Spectrally Engineering Photonic Entanglement with a Time Lens

A time lens, which can be used to reshape the spectral and temporal properties of light, requires the ultrafast manipulation of optical signals and presents a significant challenge for single-photon application. In this work, we construct a time lens based on dispersion and sum-frequency generation to spectrally engineer single photons from an entangled pair. The strong frequency anticorrelations between photons produced from spontaneous parametric down-conversion are converted to positive correlations after the time lens, consistent with a negative-magnification system. The temporal imaging of single photons enables new techniques for time-frequency quantum state engineering.

Figure 1

Temporal shaping with an up-conversion time lens. (a) In a spatial imaging system, free-space propagation spreads the spatial extent of the beam such that each portion of the beam has a distinct transverse momentum, visualized with arrows. The lens shifts the momenta in a spatially dependent fashion, which effectively reverses the momenta for off-center components, and the beam refocuses with further spatial propagation. (b) The temporal imaging system operates through an analogous principle, where chromatic dispersion spreads the temporal profile of the beam such that each temporal slice of the beam has a distinct central frequency, ranging from a redshifted leading edge $R$ to a blueshifted tail $B$. The time lens introduces a time-dependent frequency shift, which can reverse the frequency shifts and allow the wave packet to refocus itself after more chromatic dispersion is applied. The temporal structure of the pulse will be reversed, akin to an imaging system with negative magnification. In our realization, we use sum-frequency generation with a dispersed escort pulse to implement an up-conversion time lens. At each time in the interaction, the signal interacts with a different frequency of the escort, effectively enforcing a time-dependent relative frequency shift as well as a change in the carrier frequency.

Figure 2

Experimental setup. Frequency-entangled photons are created through the spontaneous parametric down-conversion of ultrafast pulses from a frequency-doubled Ti:sapphire laser. The signal photons are chirped through 34 m of single-mode fiber, while the remaining Ti:sapphire light comprises the escort pulse and antichirped in a grating-based pulse compressor. The pulses are recombined with relative delay $\tau$ for noncollinear sum-frequency generation (SFG). The up-converted signal is then isolated with bandpass filters and spectrally resolved in coincidence with the herald.

Figure 3

Joint spectra. (a) The joint spectrum measured between the signal photon and the herald immediately after down-conversion has strong frequency anticorrelations, exhibiting a statistical correlation of $-0.9702\pm 0.0002$ ($-0.9776\pm 0.0009$ when corrected for finite spectrometer resolution). (b) After sum-frequency generation, the joint spectrum between the up-converted signal photon and the herald exhibits strong positive frequency correlations, with a statistical correlation of $+0.863\pm 0.004$ ($+0.909\pm 0.005$ resolution corrected). The white lines on each plot correspond to 25% contours of the resolution-corrected Gaussian fits. Background subtraction has not been employed in either image.

Figure 4

Tunability of the joint spectra. The center frequency of the joint spectrum is tunable by introducing a relative delay between the input signal and the escort pulse, as seen in the five measured joint spectra. The central wavelength of the up-converted signal changes by 0.071 nm per picosecond of delay. The herald central frequency is also seen to shift due to the escort acting partially as a temporal filter on the signal.