Population inversion through charge measurement using a superconducting single-electron transistor biased in the subgap regime

TL;DR

This paper demonstrates how a superconducting single-electron transistor can induce population inversion in a coupled two-level system through charge measurement, revealing new insights into quantum back-action and qubit readout mechanisms.

Contribution

It introduces a novel mechanism for population inversion via a superconducting SET biased in the subgap regime, and analyzes its effects on a Cooper Pair Box qubit using a real-time Keldysh approach.

Findings

Population inversion occurs during charge measurement with the SSET.

The SSET can relax the TLS even with negligible current flow.

Resonant Cooper-pair tunneling underpins the population inversion.

Abstract

We show how population inversion (PI) occurs in a two-level system (TLS) while measuring its charge using a capacitively coupled superconducting single-electron transistor (SSET), biased in the subgap regime, where the current through the SSET is carried by different cycles involving tunneling of both Cooper pairs and quasiparticles. The PI is directly associated with the resonant nature of the Cooper-pair tunneling. We also show how the SSET may strongly relax the TLS, although there is negligible current flowing through the SSET, i.e. it is turned off. The calculation of the quantum back-action noise is based on a real-time Keldysh approach. We specifically discuss the case of a Cooper Pair Box qubit with the SSET capacitively coupled as read-out device.