Transconductance quantization in a topological Josephson tunnel junction circuit

Abstract

Superconducting circuits incorporating Josephson tunnel junctions are widely used for fundamental research as well as for applications in fields such as quantum information and magnetometry. The quantum coherent nature of Josephson junctions makes them especially suitable for metrology applications. Josephson junctions suffice to form two sides of the quantum metrology triangle, relating frequency to either voltage or current, but not its base, which directly links voltage to current. We propose a five Josephson tunnel junction circuit in which simultaneous pumping of flux and charge results in quantized transconductance in units $4e^2/h=2e/{\Phi }_0$, the ratio between the Cooper pair charge and the flux quantum. The Josephson quantized Hall conductance device (JHD) is explained in terms of intertwined Cooper pair pumps driven by the AC Josephson effect. We discuss the experimental implementation as well as optimal configuration of external parameters and possible sources of error. JHD has a rich topological structure and demonstrates that Josephson tunnel junctions are universal, capable of interrelating frequency, voltage, and current via fundamental constants.

Accepted, revised version (13 pages, 8 figures)

References in corpus (14)

• Observation of Berry's Phase in a Solid State Qubit
• Observation of topological transitions in interacting quantum circuits
• Measuring a topological transition in an artificial spin 1/2 system
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Experimental determination of the Berry phase in a superconducting charge pump
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• Topological Andreev bands in three-terminal Josephson junctions
• Nanoampere pumping of Cooper pairs
• Connecting Berry's phase and the pumped charge in a Cooper pair pump
• Quantum synchronization and transresistance quantization in superconducting devices
• The Cooper Pair Pump as a Quantized Current Source
• The ampere and the electrical units in the quantum era
• Topological quantization by controlled paths: application to Cooper pairs pumps
• Current to frequency conversion in a Josephson circuit

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• Non-hermitian topology in multiterminal superconducting junctions
• Tensor Monopoles in superconducting systems
• Quantum circuits with multiterminal Josephson-Andreev junctions
• A quantum interferometer for quartets in superconducting three-terminal Josephson junctions
• Ultralong-distance quantum correlations in three-terminal Josephson junctions
• Proposal for detecting the $\pi -$shifted Cooper quartet supercurrent
• Ground state topology of a four-terminal superconducting double quantum dot
• Charge quantization and detector resolution
• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Quasiperiodic circuit quantum electrodynamics
• Two-tone spectroscopy of high-frequency quantum circuits with a Josephson emitter
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Magnetointerferometry of multiterminal Josephson junctions
• Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions
• Josephson tunnel junction arrays and Andreev weak links: linked by a single energy-phase relation
• Tunable Josephson voltage source for quantum circuits