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Tunable qubit based on a molecule of two fractional Josephson vortices

Dennis Manuel Heim, Karl Vogel, W. P. Schleich, D. Koelle, R. Kleiner, E. Goldobin

Published Aug 30, 2012• 0 citations
OpenAlex

Abstract

We propose a concept of a qubit based on two coupled fractional vortices pinned at two artificially created $\kappa$ 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 $I_\mathrm{inj}$ 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 $\kappa \propto I_\mathrm{inj}$ 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.

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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.
We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.
Abstract We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.
We report theoretical and experimental work on the development of a vortex qubit based on a microshort in an annular Josephson junction. The microshort creates a potential barrier for the vortex, which produces a double-well potential under the application of an in-plane magnetic field; the field strength tunes the barrier height. A one-dimensional model for this system is presented, from which we calculate the vortex-depinning current and attempt frequency as well as the interwell coupling. Implementation of an effective microshort is achieved via a section of insulating barrier that is locally wider in the junction plane. Using a junction with this geometry we demonstrate classical state preparation and readout. The vortex is prepared in a given potential well by sending a series of ``shaker'' bias-current pulses through the junction. Readout is accomplished by measuring the vortex-depinning current.
Qubit States Based on Fractional Vortices in 0−π0-π0−π Josephson Junctions
We investigate the static properties of 0−π0-π0−π Josephson junctions and their potential application as superconducting qubits. We show that fractional vortex and fractional antivortex configurations give rise to a bistable free-energy landscape with stable minima corresponding to topologically distinct fractional-vortex states. In the long-junction limit the two configurations correspond to stable equilibrium states, whereas in the short-junction limit the reduced barrier suggests enhanced quantum tunneling and hybridization between them. These results suggest that 0−π0-π0−π Josephson junctions may provide a physically meaningful platform for qubit-like two-level dynamics, provided that a finite tunneling amplitude exists between the fractional-vortex and fractional-antivortex states.
The design of a qubit based on a single Josephson vortex trapped in a shaped long Josephson junction is discussed in detail. The vortex potential is formed due to its interaction with an in-plane magnetic field and a bias current applied to the junction. The profile of the potential is calculated using a standard perturbation approach. We examine the dependence of the potential properties on the junction shape and its electrical parameters and discuss the requirements for observing quantum effects in this system. We have developed and experimentally tested methods for the preparation and read-out of vortex states of this qubit in the classical regime.
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.