Tunneling and relaxation of single quasiparticles in a normal-superconductor-normal single-electron transistor

Abstract

We investigate the properties of a hybrid single-electron transistor, involving a small superconducting island sandwiched between normal metal leads, which is driven by dc plus ac voltages. In order to describe its properties we derive from the microscopic theory a set of coupled equations. They consist of a master equation for the probability to find excess charges on the island, with rates depending on the distribution of nonequilibrium quasiparticles. Their dynamics follows from a kinetic equation which accounts for the excitation by singleelectron tunneling as well as the relaxation and eventual recombination due to the interaction with phonons. Our low-temperature results compare well with recent experimental findings obtained for ac-driven hybrid single-electron turnstiles.

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

“…It is this excess energy which can lead to higher effective electron temperatures, an effect which has been observed in qubit [40,49,50] and SET experiments [35]. The effective temperature seen by the charge carriers can depend in general on the bias conditions, junction properties, the superconducting gap and even the timescale over which the experiment is conducted [35,51,52]. For simplicity in the remainder of this analysis, we assume an electron temperature of T = 200 mK.…”

Clocked single-spin source based on a spin-split superconductor

“…Starting from the Hamiltonian in equation (1), the operatorn in the Hamiltonian is reinterpreted asˆ| | ñ = ñ n n nn and the tunneling part of the Hamiltonian is redefined by adding operators in the | ñ n -subspace, leading to for the Zeeman-split island. As pointed out in the main text, the parity effect in the superconducting island [21,22,24] is crucial for the spin-pump operation. To account for the parity effect in our approach, it is important to keep track of the island quasiparticle excitations of both spin directions by extending the introduced charge states by the quasiparticle numbers  N and  N .…”

“…Similarly to previous studies on S/N hybrid structures, see e.g. [24] and appendixC, we derive a Master equation in the sequential tunneling limit, describing the time evolution of the occupation probabilities in the SFISFIS setup…”

Creating photon-number squeezed strong microwave fields by a Cooper-pair injection laser

“…In particular, we demonstrate that in a specific experimentally feasible parameter regime, squeezing at a high photon number can be achieved even in the presence of maximum gate-charge disorder. It follows that this device is robust against strong thermal noise in the DC-voltage bias 34 and nonequilibrium quasiparticles in the CPTs [35][36][37][38] .…”