Ultrafast quantum interferometry with energy-time entangled photons

Many quantum advantages in metrology and communication arise from interferometric phenomena. Such phenomena can occur on ultrafast timescales, particularly when energy-time entangled photons are employed. These have been relatively unexplored as their observation necessitates time resolution much shorter than conventional photon counters. Integrating nonlinear optical gating with conventional photon counters can overcome this limitation and enable subpicosecond time resolution. Here, using this technique and a Franson interferometer, we demonstrate high-visibility quantum interference with two entangled photons, where the one- and two-photon coherence times are both subpicosecond. We directly observe the spectral and temporal interference patterns, measure a visibility in the two-photon coincidence rate of $(85.3\pm 0.4)\%$, and report a Clauser–Horne–Shimony–Holt–Bell parameter of $2.42\pm 0.02$, violating the local-hidden variable bound by 21 standard deviations. The demonstration of energy-time entanglement with ultrafast interferometry provides opportunities for examining and exploiting entanglement in previously inaccessible regimes.

Figure 1

Franson interferometer concept diagram. (a) Nonlocal interference can be seen by sending each photon of a two-photon energy-time entangled pair through an unbalanced interferometer. Each photon is split into early and late time bins and recombined with a phase applied to one bin. (b) In each arm of the Franson interferometer, the delays and phases are implemented through birefringent material and wave plates, creating a path difference on subpicosecond timescales between the short and long paths. A birefringent crystal ($\alpha$-BBO) splits a horizontally polarized photon into a diagonal and a delayed antidiagonal mode. A quarter-wave plate (QWP) converts diagonal and antidiagonal to left- and right-circularly polarized light. A half-wave plate (HWP) introduces a phase between the circularly polarized photons. Both polarizations are then projected into the horizontal state with a polarizing beam splitter (PBS). See Appendix pp2 for further details.

Figure 2

Experimental setup. (a) A Ti:sapphire laser pulse [775 nm, 3.8 W average power, 0.120 ps (s.d.) pulse width], is frequency doubled in 2 mm of $\beta$-bismuth borate (BiBO). After spectral filtering with a 0.2 nm FHWM bandpass filter, the second harmonic [387.6 nm, 300 mW average power, approximately 0.940 ps (s.d.) coherence time] pumps a 5 mm BiBO crystal for type-I spontaneous parametric downconversion (SPDC) generating frequency entangled photons centered at 730 and 827 nm. The photons are separated by a dichroic mirror and their bandwidth is controlled by using tunable edge filters. Each photon passes through an unbalanced interferometer consisting of $\alpha$-BBO, QWP, HWP, and PBS. We use 2.00 and 2.25 mm of $\alpha$-BBO to create a difference between the short and long paths of ${\tau }_s=0.820$ ps and ${\tau }_i=0.910$ ps on the signal and idler side, respectively. The output of the Franson interferometer is coupled into single-mode fibers. (b) Spectral measurements are made with single-photon spectrometers. (c) Temporal measurements are made by using ultrafast gating with a strong laser pulse. A pair of grating compressors compensates for the dispersion introduced by the fibers.

Figure 3

The joint spectral intensity and joint temporal intensity of the two-photon state shown (a), (d) before and (b), (c), (e), (f) after the Franson interferometer. After the interferometer, different fringe patterns are observed in the joint spectrum for (b) constructive and (c) destructive interference. The interferometer shifts the temporal profile in (d) creating four different combinations of paths: short-short, short-long, long-short, and long-long. We observe (e) constructive and (f) destructive interference in the central peak between the cases where the photons both take the short path and both take the long path. These correspond to two-photon states where the signal and idler phases sum to (b), (e) ${\varphi }_i+{\varphi }_s=0$, and (c), (f) ${\varphi }_i+{\varphi }_s=\pi$.

Figure 4

Two-photon interference fringes. Franson interference between the upconverted signal and idler pair is measured by varying the signal and idler phases while setting the idler gate delay and signal gate delay halfway between the short and long paths of each side of the Franson interferometer. (a) We observe high-visibility interference with fringe oscillations along the diagonal which depend on the sum of the two phases ${\varphi }_s+{\varphi }_i$. (b) Weighted average of the coincidences and weighted average of the singles for the signal and idler pair as viewed as a function of their phase sum. Interference fringes display oscillations of $(85.3\pm 0.4)\%$ visibility, while the singles detection events show no apparent oscillations.

Figure 5

Spectral bandwidths and temporal widths for a frequency anticorrelated two-photon SPDC state. (a) The single-photon spectral bandwidth $\mathrm{\Delta }\omega$ is given by the marginal distribution obtained by projecting the joint spectral intensity onto either the signal or idler axes. The single-photon coherence time, the timescale over which interference in the single-photon rates can occur, is related to the inverse of the single-photon spectral bandwidth, ${\tau }_c^{\left(1\right)}=1/\mathrm{\Delta }\omega$. (b) The heralded spectral bandwidths $\mathrm{\Delta }{\omega }_h$ are the spectral bandwidths of the signal or idler photon when the frequency of the other is fixed. (c) The two-photon spectral bandwidths for the semiminor, $\mathrm{\Delta }({\omega }_s+{\omega }_i)$, and semimajor axes, $\mathrm{\Delta }({\omega }_s-{\omega }_i)$, are obtained by projecting the joint spectral intensity along the corresponding diagonal axes ${\omega }_s\pm {\omega }_i$. The two-photon coherence time, the timescale over which interference in the coincidences can occur, is related to the inverse of the two-photon spectral bandwidth, ${\tau }_c^{\left(2\right)}=1/\mathrm{\Delta }({\omega }_s+{\omega }_i)$. (d)–(f) The marginal temporal widths $\mathrm{\Delta }t$, the heralded temporal widths $\mathrm{\Delta }{t}_h$, as well as the two-photon temporal widths $\mathrm{\Delta }(t_s\pm t_i)$ are obtained from the joint temporal intensity in the same way as their spectral analogs.