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AIP conference proceedings

Coherent Tunneling of Cooper Pairs in Asymmetric Single-Cooper-Pair Transistors

Juha Leppäkangas, E. V. Thuneberg

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We have calculated the I — V characteristics of voltage biased asymmetric single‐Cooper‐pair transistors (SCPT), resulting from coherent Cooper pair tunneling across both the Josephson junctions (JJ), weak dissipation due the electromagnetic environment (EE) satisfying Re[Z(ω)] ≪ RQ, and quasiparticles. Due to the asymmetry, the smaller JJ is effectively probing the macroscopic quantum states of the island. A resonance occurs whenever the energy released in a tunneling of a single, or several, Cooper pair(s) across the smaller JJ matches to the energy needed to excite the island.

DOI
10.1063/1.2355017

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We have calculated the I — V characteristics of voltage biased asymmetric single‐Cooper‐pair transistors (SCPT), resulting from coherent Cooper pair tunneling across both the Josephson junctions (JJ), weak dissipation due the electromagnetic environment (EE) satisfying Re[Z(ω)] ≪ RQ, and quasiparticles. Due to the asymmetry, the smaller JJ is effectively probing the macroscopic quantum states of the island. A resonance occurs whenever the energy released in a tunneling of a single, or several, Cooper pair(s) across the smaller JJ matches to the energy needed to excite the island.
We analyze tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors. Also tunneling of Cooper pairs across two capacitively coupled Cooper-pair boxes is considered, when the capacitive coupling and Cooper pair tunneling are provided by a small Josephson junction between the islands. The theoretical analysis is done at subgap voltages, where the current-voltage characteristics depend strongly on the macroscopic eigenstates of the island(s) and their coupling to the dissipative environment. As the environment we use an impedance which satisfies $\mathrm{Re}[Z(\ensuremath{\omega})]⪡{R}_{Q}$ and a few LCLCLC oscillators in series with $Z(\ensuremath{\omega})$. The numerically calculated $I\text{\ensuremath{-}}V$ curves are compared with experiments where the quantum states of mesoscopic SQUIDs are probed with inelastic Cooper pair tunneling. The main features of the observed $I\text{\ensuremath{-}}V$ data are reproduced. Especially, we find traces of band structure in the higher excited states of the Cooper-pair boxes as well as traces of multiphoton processes between two Cooper-pair boxes in the regime of large Josephson coupling EJ⪢EC{E}_{J}⪢{E}_{C}EJ​⪢EC​.
We analyze how decoherence appears in the $I\text{\ensuremath{-}}V$ characteristics of a voltage-biased single-Cooper-pair transistor. Especially the effect on resonant single or several Cooper-pair tunneling is studied. We consider both a symmetric and an asymmetric transistor. As a decoherence source we use a small resistive impedance $(\text{Re}[Z(\ensuremath{\omega})]⪡{R}_{Q}=h/4{e}^{2})$ in series with the transistor, which provides both thermal and quantum fluctuations of the voltage. Additional decoherence sources are quasiparticle tunneling across the Josephson junctions and quantum fff noise caused by spurious charge fluctuators nearby the island. The analysis is based on a real-time diagrammatic technique which includes Zeno-type effects in the charge transport, where the tunneling is slowed down due to strong decoherence. As compared to the Pauli-master-equation treatment of the problem, the present results are more consistent with experiments where many of the predicted sharp resonant structures are missing or weakened due to decoherence.
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.
The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.