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arXiv:1503.01905 · Physical Review B

Parity effect in Josephson junction arrays

Jared H. Cole, Andreas Heimes, T. Duty, Michael Marthaler

Published May 8, 2015• 13 citations
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Abstract

We study the parity effect and transport due to quasiparticles in circuits comprised of many superconducting islands. We develop a general approach and show that it is equivalent to previous methods for describing the parity effect in their more limited regimes of validity. As an example we study transport through linear arrays of Josephson junctions in the limit of negligible Josephson energy and observe the emergence of the parity effect with decreasing number of nonequilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multijunction arrays the parity effect manifests in qualitatively different ways to the two-junction case. The role of charge disorder is also studied as this hides much of the parity physics that would otherwise be observed. Nonetheless, we see that the current through a multijunction array at low bias is limited by the formation of metastable even-parity states.

DOI
10.1103/physrevb.91.184505

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We study the parity effect and transport due to quasiparticles in circuits comprised of many superconducting islands. We develop a general approach and show that it is equivalent to previous methods for describing the parity effect in their more limited regimes of validity. As an example we study transport through linear arrays of Josephson junctions in the limit of negligible Josephson energy and observe the emergence of the parity effect with decreasing number of nonequilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multijunction arrays the parity effect manifests in qualitatively different ways to the two-junction case. The role of charge disorder is also studied as this hides much of the parity physics that would otherwise be observed. Nonetheless, we see that the current through a multijunction array at low bias is limited by the formation of metastable even-parity states.
The transport properties of a small superconductor--normal-metal--superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current Ic{\mathit{I}}_{\mathit{c}}Ic​ through such a system as a function of the gate voltage Vg{\mathit{V}}_{\mathit{g}}Vg​ taking into account parity effects in the superconductors. The dependence Ic{\mathit{I}}_{\mathit{c}}Ic​(Vg{\mathit{V}}_{\mathit{g}}Vg​) shows resonant singularities and has a qualitatively different character for \ensuremath{\Delta}EC{\mathit{E}}_{\mathit{C}}EC​ and \ensuremath{\Delta}>EC{\mathit{E}}_{\mathit{C}}EC​, \ensuremath{\Delta} being the superconducting gap and EC{\mathit{E}}_{\mathit{C}}EC​=e2{\mathit{e}}^{2}e2/2C being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.
Current-biased Josephson junctions are prime candidates for the realization of quantum bits; however, a present limitation is their coherence time. In this paper it is shown qualitatively that quasiparticles create decoherence. We can decrease the number of quasiparticles present in the junctions by two methods - reducing the creation rate with current shunts and increasing the depletion rate with normal-metal traps. Experimental data demonstrate that both methods are required to significantly reduce the number of quasiparticles and increase the system's coherence. We conclude that these methods are effective and that the design of Josephson-junction qubits must consider the role of quasiparticles.
We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kilohertz. We demonstrate that the pair breaking is caused by the backaction of the single-electron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time.
We investigate quasiparticle tunneling in a Cooper-pair box which is embedded in a superconducting ring to allow control of the total phase difference across the island. The phase affects the transition rate between different electron number parity states of the island, which can be observed in experiment by established means. The phase dependence also leads to what is known as the $\mathrm{cos}\ensuremath{\phi}$ term in the tunneling characteristics of classical Josephson junctions. This effect has remained controversial for decades; the proposed scheme opens an independent way to probe it.
We study correlated transport in a Josephson junction array for small Josephson energies. In this regime transport is dominated by Cooper-pair hopping, although we observe that quasiparticles can not be neglected. We assume that the energy dissipated by a Cooper-pair is absorbed by the intrinsic impedance of the array. This allows us to formulate explicit Cooper-pair hopping rates without adding any parameters to the system. We show that the current through the array is correlated and crucially, these correlations rely fundamentally on the interplay between the Cooper-pairs and equilibrium quasiparticles.
We study correlated transport in a Josephson junction array for small Josephson energies. In this regime transport is dominated by Cooper-pair hopping, although we observe that quasiparticles can not be neglected. We assume that the energy dissipated by a Cooper-pair is absorbed by the intrinsic impedance of the array. This allows us to formulate explicit Cooper-pair hopping rates without adding any parameters to the system. We show that the current through the array is correlated and crucially, these correlations rely fundamentally on the interplay between the Cooper-pairs and equilibrium quasiparticles.