Theory of microwave single-photon detection using an impedance-matched<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math>system

Abstract

By properly driving a qubit-resonator system in the strong dispersive regime, we implement an ``impedance-matched'' $\ensuremath{\Lambda}$ system in the dressed states, where a resonant single photon deterministically induces a Raman transition and excites the qubit. Combining this effect and a fast dispersive readout of the qubit, we realize a detector of itinerant microwave photons. We theoretically analyze the single-photon response of the $\ensuremath{\Lambda}$ system and evaluate its performance as a detector. We achieve a high detection efficiency without relying on precise temporal control of the input pulse shape and under a conservative estimate of the system parameters. The detector can also be reset quickly by applying microwave pulses, which allows a short dead time and a high repetition rate.