Correlated transport through junction arrays in the small Josephson energy limit: incoherent Cooper-pairs and hot electrons

Cole, Jared H.; Leppäkangas, Juha; Marthaler, Michael

doi:10.1088/1367-2630/16/6/063019

Cited by 12 publications

(18 citation statements)

References 56 publications

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“…when the contribution from the two types of diagrams in higher orders stays small. The results clarify the limits of our previous works on lasing in systems under strong noise 19,20 , incoherent Cooper-pair tunneling in Josephson junction arrays 21 , as well as inelastic Cooper-pair tunneling across voltagebiased Josephson junctions in the Coulomb blockade regime 22,23 . As we discussed in section V A 1, interesting is the connection of the used noise spectral function to 1/f -noise.…”

Section: Discussionsupporting

confidence: 83%

“…In larger coupled systems containing these qubits, a description based on polaronic hopping has also already been studied 18 . This article represents a continuation of our work on lasing in systems under strong noise 19,20 and incoherent Cooper-pair tunneling in Josephson junction arrays 21 . In both cases we used the lowest-order results of our expansion theory, and here we present for the first time the higher-order expansion which as used to analyze the convergence conditions.…”

Section: Introductionmentioning

confidence: 88%

“…The spectral function is characterized by height ǫ C k B T /ω R and width ω R . This can be an important regime, even at milli-Kelvin temperatures 16,21,22 , since cut-off frequencies can be even smaller.…”

Section: A Cut-off Freqencies Smaller Than Temperaturementioning

confidence: 99%

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Diagrammatic description of a system coupled strongly to a bosonic bath

Marthaler

Leppäkangas

2016

Phys. Rev. B

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We study a system-bath description in the strong coupling regime where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through a unitary transformation it can be possible to find a more suitable small expansion parameter. Within such approach we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a nondiagonal hopping term. The lowest-order expansion is equivalent to the so-called P (E)-theory or non-interacting blip approximation (NIBA). The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the convergence of this expansion depends on the form of the spectral function with significant weight at zero frequency.

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Section: Discussionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 88%

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Diagrammatic description of a system coupled strongly to a bosonic bath

Marthaler

Leppäkangas

2016

Phys. Rev. B

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“…charge-charge correlation effects are strongest due to the low filling of the array 48,50,52 which is also the regime that should show parity effects most clearly.…”

Section: The Parity Effect In Josephson Junction Arraysmentioning

confidence: 99%

Parity effect in Josephson junction arrays

et al. 2015

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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 non-equilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multi-junction 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 which would otherwise be observed. Nonetheless, we see that the current through a multi-junction array at low bias is limited by the formation of meta-stable even-parity states.PACS numbers: 73.23. Hk,85.25.Cp, In superconducting circuits of small dimensions, charging effects play an important role. On the one hand the Coulomb blockade leads to charge pinning and an effective suppression of electronic transport at low bias voltage. On the other hand the superconducting nature manifests in the parity effect, i.e. given a odd number of electrons on the superconductor there is one remaining quasiparticle dominating the transport properties in the low bias regime 1-8 . Strictly speaking this picture is true for equilibrium and very low temperatures. However if a non-equilibrium situation is imposed, e.g. by applying a finite bias voltage, the average number of quasiparticles may be increased. Recently such non-equilibrium quasiparticle effects have been investigated in superconducting qubits 9-14 and single electron transistors (SETs) [15][16][17][18][19] . In this context the interplay of charge transport, the excitation of non-equilibrium quasiparticles and the observation of the parity effect has been the subject of recent experiments with SETs 18 . Based on related theoretical modelling 19-21 we extend the prevailing transport theory of multi-junction circuits and show that this approach removes the ambiguities of previous approaches when including parity effects for more than one superconducting island, although our approach is equivalent to earlier work in the appropriate limits. As an example, we perform the first analysis of the parity effect in linear multijunction arrays and make a number of predictions for the electronic transport signatures that can be identified with the parity effect in these systems.

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“…This gives us an equation of motion identical to equation (20), but with the slanted definitions of  Q, ¡  and . The form of the coupling matrix for the slanted array is the same as that of the capacitance matrix for a linear Josephson junction array (with the identifications a  C J and  C 1 G ), and so it can be inverted analytically using the same methods [23,31].…”

Section: Theoretical Modelmentioning

confidence: 99%

Coulomb drag and depinning in bilinear Josephson junction arrays

2017

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Coulomb drag and depinning are electronic transport phenomena that occur in low-dimensional nanostructures. Recently, both phenomena have been reported in bilinear Josephson junction arrays. These devices provide a unique opportunity to study the interplay of Coulomb drag and depinning in a system where all relevant parameters can be controlled experimentally. We explain the Coulomb drag and depinning characteristics in the I-V curve of the bilinear Josephson junction array by adopting a quasicharge model which has previously proven useful in describing threshold phenomena in linear Josephson junction arrays. Simulations are performed for a range of coupling strengths, where numerically obtained I-V curves match well with what has been previously observed experimentally. Analytic expressions for the ratio between the active and passive currents are derived from depinning arguments. Novel phenomena are predicted at voltages higher than those for which experimental results have been reported to date.

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Correlated transport through junction arrays in the small Josephson energy limit: incoherent Cooper-pairs and hot electrons

Cited by 12 publications

References 56 publications

Diagrammatic description of a system coupled strongly to a bosonic bath

Diagrammatic description of a system coupled strongly to a bosonic bath

Parity effect in Josephson junction arrays

Coulomb drag and depinning in bilinear Josephson junction arrays

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