Experimental evidence that a photon can spend a negative amount of time in an atom cloud.

If a photon resonant with an atomic transition is transmitted through a cloud of atoms, how much time do atoms spend in their excited state? One potential answer is that excited atoms are the ones that lead to loss through spontaneous emission and that, therefore, post-selecting on transmission would lead to no atomic excitation. Alternatively, one might expect that because transmitted photons pass through the entire medium, they induce more atomic excitation than photons lost partway through the medium. To address this question, we previously used the cross-Kerr effect to measure the atomic excitation time and correlate it with photon transmission through a cloud of rubidium atoms. Our results indicated that the time atoms spend in the excited state due to a transmitted photon is not zero but comparable to that of the average incident photon, regardless of whether it is transmitted. Our measurement can be understood semi-classically in terms of coherent forward emission, but a quantum description was needed to make quantitative predictions which can be compared to an experiment. Eventually, we found such a description using quantum trajectory theory and the weak value formalism. To our surprise, the formalism predicted that the time atoms spend excited due to a transmitted photon is always equal to the group delay of the transmitted photon, even when that quantity is negative! I will present recent experiments which have confirmed this prediction. These experiments establish a rigorous equivalence between the atomic excitation time and the group delay even on resonance and necessitate a reinterpretation of the physical meaning of negative group delays in optics.