Investigation of resonant and transient phenomena in Josephson junction flux qubits

Abstract

We present an analytical and computational study of resonances and transient responses in a classical Josephson junction system. A theoretical basis for resonances in a superconducting loop with three junctions is presented, outlining both the direct relationship between the dynamics of single-and multijunction systems and the direct relationships between observations of the classical counterparts to Rabi oscillations, Ramsey fringes, and spin-echo oscillations in this class of systems. We show simulation data along with analytical analyses of the classical model, and the results are related to previously reported experiments conducted on three junction loops. We further investigate the effect of off-resonant microwave perturbations to, e.g., the Rabi-type response of the Josephson system, and we relate this response back to the nonlinear and multivalued resonance behavior previously reported for a single Josephson junction. The close relationships between single and multijunction behaviors demonstrate the underlying dynamical mechanism for a whole class of classical counterparts to expected quantum-mechanical observations in a variety of systems, namely, the resonant and transient behavior of a particle in an anharmonic potential well with subsequent escape.

A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures

“…However, it was soon demonstrated that even these features could be explained as consequences of the RCSJ model of Josephson systems. Both Ramsey fringes [55] and spin echo oscillations were reproduced for a single junction system [56] and for SQUIDs [57]. Ramsey fringes and spin echo-like effects could be activated in Josephson junction systems by appropriate combined sequences of pumping and probe pulses.…”

“…38 (Fig 4 from [52]) we show Rabi oscillations and Ramsey fringes measured on a SQUID system investigated from the "quantum" point of view, (Fig. 5 from [57]) we show results of RCSJ simulations of the same system. As can be seen in these cases, like in all the others already discussed, the agreement of the RCSJ output with the experiments is remarkable.…”

“…Figure 5from[57].FIG. 40: Diagram from [58] representing the equivalent circuit of the experimental system.…”

Qubit-photon bound states in superconducting metamaterials

“…The quantum-mechanical versus a (semi)classical description of the qubit-EM field coupled systems still has certain controversies [42]. Nevertheless, at low temperatures, a fully quantum treatment is justified, while the dissipation is negligible.…”

Gradiometric flux qubits with a tunable gap

“…The resulting symmetric and anti-symmetric superposition states form the ground and excited states of the flux qubit separated by the minimal energy splittingh . Note that our terminology follows the most popular approach based on macroscopic quantum tunneling [21]; however, interpretations based on the resistively and capacitively shunted junction model [34][35][36] have not been ruled out yet. In the basis of the persistent current states and near the symmetry point, the Hamiltonian describing the flux qubit can be written as [26]…”