
Phase slip phenomenon can be excited with thermal energy when you are close to the transition temperature known as thermal phase slips (TPS) but at lower temperature only quantum tunnelling can explain it since thermal energy is rather lower than the barrier height. So at lower temperature it QPS. There this phenomenon can be incoherent or coherent. Using dc transport properties, incoherent QPS you can be observed by having resistive superconductivity. However, you can observed complete blockade of current below some characteristic voltage termed as critical voltage. In simple words this is the other part of the picture of Josephson junctions because of charge-phase relation. In JJs we can control the phase but in coherent-QPS junctions we control the charge. Thus you can observe quantum current steps in coherent-QPS nanowire junction by micro-wave irradiation just like Shapiro steps in case of JJs (voltage steps). The washboard equation you are mention is for JJs; you have to change phase into charge and Ej to Es(phase slip energy). I recommend you following article https://www.nature.com/articles/nphys234 [I am sure you have already looked at it.]
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