Measuring the interferences between past and future quantum states in the resonant fluorescence of a superconducting qubit

Abstract

When an atom or substance is irradiated, it can reemit some radiation by fluorescence, a process in which the transition from excited to ground state produces a photon. For a two-level system irradiated at resonance, the Rabi oscillations between ground and excited states leave a footprint in the resonant fluorescence. This can be seen in the fluorescence spectral density by the appearance of the so- called Mollow triplet, which is made of two side peaks around resonance. In a quantum information viewpoint, one may ask what information about the qubit is contained in the fluorescence. In order to answer this question optimally, one needs a system where both the qubit state and the fluorescence field can be measured in time. Superconducting qubits in cavity are fit for this task. We resonantly drove a superconducting qubit in a non-resonant cavity and measured the transmitted field as a function of time. Using the coupling between qubit and cavity it was also possible to measure whether the qubit was in ground or excited state at an arbitrary time. This experiment demonstrates how information about the qubit leaks out through fluorescence. In particular, the average values of the fluorescence measurement pre and post-selected on the qubit state exhibit non-classical weak values and perform a direct tomography of the non-hermitian field operator. This work provides a direct illustration of weak values in open systems which is perfectly explained by a recent theory.