From quantum circuit refrigeration to lasing: master equation approach

Recently, a “quantum circuit refrigerator” (QCR) consisting of a voltage biased superconductor–insulator–normal-metal–insulator–superconductor (SINIS) tunnel junction has been experimentally demonstrated to cool superconducting resonators [1], in agreement with theoretical expectations [2]. Theory also predict that the QCR can reset superconducting qubits fast and accurately [3]. Here we discuss a master equation approach to the dynamics of a QCR coupled to a two-level system. We find that the time evolution of the distribution function for the charge on the normal metal is slow on the scale of the qubit reset time; therefore, one can neglect the charge dynamics when calculating the reset time, validating the assumptions in Refs. [2, 3]. Replacing the normal-metal island with a quantum dot, we find an operation regime where the photon-assisted tunneling can serve as a pumping mechanism. Using our master equation approach, we investigate the possibility of lasing by coupling the quantum dot QCR to a resonator.

[1] K. Y. Tan et.al., Nat. Commun. 8 15189 (2017)
[2] M. Silveri et.al., Phys. Rev. B 96, 094524 (2017)
[3] H. Hsu et.al., Phys. Rev. B 101, 235422 (2020)