We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximatingthe low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
exhibits a robust ground-state degeneracy and wave functions with disjoint support for appropriate circuit parameters."]In this protected regime, Cooper-pair excitons form the relevant low-energy excitations. Based on a full circuit analysis of the current-mirror device, we introduce an effective model that systematically captures the relevant low-energy degrees of freedom, and is amenable to diagonalization using Density Matrix Renormalization Group (DMRG) methods. We find excellent agreement between DMRG and exact diagonalization, and can push DMRG simulations to much larger circuit sizes than feasible for exact diagonalization. We discuss the spectral properties of the current-mirror circuit, and predict coherence times exceeding 1 ms in parameter regimes believed to be within reach of experiments.
We present design and simulation of a Josephson parametric amplifier with bandwidth exceeding 1.6 GHz, and with high saturation power approaching -90 dBm at a gain of 22.8 dB. An improvementby a factor of roughly 50 in bandwidth over the state of the art is achieved by using well-established impedance matching techniques. An improvement by a factor of roughly 100 in saturation power over the state of the art is achieved by implementing the Josephson nonlinear element as an array of rf-SQUIDs with a total of 40 junctions. WRSpice simulations of the circuit are in excellent agreement with the calculated gain and saturation characteristics.
We demonstrate Josephson junction based double-balanced mixer and phase shifter circuits operating at 6-10 GHz, and integrate these components to implement both a monolithic amplitude/phasevector modulator and a quadrature mixer. The devices are actuated by flux signals, dissipate no power on chip, exhibit input saturation powers in excess of 1 nW, and provide cryogenic microwave modulation solutions for integrated control of superconducting qubits.