QCJC: Devoret and Schoelkopf 2000

Here is an interesting article from the early days of the lab!

This was a review article published by Devoret and Schoelkopf in 2000, just as charge qubits were becoming more mainstream. The charge qubit, created from island Josephson Junctions, were first beginning to be realized as possible two-state qubit systems. However, one challenge was that such charge qubits have very small amounts of charge – on the order of single electrons. It is very difficult to detect single electrons, especially in noisy channels. To overcome this, a lot of investigation was put into Single Electron Transistors (SETs).

This review article begins with a explanation of the commonly used Field-Effect Transistors (FETs), which are often realized as MOSFETs. Such devices have two conducting sites, a source and a drain, and a semiconducting region in the center. That semiconducting region will act as a potential barrier that can be controlled by some amount of external voltage, changing the number of charge carriers that would exist in that island region. When there is no voltage, the potential barrier would block all flow of electrons, and prevent current from flowing, while the application of voltage would lower the barrier.

While the FET is primarily classical in nature, the SET explicitly uses the quantum tunneling of single electrons across an island with barriers on either side. These barriers are small, such that electrons are able to tunnel across. However, certain transitions are forbidden, when there are a certain number of electrons in the island. Specifically, at low temperatures, when there are an integer number of electrons in the island, no current will flow. However, when there are a half number of electrons, tunnel events are able to take place. As a result, the SET would act as a charge amplifier – it would be able to introduce gain that can be measured as current.

The majority of the remainder of the paper is dealing with characterizing noise in quantum amplifiers. They calculate how quantum noise is introduced through different mechanisms, including the back-action of the amplifier, as well as noise impedance. Through the remainder of the paper, the authors argue that the SET is able to reach the quantum limit of noise, as determined by the Heisenberg uncertainty principle. There is always some amount of noise introduced, but it is close to the quantum limit.

Finally, the paper authors theorize that the SET can therefore be used as a measurement device for the charge qubit, otherwise known as the Cooper-pair box. However, such a measurement requires a continuous measurement, which decohered the qubit. One possible improvement was the radio-frequency controlled SET, or the rf-SET, which was invented by Schoelkopf a few years earlier. At that time, the paper authors were trying to determine if the rf-SET would be practical as a true quantum computer read-out mechanism. Yet just 4 years later, the strong coupling from transmon to cavity would be discovered. While we no longer rely on rf-SET in our experiments (to my knowledge), the same language of quantum amplifiers is still often used in terms of the Josephson Parametric Amplifier and the SNAIL Parametric Amplifiers.

Citation: Devoret, M. H. and Schoelkopf, R. J. Amplifying Quantum Signals with the Single-Electron Transistor Nature 406 1039-1046 (2000)

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