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arXiv:0809.1346 · Physical Review Letters

Semifluxon Molecule under Control

Andreas Dewes, T. Gaber, D. Koelle, R. Kleiner, E. Goldobin

Published Dec 9, 2008• 23 citations
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Abstract

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.

DOI
10.1103/physrevlett.101.247001

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Josephson junctions with a phase drop of \ensuremathπ\ensuremath{\pi}\ensuremathπ in the ground state allow us to create vortices of supercurrent carrying only half of the magnetic flux quantum \ensuremathΦ0\ensuremath≈2.07\ifmmode×\else\texttimes\fi10\ensuremath−15  Wb{\ensuremath{\Phi}}_{0}\ensuremath{\approx}2.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{Wb}\ensuremathΦ0​\ensuremath≈2.07\ifmmode×\else\texttimes\fi10\ensuremath−15  Wb. Such semifluxons have twofold degenerate ground states denoted \ensuremath↑\ensuremath{\uparrow}\ensuremath↑ (with flux +\ensuremathΦ0/2+{\ensuremath{\Phi}}_{0}/2+\ensuremathΦ0​/2 and supercurrent circulating clockwise) and \ensuremath↓\ensuremath{\downarrow}\ensuremath↓ (with flux \ensuremath−\ensuremathΦ0/2\ensuremath{-}{\ensuremath{\Phi}}_{0}/2\ensuremath−\ensuremathΦ0​/2 and supercurrent circulating counterclockwise). We investigate a molecule consisting of two coupled semifluxons in a 0-\ensuremathπ\ensuremath{\pi}\ensuremathπ-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-\ensuremathπ\ensuremath{\pi}\ensuremathπ-0 junction, we demonstrate controllable manipulation and switching between two states, \ensuremath↑\ensuremath↓\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath↑\ensuremath↓ and \ensuremath↓\ensuremath↑\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath↓\ensuremath↑, of a semifluxon molecule. These results provide a major step towards employing semifluxons as bits or qubits for classical and quantum digital electronics.
Josephson junctions (JJs) and junction arrays are well-studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to devise two different types of junctions: depending on the sign of the critical current density , they are called 0- or π-junctions. In turn, a 0–π junction is formed by joining two of these junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0–π boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0–π JJ is created by the phase of a complex valued Rabi frequency and we derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.
Josephson junctions and junction arrays are well studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to device two different types of junctions: depending on the sign of the critical current density, they are called 0- or pi-junction. In turn, a 0-pi junction is formed by joining two of such junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0-pi boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0-pi Josephson junction is created by the phase of a complex valued Rabi-frequency and we a derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.
The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.
We propose a concept of a qubit based on two coupled fractional vortices pinned at two artificially created κ\kappaκ discontinuities of the Josephson phase in a long Josephson junction. Each discontinuity can be created by a pair of tiny current injectors with the current IinjI_\mathrm{inj}Iinj​ applied. We map the dynamics of the system to the dynamics of a single particle in a double-well potential and calculate the effective parameters of this potential. By tuning the discontinuities κ∝Iinj\kappa \propto I_\mathrm{inj}κ∝Iinj​ during the experiment we are able to control the parameters of the effective double-well potential as well as to initialize the fractional vortex molecule to a desired state. The system can be used to study macroscopic quantum phenomena involving tailored vortex matter.
In recent years, various novel phenomena such as π-state (π-junction) and long-ranged supercurrents emerged in ferromagnetic Josephson junctions (superconductor/ferromagnet/superconductor junctions) have been studied so actively. An attractive device application of the ferromagnetic π-junction is a flux-bias-free superconducting flux quantum bit (qubit). By inserting the π-junction in the superconducting loop of the flux qubit, an external flux bias corresponding to half flux quantum, which is required for the operation of the conventional flux qubits, becomes unnecessary. This flux-bias-free feature is a great advantage in the realization of large-scale quantum circuits with many qubits. In the talk, we will present recent progress on the development of NbN-based ferromagnetic Josephson junctions which is suitable for the quantum circuits. We also show the experimental results on the several types of the quantum circuits with the NbN-based ferromagnetic π-junction.