Microwave Spectroscopy of a Cooper-Pair Transistor Coupled to a Lumped-Element Resonator

TL;DR

This study investigates the microwave response of a Cooper-pair transistor coupled to a resonator, revealing how its resonance frequency varies with charge and magnetic flux, and demonstrating potential for sensitive charge detection.

Contribution

The paper presents a detailed experimental and theoretical analysis of the microwave response of a CPT-resonator system, showing excellent agreement with simulations across a wide energy range.

Findings

Resonance frequency depends strongly on charge and magnetic flux.

Excellent match between experimental data and circuit Hamiltonian simulations.

Potential application in sensitive charge measurement techniques.

Abstract

We have studied the microwave response of a single Cooper-pair transistor (CPT) coupled to a lumped-element microwave resonator. The resonance frequency of this circuit, $f_{r}$, was measured as a function of the charge $n_{g}$ induced on the CPT island by the gate electrode, and the phase difference across the CPT, $\phi_{B}$, which was controlled by the magnetic flux in the superconducting loop containing the CPT. The observed $f_{r}(n_{g},\phi_{B})$ dependences reflect the variations of the CPT Josephson inductance with $n_{g}$ and $\phi_{B}$ as well as the CPT excitation when the microwaves induce transitions between different quantum states of the CPT. The results are in excellent agreement with our simulations based on the numerical diagonalization of the circuit Hamiltonian. This agreement over the whole range of $n_{g}$ and $\phi_{B}$ is unexpected, because the relevant energies vary widely, from 0.1K to 3K. The observed strong dependence $f_{r}(n_{g},\phi_{B})$ near the resonance excitation of the CPT provides a tool for sensitive charge measurements.