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

Abstract

When a pulse of light traverses a material, it incurs a time delay referred to as the group delay. Should the group delay experienced by photons be attributed to the time they spend as atomic excitations? However reasonable this connection may seem, it appears problematic when the frequency of the light is close to the atomic resonance, as the group delay becomes negative in this regime. To address this question, we use the cross-Kerr effect to probe the degree of atomic excitation caused by a resonant transmitted photon, by measuring the phase shift on a separate beam that is weak and off-resonant. Our results, over a range of pulse durations and optical depths, are consistent with the recent theoretical prediction that the mean atomic excitation time caused by a transmitted photon (as measured via the time integral of the observed phase shift) equals the group delay experienced by the light. Specifically, we measure mean atomic excitation times ranging from $(-0.82\pm 0.31) \tau_0$ for the most narrowband pulse to $(0.54\pm 0.28) \tau_0$ for the most broadband pulse, where $\tau_0$ is the non-post-selected excitation time, given by the scattering (absorption) probability multiplied by the atomic lifetime $\tau_{\rm sp}$. These results suggest that negative values taken by times such as the group delay have more physical significance than has generally been appreciated.