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arXiv:0812.2394 · Physical Review B

Coherent superpositions of single semifluxon states in a 0−π Josephson junction

E. Goldobin, Karl Vogel, Wolfgang P. Schleich, D. Koelle, R. Kleiner

Published Feb 22, 2010• 5 citations
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Abstract

We consider a symmetric $0\text{\ensuremath{-}}\ensuremath{\pi}$ Josephson junction of length $L$, which classically can be in one of two degenerate ground states $\ensuremath{\uparrow}$ or $\ensuremath{\downarrow}$, corresponding to supercurrents circulating clockwise or counterclockwise around the $0\text{\ensuremath{-}}\ensuremath{\pi}$ boundary. When the length $L$ of the junction becomes smaller than the Josephson penetration depth ${\ensuremath{\lambda}}_{J}$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling to the neighboring well. We map this problem to the dynamics of a single particle in a periodic double-well potential and estimate parameters for which macroscopic quantum coherence may be observed experimentally. We conclude that this system is not very promising to build a qubit because (a) it requires very low temperatures to reach the quantum regime, (b) its tiny flux is hard to read out, and (c) it is very sensitive to the asymmetries between the 0 and $\ensuremath{\pi}$ parts of the junction.

DOI
10.1103/physrevb.81.054514

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Josephson junctions with a phase drop of $\ensuremath{\pi}$ in the ground state allow us to create vortices of supercurrent carrying only half of the magnetic flux quantum ${\ensuremath{\Phi}}_{0}\ensuremath{\approx}2.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{Wb}$. Such semifluxons have twofold degenerate ground states denoted $\ensuremath{\uparrow}$ (with flux $+{\ensuremath{\Phi}}_{0}/2$ and supercurrent circulating clockwise) and $\ensuremath{\downarrow}$ (with flux $\ensuremath{-}{\ensuremath{\Phi}}_{0}/2$ and supercurrent circulating counterclockwise). We investigate a molecule consisting of two coupled semifluxons in a 0-$\ensuremath{\pi}$-0 long Josephson junction. The fluxes (polarities) of semifluxons are measured by two on-chip SQUIDs. By varying the dc bias current applied to the 0-$\ensuremath{\pi}$-0 junction, we demonstrate controllable manipulation and switching between two states, $\ensuremath{\uparrow}\ensuremath{\downarrow}$ and $\ensuremath{\downarrow}\ensuremath{\uparrow}$, of a semifluxon molecule. These results provide a major step towards employing semifluxons as bits or qubits for classical and quantum digital electronics.
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We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature Tcr{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}T<Tcr​ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
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We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature TcrT_{cr}Tcr​ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux ΦΦΦ. Beyond that we predict a narrow peak in the dependence of Tcr(Φ)T_{cr}(Φ)Tcr​(Φ) occurring in the intermediate range of ΦΦΦ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113 ) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the qubit. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux qubit. In particular, when the number of Josephson junctions is increased, several low-energy modes can have frequencies lower than the qubit frequency. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of oscillations between the two counterpropagating current states at short times, followed by oscillation-like revivals at later times. We analyze how the system approaches such a dynamics as the ring's length is increased and discuss possible experimental implications of this non-adiabatic regime.