Theoretical study of reflection spectroscopy for superconducting quantum parametrons

TL;DR

This paper provides a theoretical framework for reflection spectroscopy of superconducting parametrons, enabling extraction of energy level information and coupling strengths crucial for quantum computing applications.

Contribution

It develops a method to calculate the reflection coefficient and extract key parameters of superconducting parametrons under oscillating pump fields.

Findings

Reflection spectra reveal energy level populations as dips or peaks.

Coupling strengths can be directly measured from decay rates.

Theoretical formulas facilitate parameter calibration in experiments.

Abstract

Superconducting parametrons in the single-photon Kerr regime, also called KPOs, have been attracting increasing attention in terms of their applications to quantum annealing and universal quantum computation. It is of practical importance to obtain information of superconducting parametrons operating under an oscillating pump field. Spectroscopy can provide information of a superconducting parametron under examination, such as energy level structure, and also useful information for calibration of the pump field. We theoretically study the reflection spectroscopy of superconducting parametrons, and develop a method to obtain the reflection coefficient. We present formulae of the reflection coefficient, the nominal external and the internal decay rates, and examine the obtained spectra. It is shown that the difference of the populations of energy levels manifests itself as a dip or peak in the amplitude of the reflection coefficient, and one can directly extract the coupling strength between the energy levels by measuring the nominal decay rates when the pump field is sufficiently large.