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

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 we 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 an alternative approach to quantum operations beyond the uncertainty limit.