**Subproject Leader**: Alexey Ustinov

**Contributing Scientists: **

Present: Jochen Zimmer

Past: Johannes Rotzinger, Mario Salerno

**Subproject Leader**: Alexey Ustinov

**Contributing Scientists: **

Present: Jochen Zimmer

Past: Johannes Rotzinger, Mario Salerno

**Charge solitons for quantum metrology**

Charge solitons are collective excitations in an array of small Josephson junctions. Every soliton carries exactly the charge *2*e 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*

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*_{B}*T*. 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*_{J}* ^{2}* [1]. The resistive slope can thus be interpreted via the so-called

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.

The “compact” charge solitons model derived by CFN theorists led by A. Shnirman suggests that the conductance scaling proportional to ~ E_{J}^{2} [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.

[1] |
R. Schäfer, W. Cui, B. Kießig, K. Grube, H. Rotzinger, and A. V. Ustinov, Cooper pair propagation in Josephson junction chains, in preparation (2011) |

[2] |
Y. Koval, M. V. Fistul, and A. V. Ustinov, Incoherent microwave-induced resistive states of small Josephson junctions, Low Temp. Phys. 36, 951 (2010) |

[3] |
K. Fedorov, M. V. Fistul, and A. V. Ustinov, Pinning of charge and flux solitons in disordered Josephson junction arrays, Phys. Rev. B 84, 014526 (2011) |

List of Publications 2006-2011 as PDF

Subproject Report 2006-2010 as PDF