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arXiv:2505.11873

Qubit States Based on Fractional Vortices in $0-π$ Josephson Junctions

N. Stefanakis

Published May 17, 2025• 0 citations
arXivHTMLPDF

Abstract

We investigate the static properties of $0-π$ 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 $0-π$ 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.

DOI
10.48550/arxiv.2505.11873

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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.
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Long Josephson tunnel junctions are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.
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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 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.