Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing

Measuring a spin-1/2 along one direction projectively maximally randomizes the outcome of a following measurement along a perpendicular direction. Here, using either projective or weak measurements, we explore the dynamics of a superconducting qubit for which we measure simultaneously the three components x, y and z of the Bloch vector.

The x and y components are obtained by measuring the two quadratures of the fluorescence field emitted by the qubit. Conversely the z component is accessed by probing an off-resonant cavity dispersively coupled to the qubit. The frequency of the cavity depends on the energy of the qubit and the strength of this last measurement can be tuned from weak to strong in situ by varying the power of the probe.

In this experiment, the tracked system state diffuses inside the Bloch sphere and performs a random walk whose steps obey specific rules revealing the backaction of incompatible quantum measurements. The associated quantum trajectories follow a variety of dynamics ranging from diffusion to Zeno blockade. Their peculiar dynamics highlight the non trivial interplay between the backaction of the two aforementioned incompatible measurements.