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arXiv:cond-mat/0612556 · Applied Physics Letters

Nanoampere pumping of Cooper pairs

Juha J. Vartiainen, Mikko Möttönen, Jukka P. Pekola, A. Kemppinen

Published Feb 19, 2007• 64 citations
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Abstract

The authors have employed a tunable Cooper-pair transistor, the sluice, with radio frequency control to pump current over a resistive circuit. They find that the charge transferred per pumping cycle can be controlled with the resolution of a single Cooper pair up to hundreds of pairs. The achieved nanoampere current features more than an order of magnitude improvement over the previously reported results and it is close to the theoretical maximum value for the measured sample.

DOI
10.1063/1.2709967

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The authors have employed a tunable Cooper-pair transistor, the sluice, with radio frequency control to pump current over a resistive circuit. They find that the charge transferred per pumping cycle can be controlled with the resolution of a single Cooper pair up to hundreds of pairs. The achieved nanoampere current features more than an order of magnitude improvement over the previously reported results and it is close to the theoretical maximum value for the measured sample.
We have carried out first measurements on a novel type of a charge pump nicknamed the Cooper pair "sluice". The device is an adiabatic flux-assisted Cooper pair pump consisting of a mesoscopic superconducting island and of two SQUID loops. The operation is based on the periodic manipulation of a single voltage gate and two input coils controlling the magnetic flux through the SQUID loops. Based on theoretical estimates the device is capable of producing as high as 0.1 nA currents at better than 10-accuracy and looks thus like a promising candidate for the current source in completing the quantum measurement triangle. In spite of several nonidealities in our preliminary measurement setup, we have succeeded in verifying the pumping behavior of the sluice. The pumped currents were quite high, several hundred pA, but the accuracy needs to be increased. The results obtained so far suggest various ways of improving the measurement setup
We demonstrate controlled pumping of Cooper pairs down to the level of a single pair per cycle, using an rf-driven Cooper-pair sluice. We also investigate the breakdown of the adiabatic dynamics in two different ways. By transferring many Cooper pairs at a time, we observe a crossover between pure Cooper-pair and mixed Cooper-pair-quasiparticle transport. By tuning the Josephson coupling that governs Cooper-pair tunneling, we characterize Landau-Zener transitions in our device. Our data are quantitatively accounted for by a simple model including decoherence effects.
We introduce a Cooper pair "sluice" for the implementation of a frequency-locked current source. The device consists of two mesoscopic SQUIDs and of a single superconducting island with a gate. We demonstrate theoretically that it is possible to obtain a current as high as 0.1 nA at better than ppm accuracy via periodically modulating both the gate charge and the effective Josephson coupling. We find that the device is tolerant against background charge noise and operates well even in a dissipative environment. The effect of the imperfect suppression of the Josephson coupling and the finite operating frequency are also investigated.
We introduce and discuss a scheme for Cooper-pair pumping. The scheme relies on the coherent transfer of a superposition of charge states across a superconducting island and is realized by adiabatic manipulation of magnetic fluxes. Differently from previous implementations, it does not require any modulation of electrostatic potentials. We find a peculiar dependence of the pumped charge on the superconducting phase bias across the pump and that an arbitrarily large amount of charge can be pumped in a single cycle when the phase bias is $\ensuremath{\pi}$. We explain these features and their relation to the adiabatic theorem.
We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump---the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. To our knowledge the experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.
We derive a general formula for the charge pumped in a superconducting nanocircuit. Our expression generalizes previous results in several ways; it is applicable in both the adiabatic and in the nonadiabatic regimes and it takes into account also the effect of an external environment. More specifically, by applying Floquet theory to Cooper pair pumping, we show that under a cyclic evolution the total charge transferred through the circuit is proportional to the derivative of the associated Floquet quasi-energy with respect to the superconducting phase difference. In the presence of an external environment the expression for the transferred charge acquires a transparent form in the Floquet representation. It is given by the weighted sum of the charge transferred in each Floquet state, the weights being the diagonal components of the stationary density matrix of the system expressed in the Floquet basis. To test the power of this formulation we apply it to the study of pumping in a Cooper pair sluice. We reproduce the known results in the adiabatic regime and we show new data in the nonadiabatic case.