We interpret a recent pioneering experiment [Zgirski M. et al., Phys. Rev. Lett., 106 (2011) 257003] on quasiparticle manipulation in a superconducting break junction in terms of spin blockade drawing analogy with spin qubits. We propose a novel qubi
t design that exploits the spin state of two trapped quasiparticles. We detail the coherent control of all four spin states by resonant quantum manipulation and compute the corresponding Rabi frequencies. The read-out technique is based on the spin-blockade that inhibits quasiparticle recombination in triplet states. We provide extensive microscopic estimations of the parameters of our model.
We study theoretically dynamics in a Josephson junction coupled to a mechanical resonator looking at the signatures of the resonance in d.c. electrical response of the junction. Such a system can be realized experimentally as a suspended ultra-clean
carbon nanotube brought in contact with two superconducting leads. A nearby gate electrode can be used to tune the junction parameters and to excite mechanical motion. We augment theoretical estimations with the values of setup parameters measured in the samples fabricated. We show that charging effects in the junction give rise to a mechanical force that depends on the superconducting phase difference. The force can excite the resonant mode provided the superconducting current in the junction has oscillating components with a frequency matching the resonant frequency of the mechanical resonator. We develop a model that encompasses the coupling of electrical and mechanical dynamics. We compute the mechanical response (the effect of mechanical motion) in the regime of phase bias and d.c. voltage bias. We thoroughly investigate the regime of combined a.c. and d.c. bias where Shapiro steps are developed and reveal several distinct regimes characteristic for this effect. Our results can be immediately applied in the context of experimental detection of the mechanical motion in realistic superconducting nano-mechanical devices.
Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson junction circuit. In contrast to most optical systems, a significant part of emitted
radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts each encompassing 2N photons, this accounts for the bunching of the photon pairs produced in course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.
We propose and theoretically investigate spin superconducting qubits. Spin superconducting qubit consists of a single spin confined in a Josephson junction. We show that owing to spin-orbit interaction, superconducting difference across the junction
can polarize this spin. We demonstrate that this enables single qubit operations and more complicated quantum gates, where spins of different qubits interact via a mutual inductance of superconducting loop where the junctions are embedded. Recent experimental realizations of Josephson junctions made of semiconductor quantum dots in contact with superconducting leads have shown that the number of electrons in the quantum dot can be tuned by a gate voltage. Spin superconducting qubit is realized when the number of electrons is odd. We discuss the qubit properties at phenomenological level. We present a microscopic theory that enables us to make accurate estimations of the qubit parameters by evaluating the spin-dependent Josephson energy in the framework of fourth-order perturbation theory.
