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Bulletin of the American Physical Society

Quantum Simulation of Luttinger Liquids in Josephson Transmission Lines

Roman Kuzmin, Nicholas Grabon, Nitish Mehta, Raymond Mencia, Natalia Pankratova, Moshe Goldstein, Vladimir Manucharyan

Published Mar 6, 2018• 0 citations
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We study a dynamic boundary, e.g., a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K. We demonstrate that for N≥2 there is a quantum phase transition at K≥1/2, where the TLL phases lock together at the particle position, resulting in a nonzero transconductance equal to e^{2}/Nh. The transition line terminates for strong coupling at K=1-(1/N), consistent with results at large N. Another type of a dynamic boundary is a superconducting (or a Bose-Einstein condensate) grain coupled to N≥2 TLLs; here the transition signals also the onset of a relevant Josephson coupling.
We present a new type of Josephson transmission line (JTL) in which discrete multilayer Josephson junctions are employed instead of the standard single tri-layer junction technology. It is shown via numerical simulation that such a structure supports the propagation of multiple flux quantum solitons, which are represented in this system by a 2πn kink in the phase difference across a multilayer junction of n superconductor-insulator-superconductor layers. As a practical aspect, parallel and series connected multilayer junctions in a JTL can significantly reduce the need for microstrip line inductance, thereby providing the optimal conditions for large scale integration of JTL-based logic and memory circuitry. In this article we investigate in detail through numerical simulation the properties of JTL designs with multilayer junctions, incorporating expected variations in junction characteristics. A brief description of the current fabrication of multilayer junctions for flux quantum circuitry will be provided.