Direct Characterization of Ultrafast Energy-Time Entangled Photon Pairs

Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.

Figure 1

Experimental setup. (a) Frequency-entangled photons are created through spontaneous parametric down-conversion of an ultrafast pulse from a frequency-doubled Ti:sapphire laser. Measurements of either the frequency or the time of arrival of each photon can be performed in coincidence. (b) Spectral measurements are made with dual single-photon monochromators. Temporal measurements are performed using optically gated single-photon detection. The gating is implemented via noncollinear sum-frequency generation between a strong gate pulse from the Ti:Sapph laser and the signal or idler. The dispersion of the signal and idler photons is controlled with a combination of single-mode fibers and grating compressors before the up-conversion. The up-converted signal is filtered with bandpass filters which remove the background second harmonic generation from the gate pulse. Temporal and frequency measurements are performed in coincidence to observe the spectral and temporal features of the photons.

Figure 2

Spectral and temporal characterization of ultrafast photons. A combination of spectral and temporal measurements are made in coincidence in order to measure (a) the joint spectrum, (d) the joint temporal intensity, as well as (b),(c) the cross-correlations between the time (frequency) of the idler and the frequency (time) of the signal. (a) Frequency anticorrelations with statistical correlation $-0.9951\pm 0.0001$ are accompanied with (d) positive correlations $0.987\pm 0.004$ in the signal-idler arrival times. The time-frequency plots (b),(c) show little correlation—$(0.111\pm 0.008)$ and ($-0.106\pm 0.008$), respectively—indicating low dispersion in the signal and idler photons. White lines on all plots correspond to $1\sigma$ and $2\sigma$ contours of two-dimensional Gaussian fits.

Figure 3

Histograms of the frequency and time of arrival correlations between signal and idler photons. Coincidences are confined to a small region in (a) with $\mathrm{\Delta }({\omega }_s+{\omega }_i)=(1.429\pm 0.006){\mathrm{ps}}^{-1}$ ($1.329\pm 0.007{\mathrm{ps}}^{-1}$ when corrected for the finite resolution of the gate), compared to (b) with $\mathrm{\Delta }({\omega }_s-{\omega }_i)=(18.16\pm 0.05){\mathrm{ps}}^{-1}$ ($18.16\pm 0.05{\mathrm{ps}}^{-1}$), indicating strong anticorrelations in frequency. Likewise, coincidences are localized in (d) with $\mathrm{\Delta }(t_s-t_i)=0.203\pm 0.005\mathrm{ps}$ ($0.110\pm 0.010\mathrm{ps}$), compared to (c) with $\mathrm{\Delta }(t_s+t_i)=1.066\pm 0.016\mathrm{ps}$ ($1.052\pm 0.016\mathrm{ps}$), corresponding to strong correlations in the time of arrival. From these values, we find a joint uncertainty product $\mathrm{\Delta }({\omega }_s+{\omega }_i)\mathrm{\Delta }(t_s-t_i)=0.290\pm 0.007(0.15\pm 0.01)$.

Figure 4

Nonlocal dispersion cancellation observed in the joint temporal distributions. Joint temporal intensity for the signal and idler pair (a) without dispersion, (b) with a positive dispersion of $A_s=(0.0373\pm 0.0015){\mathrm{ps}}^2$ on the signal, (c) with a negative dispersion of $A_i=(-0.0359\pm 0.0014){\mathrm{ps}}^2$ on the idler, and (d) with both a positive dispersion of $A_s=(0.0373\pm 0.0015){\mathrm{ps}}^2$ on the signal and a negative dispersion of $A_i=(-0.0359\pm 0.0014){\mathrm{ps}}^2$ on the idler. For each, we measure the uncertainty in the difference in arrival times of the signal and idler $\mathrm{\Delta }(t_s-t_i)$ and find (a) $0.235\pm 0.003\mathrm{ps}$ ($0.162\pm 0.005\mathrm{ps}$ when corrected for the finite resolution of the gate), (b) $0.708\pm 0.013\mathrm{ps}$ ($0.688\pm 0.013\mathrm{ps}$), (c) $0.714\pm 0.010\mathrm{ps}$ ($0.693\pm 0.011\mathrm{ps}$), (d) $0.245\pm 0.004\mathrm{ps}$ ($0.175\pm 0.006\mathrm{ps}$). We witness nonlocal dispersion cancellation in the timing uncertainty $t_s-t_i$ in (d), as the width $\mathrm{\Delta }(t_s-t_i)$ remains almost unchanged from the one measured in (a).