Simultaneous suppression of time and energy uncertainties in a single-photon frequency comb state

Abstract: A single photon prepared in a time-energy state described by a frequency comb combines the extreme precision of energy defined by a single tooth of the comb with a high sensitivity to small shifts in time defined by the narrowness of a single pulse in the long sequence of pulses that describe the frequency comb state in the time domain. We show how this simultaneous suppression of time and energy uncertainties can be described by a separation of scales and compare this with the suppression of uncertainties in the two particle correlations of an entangled state. To illustrate the sensitivity of the frequency comb states to small shifts in time and frequency, we consider the Hong-Ou-Mandel dips observed in two-photon interference when both time- and frequency shifts between the input photons are varied. It is shown that the interference of two photons in equivalent frequency comb states results in a two dimensional Hong-Ou-Mandel dip that is narrow in both time and frequency, while the corresponding entangled photon pairs are only sensitive to temporal shifts. Frequency comb states thus represent a unique and different approach towards quantum operations beyond the uncertainty limit.