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TT: Fachverband Tiefe Temperaturen
TT 30: Focus Session: Exploring Quantum Entanglement with Superconducting Qubits and Resonators (joint session QI/TT)
TT 30.10: Talk
Tuesday, March 19, 2024, 13:00–13:15, HFT-FT 131
Quantum phases in frustrated arrays of Josephson junctions: Effective XY spin models — •Benedikt Pernack, Mikhail V. Fistul, and Ilya M. Eremin — Theoretische Physik III, Ruhr-Universität Bochum, Bochum, Germany
Motivated by experiments on superconducting qubit networks [1,2], we present here a detailed analysis of collective quantum phases occurring in frustrated quasi-1D saw-tooth arrays of small (quantum) Josephson junctions (f-JJAs). Frustration is introduced through the periodic arrangement of 0- and π-Josephson junctions with the Josephson coupling energies of different signs. In the frustrated regime the classical ground state is highly degenerate and formed by various patterns of vortex/antivortex penetrating each basic cell of an f-JJA.
In the quantum frustrated regime using the variational approach we derive an effective XY spin Hamiltonian. Depending on the length L of an f-JJA we obtain two very different regimes: a) L ≪ Lcr=√C/C0, where C and C0 are a 0-Josephson junction and superconducting island capacitances, accordingly, the quantum superposition of vortex and antivortex in a single cell dominates; b) L ≫ Lcr=√C/C0, the quantum superposition of vortex and antivortex is strongly suppressed, and a long (short) exchange interaction is established. In latter case using mean-field analysis and numerical diagonalization of the effective XY spin model, we characterize quantum phases in various f-JJAs.
Keywords: network of superconducting islands; frustrated Josephson junction arrays; network of supercoflux qubits; Josephson coupling and charging energies; xy spin model with a long-range interaction