The ability to detect the presence of a single, travelling photon without destroying it has been a long standing project in optics and is fundamental for applications in quantum informationand measurement. The realization of such a detector has been complicated by the fact that photon- photon interactions are very weak at optical frequencies. At microwave frequencies, very strong photon-photon interactions have been demonstrated. Here however, the single-photon detector has been elusive due to the low energy of the microwave photon. In this article, we present a realistic proposal for quantum nondemolition measurements of a single propagating microwave photon. The detector design is built on a of chain of artificial atoms connected through circulators which break time-reversal symmetry, making both signal and probe photons propagate in one direction only. Our analysis is based on the theory of cascaded quantum systems and quantum trajectories which takes the full dynamics of the atom-field interaction into account. We show that a signal-to-noise ratio above one can be realized with current state of the art microwave technology.
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 polarisabilitymodel 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.