Can a weak measurement of photon number in an interferometer be negative? Experimental progress.

We demonstrate experimental progress towards a distinctly quantum measurement: when a single-photon is found to be in a particular final state ("post-selected") after a polarization interferometer, a weak measurement of the number of photons in one of the arms is predicted to yield a negative number. We perform this weak measurement of photon number by sending light through a cold cloud of 85-Rubidium atoms in an EIT configuration, in which a dispersive cross-Kerr optical nonlinearity writes a phase shift on a continuous-wave “probe” beam, proportional to the photon number of a “signal” beam. A single signal photon is sent into a polarization interferometer, in which only one of the two polarizations (corresponding to one “arm” of the interferometer) drives this nonlinear effect. Our measurement, together with the weak value amplification experiment of Hallaji et al. (Nature Physics 13, 540-544 (2017), where they measured the photon number in the opposing arm for a resulting positive, but amplified, value), give us an more complete picture about the atom-light interaction of a single photon in dispersive medium.