Aberration-corrected quantum temporal imaging system

Abstract

We describe the design of a temporal imaging system that simultaneously reshapes the temporal profile and converts the frequency of a photonic wave packet, while preserving its quantum state. A field lens, which imparts a temporal quadratic phase modulation, is used to correct for the residual phase caused by field curvature in the image, thus enabling temporal imaging for phase-sensitive quantum applications. We show how this system can be used for temporal imaging of time-bin entangled photonic wave packets and compare the field lens correction technique to systems based on a temporal telescope and far-field imaging. The field-lens approach removes the residual phase using four dispersive elements. The group delay dispersion $D$ is constrained by the available bandwidth $\ensuremath{\Delta}\ensuremath{\nu}$ by $D>t/\ensuremath{\Delta}\ensuremath{\nu}$, where $t$ is the temporal width of the wave form associated with the dispersion $D$. This is compared to the much larger dispersion $D\ensuremath{\gg}\ensuremath{\pi}{t}^{2}/8$ required to satisfy the Fraunhofer condition in the far-field approach.