Zero-Area Single-Photon Pulses

Broadband single photons are usually considered not to couple efficiently to atomic gases because of the large mismatch in bandwidth. Contrary to this intuitive picture, here we demonstrate that the interaction of ultrashort single photons with a dense resonant atomic sample deeply modifies the temporal shape of their wave packet mode without degrading their nonclassical character, and effectively generates zero-area single-photon pulses. This is a clear signature of strong transient coupling between single broadband (THz-level) light quanta and atoms, with intriguing fundamental implications and possible new applications to the storage of quantum information.

Figure 1

Experimental setup. Heralded single-photon pulses interact with a resonant Rb vapor and are analyzed by a balanced homodyne detector (BHD). A seed coherent pulse is used to provide reference classical pulses in the same spatiotemporal mode of the single photons. HT is a high-transmission beam splitter, LBO is a lithium triborate crystal for second harmonic generation. All other symbols are defined in the text.

Figure 2

Experimental visibility of the interference fringes as a function of the delay (linear cross-correlation) between an unmodulated LO pulse of $\approx 100\mathrm{fs}$ FWHM duration and classical pulses passing through the resonant Rb cell. At higher temperatures, corresponding to higher estimated Rb densities, the pulses are seen to acquire a typical zero-area shape extending over several picoseconds. Solid black curves are field amplitudes calculated according to Eq. (1), with optical depths ${\alpha }_{0}l=70,180,440,1000,2200$ (from top to bottom), and using for $T_2$ the Doppler inhomogeneous lifetimes (between 280 and 260 ps) at the measured temperatures.

Figure 3

Measured homodyne efficiency curves (in logarithmic scale) as a function of the delay between the unmodulated LO pulses and heralded single photons that interacted with the Rb atoms in the cell. The temporal mode of the single photons is heavily distorted at sufficiently high cell temperatures. Theoretical intensity curves calculated with the same parameters of Fig. 2 are shown in the insets.

Figure 4

Experimental data and theoretical calculations for the maximum homodyne efficiency in the detection of distorted single-photon wave packets. Red (light gray) points, experimental data for detection with unmodulated LO; blue (dark gray) points, experimental data with optimally shaped LO; red (light gray) and blue (dark gray) solid curves, expected maximum homodyne efficiency in the two cases (including the effect of limited spectral resolution in the LO shaper). (a) and (b) show the reconstructed Wigner functions of the states, corrected for a detection efficiency of 78.5%, as measured in the LO mode for the two cases at $115°\mathrm{C}$, with and without LO shaping, respectively.