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arXiv:cond-mat/0210539

Population inversion through charge measurement using a superconducting single-electron transistor biased in the subgap regime

Göran Johansson

Published Oct 24, 2002• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0210539

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We study the quantum charge noise and measurement properties of the double Cooper-pair resonance point in a superconducting single-electron transistor (SSET) coupled to a Josephson charge qubit. Using a density-matrix approach for the coupled system, we obtain a full description of the measurement backaction; for weak coupling, this is used to extract the quantum charge noise. Unlike the case of a nonsuperconducting SET, the backaction here can induce population inversion in the qubit. We find that the Cooper-pair resonance process allows for a much better measurement than a similar nonsuperconducting SET, and can approach the quantum limit of efficiency.
The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.
We analyze the charge dynamics of a superconducting single-electron transistor (SSET) in the regime where charge transport occurs via Cooper-pair resonances. Using an approximate description of the system Hamiltonian, in terms of a series of resonant doublets, we derive a Born-Markov master equation describing the dynamics of the SSET. The average current displays sharp peaks at the Cooper-pair resonances and we find that the charge noise spectrum has a characteristic structure which consists of a series of asymmetric triplets of peaks. The strongest feature in the charge noise spectrum is the triplet of peaks centered at zero frequency which has a peak spacing equal to the level separation within the doublets and is similar to the triplet in the spectrum of a driven, damped, two-level system. We also explore the backaction that the SSET charge noise would have on an oscillator coupled to the island charge, measurement of which provides a way of probing the charge noise spectrum.
We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.
Abstract Single‐charge tunneling through a voltage‐biased SSS transistor with a capacitively coupled gate and an electromagnetic environment is considered. The dc Cooper‐pair current in the blockade region of quasiparticle tunneling is studied. Basing on a two‐level approximation, which can be used in the realistic case of low temperatures and small environment resistances, the mean dc Cooperpair current, the noise power spectrum, and the charge resolution are calculated as functions of the driving voltage and the external charge on the island.
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.