Spin, Vibrations and Radiation in Superconducting Junctions

Abstract

This thesis presents the theoretical study of superconducting transport in several devices based on superconducting junctions. The important feature of these devices is that the transport properties of the junction are modified by the interaction with another physical system integrated in the superconducting circuit. The first device discussed is the spin superconducting qubit presented in Chapter 3. Such a unit combines the natural representation of a two level system in terms of electron spin and the advantages of superconducting qubits. We have shown that in spin superconducting qubits the flux and spin degrees of freedom can be easily entangled. Importantly, we have demonstrated feasibility of all electric manipulation of superconducting qubits and more complicated quantum gates made of such qubits. The microscopic analysis of quantum transport through the spin superconducting junction allows us to estimate the spin-dependent part of the Josephson energy. We demonstrate that it can be made sufficiently large, at least for semiconducting devices where spin-orbit interaction is intrinsically strong. The second device discussed in Chapter 4 is a novel qubit design using the spin states of two superconducting quasiparticles trapped in a superconducting junction. Read-out of the qubit is based on spin-blockade that inhibits recombination of quasiparticles in the triplet state. We have detailed the resonant manipulation of singlet-to-triplet and triplet-to-triplet transitions and have described the operation of the qubit. Experimental realization of our proposal would unambiguously demonstrate for the first time the spin properties of superconducting quasiparticles. In the third device studied in Chapter 5 the superconducting transport is modified by the excitation of a mechanical resonator integrated in the superconducting junction. We have demonstrated that the mechanical oscillations can be rectified giving rise to additional d.c. current that can be used for detection. The resonator can be driven by the a.c. voltage applied to the gate electrode as well as a mechanical force that depends on the superconducting phase difference at the junction, termed the Josephson force. We have presented a general and detailed analysis of the coupling between electrical and mechanical degrees of freedom, and have discussed the competing non-linear scales. The analysis has enabled us to derive analytical formulas for the response of the device to mechanical excitations in a wide interval of excitation strengths and for various biasing schemes. In Chapter 6 we have studied the full counting statistics of the radiation emitted by a Josephson junction circuit in the regime of parametric resonance. This is important in view of recent experiments that enable the detection of full power dissipated. We present the interpretation of the statistics in terms of bursts of multiple pairs of photons. This interpretation has been supported by investigating the time-dependent and frequency-resolved correlations.