Single-Photon Hologram of a Zero-Area Pulse

Single photons exhibit inherently quantum and unintuitive properties such as the Hong-Ou-Mandel effect, demonstrating their bosonic and quantized nature, yet at the same time may correspond to single excitations of spatial or temporal modes with a very complex structure. Those two features are rarely seen together. Here we experimentally demonstrate how the Hong-Ou-Mandel effect can be spectrally resolved and harnessed to characterize a complex temporal mode of a single-photon—a zero-area pulse—obtained via a resonant interaction of a terahertz-bandwidth photon with a narrow gigahertz-wide atomic transition of atomic vapor. The combination of bosonic quantum behavior with bandwidth-mismatched light-atom interaction is of fundamental importance for deeper understanding of both phenomena, as well as their engineering offering applications in characterization of ultrafast transient processes.

Figure 1

Spectral single-photon holography of an ultrafast ZA photon. Starting from a pair of identical broadband (10 nm, 100 fs) single photons (signal, idler), one (signal) interacts with hot ${}^{87}\mathrm{Rb}$ vapor, forming a ZA temporal shape and acquiring a spectral phase. Signal and idler photons are interfered on a balanced BS where output $\pm$ modes are spectrally resolved via diffraction gratings. Coincidence detection between wavelength ${\lambda }_{\pm }$ components shows a footprint of the ZA single photon’s SPHI—a manifest of the HOM effect. Inset: simulated map of spectrally resolved (${\lambda }_{\pm }$) coincidences—an analog of classical interferogram.

Figure 2

(a) Source of single-photon pairs. 100 fs pulses from Ti:Sapphire laser (central wavelength 795 nm) are frequency doubled in a BBO crystal (BBO-SHG) and used to pump type-I SPDC in the second crystal (BBO). Pairs of photons are spectrally filtered (IF, see main text) and coupled to single-mode polarization-maintaining (PM) fibers (single mode, SM) which select highest-correlated transverse modes from the SPDC emission cone. Dichroic mirrors (DM for $\approx 800\mathrm{nm}$, DMB for $\approx 400\mathrm{nm}$) and a 400 nm bandpass (40 nm FWHM) interference filter (IFB-IF for 400 nm) separate pumping beams. Quarter- and half-wave plates (QWPs and HWPs, respectively) allow for polarization matching to the PM fiber. (b) Setup for SSPH. Signal photon passes through heated Rb cell, interacting resonantly with D1 Rb line and obtaining a SPHI profile. The output $\pm$ modes of the interferometer are spatially separated on another PBS. Imaging setup (focal length $f_1=150\mathrm{mm}$) superimposes the $\pm$ modes spatially on a diffraction grating while separating them angularly. The last HWP in the ($+$) mode path rotates the polarization to be perpendicular to the grating grooves, ensuring maximal efficiency. The grating is far-field imaged (focal length $f_2=300\mathrm{mm}$) onto an intensified single-photon–sensitive camera (I-sCMOS), spatially separating the spectral components of $\pm$ modes into distinct camera frame regions ($\pm$).

Figure 3

Spectral single-photon holograms of an ultrafast 100 fs photon resonantly interacting with Rb vapor heated to (a) $T_1=188°\mathrm{C}$, (b) $T_2=174°\mathrm{C}$, (c) $T_3=86°\mathrm{C}$. Left column: experimental results, i.e., the observed photon-number covariance $\mathcal{C}({\lambda }_{+},{\lambda }_{-})$ (coincidences with subtracted background) in spectral coordinates ${\lambda }_{\pm }-{\lambda }_0$ between $\pm$ ports of a BS. The BS interferes the measured photon with the reference. Central column: corresponds to a theoretical prediction of a spectrally resolved coincidence probability $P_c({\lambda }_{+},{\lambda }_{-})$ with no imperfections ($\mathcal{V}=1$), as given by Eq. (4). Right column: theoretical prediction for the SPHI ${\phi }_s({\lambda }_{-}-{\lambda }_0)$ modulo $2\pi$, given by Eq. (1).