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Journal of Applied Physics

Thermal excitation of large charge offsets in a single-Cooper-pair transistor

L. R. Simkins, D. G. Rees, P. Glasson, Vladimir N Antonov, Eddy Collin, P.G. Frayne, P. J. Meeson, M. J. Lea

Published Dec 15, 2009• 5 citations
Publisher

Abstract

Charge offsets and two-level fluctuators are common in single-electron transistors with a typical magnitude of |ΔQ|<0.1e. We present measurements in a 2e-periodic single-Cooper-pair transistor which exhibited hysteretic charge offsets close to 1e. The real-time capture and escape of individual electrons in metastable trapped states was measured at very low temperatures. This enabled the dynamics of the transitions to be investigated in detail, demonstrating thermal excitation to a hysteretic tunneling transition. We show that, allowing for the hysteresis, the metastable states are in thermal equilibrium with each other. The observed temperature dependence and hysteresis can be explained by the coupling of a two-level fluctuator to a quasiparticle trap.

DOI
10.1063/1.3266012

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arXiv:cond-mat/0210539•Oct 24, 2002•0 citations
Charge offsets and two-level fluctuators are common in single-electron transistors with a typical magnitude of |ΔQ|<0.1e. We present measurements in a 2e-periodic single-Cooper-pair transistor which exhibited hysteretic charge offsets close to 1e. The real-time capture and escape of individual electrons in metastable trapped states was measured at very low temperatures. This enabled the dynamics of the transitions to be investigated in detail, demonstrating thermal excitation to a hysteretic tunneling transition. We show that, allowing for the hysteresis, the metastable states are in thermal equilibrium with each other. The observed temperature dependence and hysteresis can be explained by the coupling of a two-level fluctuator to a quasiparticle trap.
We investigate low-temperature and low-voltage-bias charge transport in a superconducting Al single electron transistor in a dissipating environment, realized as on-chip high-ohmic Cr microstrips. In samples with relatively large charging energy Ec>EJ, where EJ is the Josephson coupling energy, two transport mechanisms were found to be dominant, both based on discrete tunneling of individual Cooper pairs: Depending on the gate voltage Vg, either sequential tunneling of pairs via the transistor island [in the conducting state of the transistor around the points Qg≡CgVg=e mod (2e), where Cg is the gate capacitance] or their cotunneling through the transistor (for Qg away of these points) was found to prevail in the net current. As the conducting state of our transistors had been found to be subject to quasiparticle poisoning, high-frequency gate cycling (at f∼1 MHz) was applied to study the sequential tunneling mechanism. A simple model based on the master equation was found to be in a good agreement with the experimental data.
This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.
We present a series of measurements on nine single Cooper-pair boxes (SCBs), where the charging energy, E C , and the Josephson coupling energy, E J , have been varied. We have investigated both the ground state properties of the SCBs and their quantum coherent properties. The state of the SCBs could be manipulated by an external gate voltage and the charge was measured by coupling it capacitatively to a radio-frequency single-electron-transistor (RF-SET). By ramping the gate voltage and simultaneously measuring the charge of the SCBs using the RF-SET, we could measure the Coulomb staircases of the SCBs. For sufficiently low E C the SCBs showed a fully 2 e periodic Coulomb staircase. For samples with higher E C the staircase showed a short step for odd number of charges indicating quasi-particle 'poisoning'. However, if E C was not too large, the short step could be removed by applying a parallel magnetic field. We attribute this effect to a stronger suppression of the superconducting energy gap in the reservoir than in the box. Using microwave spectroscopy we have determined E C and E J for the SCBs. These values agree well with the shape of the Coulomb staircases which we measure. For a limited range of gate voltage, the SCBs were found to behave as model two-level quantum-mechanical systems. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with an amplitude above 70% and a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T 2 = 9 ns, at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate. Away from the charge degeneracy point, the coherence time was limited by the pure dephasing rate. The dependence of T 2 on gate charge suggested that low frequency fluctuators were the main source of dephasing away from the degeneracy point.
We show how population inversion (PI) occurs in a two-level system (TLS) while measuring its charge using a capacitively coupled superconducting single-electron transistor (SSET), biased in the subgap regime, where the current through the SSET is carried by different cycles involving tunneling of both Cooper pairs and quasiparticles. The PI is directly associated with the resonant nature of the Cooper-pair tunneling. We also show how the SSET may strongly relax the TLS, although there is negligible current flowing through the SSET, i.e. it is turned off. The calculation of the quantum back-action noise is based on a real-time Keldysh approach. We specifically discuss the case of a Cooper Pair Box qubit with the SSET capacitively coupled as read-out device.