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Bulletin of the American Physical Society

Quasiparticle Poisoning in a Cooper Pair Box caused by a measuring SET

Carlos Sánchez‐Somolinos, B. S. Palmer, M. A. Manheimer, F.C. Wellstood

Published Mar 16, 2006• 0 citations
OpenAlex

Abstract

box in the presence of quasiparticle poisoning. The model uses a master equation approach to flnd the probabilities for the box to be in the even or odd state. The transition rates between the two states are calculated assuming a flxed number of non-equilibrium quasiparticles in the leads and island of the box. We fabricated Al/AlOx/Al devices with a Cooper pair box capacitively coupled to an SET and measured the charge on the box for SET bias currents ranging from about 1 pA to 1 nA. We flnd good agreement between the theory and measurements in the temperature range from 60 mK to 300 mK. For large SET bias the poisoning in the Cooper pair box increases and the charge staircase develops additional features. Our model is capable of qualitatively reproducing the features induced by the measuring SET.

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box in the presence of quasiparticle poisoning. The model uses a master equation approach to flnd the probabilities for the box to be in the even or odd state. The transition rates between the two states are calculated assuming a flxed number of non-equilibrium quasiparticles in the leads and island of the box. We fabricated Al/AlOx/Al devices with a Cooper pair box capacitively coupled to an SET and measured the charge on the box for SET bias currents ranging from about 1 pA to 1 nA. We flnd good agreement between the theory and measurements in the temperature range from 60 mK to 300 mK. For large SET bias the poisoning in the Cooper pair box increases and the charge staircase develops additional features. Our model is capable of qualitatively reproducing the features induced by the measuring SET.
A superconducting Coulomb-blockade electrometer was used to measure the Coulomb staircase of an Al∕AlOx∕Al\mathrm{Al}∕\mathrm{Al}{\mathrm{O}}_{x}∕\mathrm{Al}Al∕AlOx​∕Al Cooper-pair box from a temperature of 30to300mK30\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}30to300mK. At the lowest temperature, the Coulomb staircase displays effects from nonequilibrium quasiparticles. As the temperature is increased, an initial decrease is found in the width of the odd steps in the staircase, which corresponds to a reduction in the probability of having a quasiparticle on the island of the box. Above 180mK180\phantom{\rule{0.3em}{0ex}}\mathrm{mK}180mK, the width of the odd steps increases, eventually producing a staircase with 1e1e1e features. We develop a steady-state model of the system and find that the presence of quasiparticles at low temperature is consistent with the assumption of Aumentado et al. [Phys. Rev. Lett. 92, 066802 (2004)] that nonequilibrium quasiparticles are generated in the leads. Above 180mK180\phantom{\rule{0.3em}{0ex}}\mathrm{mK}180mK, our results are consistent with the quasiparticle states of the island being thermally populated.
I report an investigation into using an rf Single Electron Transistor (rf-SET) to implement single shot readout of the quantum state of a Cooper pair box. I fabricated Al/AlOx/Al SETs and Cooper pair boxes using e-beam lithography and double-angle evaporation. The devices had typical charging energies of about 1 K and were measured at 30 mK in a dilution refrigerator. I built rf-SETs with an LC resonant circuit integrated on the chip and operating frequencies of 650 MHz and 1.5 GHz. The rf-SETs had a typical bandwidth of 30 MHz and the best achieved charge sensitivity was 8X10-6 erms/(Hz)1/2 at 1.5 GHz. The rf-SETs were used to measure the Coulomb staircase on the Cooper pair box. Measurements of the staircase show features due to quasiparticle poisoning that are dependent on temperature and SET bias. The data was compared to a theory I developed to extend existing theories of quasiparticle poisoning. My model is based on the calculation of tunneling rates to explain observations of parity effects in the Cooper pair box over a wide temperature range. Quantum state control of the Cooper pair box was demonstrated by using fast voltage pulses applied to the gate. Temporal oscillations of charge states and spectroscopy measurements reveal a dephasing time T2=200 ps at 30 mK, for a drive frequency of 30 GHz. The energy relaxation time T1=140 ns was determined from time domain measurements of the decay of the Cooper pair box charge. The fidelity of single shot measurements and the feasibility of this quantum readout scheme based on the results are discussed.
We demonstrate the operation of a differential single Cooper-pair box, a charge qubit consisting of two aluminum islands, isolated from ground, coupled by a pair of small-area Josephson junctions, and read out with a superconducting differential radio-frequency single electron transistor. We have tested four devices, all of which show evidence of quasiparticle poisoning. The devices are characterized with microwave spectroscopy and temperature dependence studies, and Coulomb staircases are shown to be e-periodic in all samples. However, coherent control is still possible with non-adiabatic voltage pulses. Coherent oscillation experiments and a relaxation time measurement were performed using a charge derivative readout technique.
We study the kinetics of the quasiparticle capture and emission process in a small superconducting island (Cooper-pair box) connected by a tunnel junction to a massive superconducting lead. At low temperatures, the charge on the box fluctuates between two states, even and odd in the number of electrons. Assuming that the odd-electron state has the lowest energy, we evaluate the distribution of lifetimes of the even- and odd-electron states of the Cooper-pair box. The lifetime in the even-electron state is an exponentially distributed random variable corresponding to a homogenous Poisson process of ``poisoning'' the island with a quasiparticle. The distribution of lifetimes of the odd-electron state may deviate from the exponential one. The deviations come from two sources---the peculiarity of the quasiparticle density of states in a superconductor and the possibility of quasiparticle energy relaxation via phonon emission. In addition to the lifetime distribution, we also find spectral density of charge fluctuations generated by capture and emission processes. The complex statistics of the quasiparticle dwell times in the Cooper-pair box may result in strong deviations of the noise spectrum from the Lorentzian form.
We report on the effect of the backaction of a single Cooper pair transistor electrometer (E\mathbf{E}E) on the charge state of a superconducting box (B\mathbf{B}B). The charge is eee periodic in the gate bias of B\mathbf{B}B when E\mathbf{E}E is operated near voltages $2\ensuremath{\Delta}/e$ or $4\ensuremath{\Delta}/e$. We show that this is due to quasiparticle poisoning of B\mathbf{B}B at a rate proportional to the number of quasiparticle tunneling events in E\mathbf{E}E per second. We are able to eliminate this backaction and recover 2e2e2e-charge periodicity using a new measurement method based on switching-current modulation of E\mathbf{E}E.