Operating a contextual Stern-Gerlach apparatus

We propose a contextual cavity/circuit QED analogue and extension of the Stern-Gerlach experiment, where the pseudo-spin of a two-state atomic' transition plays the role of the ``spin'', while the resonant field driving the transition stands for the ``magnetic field''. A phase-sensitive continuous detection of the cavity field coupled to the induced atomic’ dipole affects the stability of the two distinct outcomes. The dressed states comprising the latter give their place to a self-consistent spontaneous dressed-state polarization as the driving strength is lowered. The associated evolution proves anew highly contextual, underpinned by a persistent production of coherent-state superpositions for a particular setting of the monitoring device. Finally, when bistability is absent, we employ the photoelectron `atomic’ emission statistics as a diagnostic tool of the cavity field fluctuations.