Charge solitons for quantum metrology

Charge solitons are collective excitations in an array of small Josephson junctions. Every soliton carries exactly the charge 2e of a Cooper pair and its polarization charge is distributed over several superconducting islands in the array.  The dynamics of the moving charges under some reasonable approximations can be described by the sine-Gordon equation, same model which describes the motion of dual objects – fluxons in long Josephson junctions. Coherent control of the charge solitons may open way to develop a quantum mechanically precise standard of electrical current. Locking the frequency f of the charge propagation through the array should yield voltage-independent plateaus at discrete current values I_n = n⋅2e⋅f, where n = 1,2,3,... Such a frequency to current converter would allow closing the remaining open side of the quantum metrological triangle, which connects frequency, voltage and current by quantum mechanical effects.

Experimental realization

Two main characteristic energies that determine the properties of the Josephson junction arrays are the charging energy E_C and the Josephson energy E_J. In order to see charging effects, E_C must be comparable to E_J and both energies need to be much bigger than the thermal energy k_BT. With typical array parameters, this sets the required operating temperature T to be below 100 mK. It is very convenient to replace single Josephson junctions in the array by small superconducting loops with two Josephson junctions forming dc SQUIDs. This way E_J can be controlled in situ by applying an external magnetic field perpendicular to the plane of the array. For the fabrication of arrays we deploy Al-based junctions made by shadow evaporation technique. The array IV-curves exhibit a Coulomb blockade at low bias voltages accompanied by hysteresis at finite currents. Our key finding is that the conductance of the arrays scales proportionally to E_J² [1]. The resistive slope can thus be interpreted via the so-called P(I) theory as an incoherent Cooper pair tunneling process. The microwave-assisted incoherent tunneling process has its counterpart in the dual case, where we investigated experimentally and theoretically the behavior of small junctions under microwave irradiation [2]. The measured low-voltage resistive states display strongly smeared incoherent Shapiro-like steps in the IV-curves.

Theoretical work

In connection with our experiments on charge solitons, we performed a series of numerical simulations in discrete sine-Gordon model with spatial disorder associated to background charges randomly placed on the substrate [3]. We studied the maximum pinning force depending on the soliton size Λ measured in units of array cells. Good news for our experiments is that disorder effects become irrelevant for soliton size Λ ~ 5 or larger. Once the soliton size becomes much larger than the variation length scale of random charges the soliton hardly notice any pinning.

Outlook

The “compact” charge solitons model derived by CFN theorists led by A. Shnirman suggests that the conductance scaling proportional to ~ E_J² [1] can be explained in terms of the velocity-dependent soliton mass. It appears crucial to verify this in future experiments. Our further plans are to measure the soliton screening length by comparing arrays of different number of junctions, implement uniform biasing scheme, and perform systematic microwave experiments.

References

List of Publications 2006-2011 as PDF

Subproject Report 2006-2010 as PDF