V. Vadimov

Nonlinear response theory for lossy superconducting quantum circuits

  1. V. Vadimov,
  2. M. Xu,
  3. J. T. Stockburger,
  4. J. Ankerhold,
  5. and M. Möttönen
We introduce a numerically exact and yet computationally feasible nonlinear response theory developed for lossy superconducting quantum circuits based on a framework of quantum dissipation
in a minimally extended state space. Starting from the Feynman–Vernon path integral formalism for open quantum systems with the system degrees of freedom being the nonlinear elements of the circuit, we eliminate the temporally non-local influence functional of all linear elements by introducing auxiliary harmonic modes with complex-valued frequencies coupled to the non-linear degrees of freedom of the circuit. In our work, we propose a concept of time-averaged observables, inspired by experiment, and provide an explicit formula for producing their quasiprobability distribution. Furthermore, we systematically derive a weak-coupling approximation in the presence of a drive, and demonstrate the applicability of our formalism through a study on the dispersive readout of a superconducting qubit. The developed framework enables a comprehensive fully quantum-mechanical treatment of nonlinear quantum circuits coupled to their environment, without the limitations of typical approaches to weak dissipation, high temperature, and weak drive. Furthermore, we discuss the implications of our findings to the quantum measurement theory.
arxiv pdf

Single-junction quantum-circuit refrigerator

  1. V. Vadimov,
  2. A. Viitanen,
  3. T. Mörstedt,
  4. T. Ala-Nissila,
  5. and M. Möttönen
We propose a quantum-circuit refrigerator (QCR) based on photon-assisted quasiparticle tunneling through a single normal-metal–insulator–superconductor (NIS) junction. In
contrast to previous works with multiple junctions and an additional charge island for the QCR, we galvanically connect the NIS junction to an inductively shunted electrode of a superconducting microwave resonator making the device immune to low-frequency charge noise. At low characteristic impedance of the resonator and parameters relevant to a recent experiment, we observe that a semiclassical impedance model of the NIS junction reproduces the bias voltage dependence of the QCR-induced damping rate and frequency shift. For high characteristic impedances, we derive a Born–Markov master equation and use it to observe significant non-linearities in the QCR-induced dissipation and frequency shift. We further demonstrate that in this regime, the QCR can be used to initialize the linear resonator into a non-thermal state even in the absence of any microwave drive.
arxiv pdf