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arXiv:cond-mat/0105211

Radio-frequency-driven motion of single Cooper pairs across the superconducting single-electron transistor with dissipative environment

Alexander B Zorin, S. V. Lotkhov, Sergey A. Bogoslovsky, J. Niemeyer

Published May 10, 2001• 3 citations
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Abstract

We report on the effect of the frequency-locked transfer of single Cooper pairs in a superconducting single-electron Al transistor embedded in a dissipative environment (on-chip Cr resistor of R = 40 kOhm). The transistor was dc voltage biased, and the harmonic signal of frequency f of several MHz was applied to the gate. Due to the substantial rate of relaxation, the unidirectional transfer of single pairs occurred in each junction once per clock cycle and the current plateaus at I = 2ef were developed in the transistor's I-V curves. The mechanisms (supercurrent, Landau-Zener tunneling, quasiparticle tunneling, etc.) deteriorating the phase-locking regime are discussed.

DOI
10.48550/arxiv.cond-mat/0105211

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We report on the effect of the frequency-locked transfer of single Cooper pairs in a superconducting single-electron Al transistor embedded in a dissipative environment (on-chip Cr resistor of R = 40 kOhm). The transistor was dc voltage biased, and the harmonic signal of frequency f of several MHz was applied to the gate. Due to the substantial rate of relaxation, the unidirectional transfer of single pairs occurred in each junction once per clock cycle and the current plateaus at I = 2ef were developed in the transistor's I-V curves. The mechanisms (supercurrent, Landau-Zener tunneling, quasiparticle tunneling, etc.) deteriorating the phase-locking regime are discussed.
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.
We measure the high-frequency emission of a single Cooper pair transistor (SCPT) in the regime where transport is only due to tunneling of Cooper pairs. This is achieved by coupling on chip the SCPT to a superconductor-insulator-superconductor junction and by measuring the photon assisted tunneling current of quasiparticles across the junction. This technique allows a direct detection of the ac Josephson effect of the SCPT and provides evidence of Landau-Zener transitions for proper gate voltage. The emission in the regime of resonant Cooper pair tunneling is also investigated. It is interpreted in terms of transitions between charge states coupled by the Josephson effect.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
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.
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