Single-photon limit of dispersive readout of a qubit with a photodetector

TL;DR

This paper investigates the ultimate limit of dispersive qubit readout using a single-photon probe and photodetectors, demonstrating high contrast achievable within microsecond timescales by accounting for system dynamics and counter-rotating effects.

Contribution

It introduces a detailed theoretical framework for single-photon dispersive readout, including the impact of counter-rotating terms and qubit relaxation, to optimize measurement contrast.

Findings

Achieves over 75% readout contrast in 1 microsecond

Provides compact expressions for contrast optimization

Shows how counter-rotating terms improve readout fidelity

Abstract

We study the dispersive readout of a qubit in the ultimate limit of a single-photon probe. The use of a single-photon probe avoids the errors due to nonorthogonality of coherent states. A photodetector is used in the scheme we consider. The dynamics of the system is studied using the Heisenberg-Langevin equations. We treat the counter-rotating terms in the Hamiltonian perturbatively, which leads to the Bloch-Siegert shift in the resonator frequency. It is shown how this can improve the readout. The theory of photon transport through the qubit and the resonator it couples to is provided while taking the effect of the counter-rotating terms into account. To calculate the readout contrast, we use two approaches. The first one neglects the qubit relaxation and allows us to derive a compact expression for the contrast. Also, we obtain simple estimates for the system parameters to maximize the contrast. The second approach accounts for the qubit relaxation, which allows us to further improve the contrast. We demonstrate that for a readout time of 1$\mu$s, a contrast of more than 75% can be achieved for an ideal detector and single-photon source.