Breakdown of the cross-Kerr scheme for Photon Counting

TL;DR

This paper demonstrates that the cross-Kerr effect cannot reliably be used for photon counting in single photon detection systems, challenging previous assumptions about its effectiveness in quantum measurement applications.

Contribution

The study shows that the atomic three-level model for a transmon does not support the nonlinear polarization predictions of the cross-Kerr effect, questioning its suitability for photon counting.

Findings

Cross-Kerr effect cannot resolve single photon signals above quantum noise.

Transmon models do not support the nonlinear polarization predicted by the cross-Kerr effect.

Conclusions apply to both microwave and optical systems.

Abstract

We show, in the context of single photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarisability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single photon applications. Our results are presented in the context of a transmon in a one dimensional microwave waveguide, but the conclusions also apply to optical systems.