Macroscopic quantum effects emerge when the coherent behavior of countless microscopic quantum states manifests collectively at a visible scale, as exemplified by the supercurrent carried by innumerable finite-momentum Cooper pairs. By rigorously analyzing the time evolution of superconducting nanodevices including finite-momentum superconductors and quantum-dot Josephson junctions, we analytically derive the ubiquitous macroscopic supercurrent that originates from quantum interference between distinct many-body eigenstates, which we term as the dynamic interference supercurrent. The dynamic interference supercurrent in a system of two Andreev spin qubits exhibits multi-frequency Josephson effect in the absence of external voltage and is governed by the response of the many-body eigenfunctions (
∣r⟩) to variations in the superconducting phase
ϕ, determined by the
ϕ-space Berry connection
Crr′=⟨r∣∂ϕ∣r′⟩. The macroscopic dynamic interference supercurrent, an inherent property of the superposition state itself, enables an advanced quantum entanglement measurement of the Andreev spin qubits. These findings open new avenues for investigating superconducting nanodevice properties from a wave-function level, with substantial implications for advancing quantum science and technology in solid-state superconducting devices, such as quantum computer, communication, memory, and sensor.
In this thesis we present theoretical investigations of the effects of Andreev bound states on the current transport in superconducting interferometers. We also investigate the slow dynamics of the Andreev states in a superconducting point contact, and the possible application as a quantum bit. We consider superconductor-normal metal-superconductor (SNS) and normal metalsuperconductor (NS) interferometers, where the contact region is a Y-shaped normal metal wave guide, and the two connection points to the same superconducting electrode can have different phases. The electric current in the interferometer is calculated as a function of the applied voltage and the phase difference . Andreev reflection in SNS and NS interferometers incorporates two features: interference in the arms of the Y-shaped normal region, and interplay with Andreev resonances. The latter feature yields rich phase dependent current structures in the subgap voltage region. The interference effect leads to a suppression of the current structures at . We investigate the effects on the Josephson current in NS interferometers due to current injection from the normal electrode. The two main effects of the nonequilibrium situation are: nonequilibrium population of the Andreev levels, which can result in enhancement, suppression, or even sign reversal of the Josephson current, and an anomalous interference Josephson effect, which gives rise to a long range Josephson effect, increasing with the voltage up to the superconducting gap . The two Andreev states in a superconducting quantum point contact can be accessed for manipulation and measurement by embedding the point contact in a superconducting loop. We calculate an effective Hamiltonian for the slow dynamics of the Andreev two-level system in the ring. Furthermore, we discuss methods of manipulation of the Andreev levels, and coupling of qubits. The state of the Andreev two-level system can be read out by monitoring the macroscopic quantum tunneling in a current biased Josephson junction, which is embedded in the superconducting ring of the qubit. We discuss the effects on the qubit, the readout scheme and the signal-to-noise ratio. THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Coherent processes in Superconducting quantum interferometers and qubits
The new superconductivity theory that attributes the
U(1) superconductivity phase to a Berry phase arising from many-body wave functions is applied to the circuit quantization for superconducting qubits. The phase-charge duality required for the occurrence of superconductivity in the standard theory becomes irrelevant in the new theory, and the absence of a dissipative quantum phase transition in Josephson junctions is explained. It is shown that a charge-decaying term leads to the compact phase description, and the appearance of Shapiro steps is explained without introducing normal current.