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TT: Fachverband Tiefe Temperaturen
TT 49: Poster Session: Superconductivity
TT 49.45: Poster
Mittwoch, 3. April 2019, 15:00–18:30, Poster D
Quantization of non-reciprocal, singular superconducting circuits — •Martin Rymarz1,2 and David DiVincenzo1,2 — 1Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany — 2Peter Grünberg Institut: Theoretical Nanoelectronics, Research Center Jülich, D-52425 Jülich, Germany
Non-reciprocal circuit elements play an essential role for the practical realization of a solid-state quantum computer, independent of the chosen implementation. For that matter, non-reciprocal circuit elements often constitute the interface between the quantum and classical description of an electrical network.
In electrical network theory, the gyrator proposed by Tellegen in 1948 is considered to be the most fundamental non-reciprocal circuit element. The miniaturization of the actual device allows for the description of the gyrator within the lumped element model.
We propose a possible incorporation of the gyrator into circuit Quantum Electrodynamics using node fluxes. In theory effective descriptions of circuits involving gyrators can easily result in singular Lagrangians, which cannot be transformed to the corresponding Hamiltonian using the Legendre transformation since they describe constrained systems. For this reason, a generalization to the quantization of non-reciprocal, singular circuits will be presented, giving rise to physically as well as mathematically interesting models such as the Hofstadter Hamiltonian promising an implementation of the GKP code.