  In the same manner that free-space propagation and curved glass lenses are
used to shape the spatial properties of light, a combination of chromatic
dispersion and devices known as time lenses may be used to reshape its temporal
properties. These techniques have found extensive application in classical
optical signal processing based on nonlinear optics. A new set of challenges
presents itself when processing quantum signals, including noise suppression
and high fidelity requirements. In this work, we construct a single-photon time
lens based on dispersion and nonlinear sum-frequency generation to image the
spectral waveform of half of an entangled photon pair. We find that the joint
spectrum of the photon pair has strongly negative frequency correlations before
the time lens and strongly positive correlations afterwards, verifying that the
process has an overall negative spectro-temporal magnification. The temporal
imaging of energy-time entangled systems opens up a host of new possible
techniques for distinctly quantum tasks in the frequency domain, including
state engineering, and our results demonstrate that the upconversion time lens
is an essential part of the single-photon waveform manipulation toolkit.
