Enhancing Bandwidth Compression Using an Aberration-Corrected Sinusoidal Time Lens

The ability to manipulate the spectro-temporal properties of single-photon pulses is a key enabler for quantum communication and high-dimensional quantum information processing [1]. For example, spectral bandwidth compression is crucial for interfacing quantum systems that operate at different spectral ranges [1]. Efficient bandwidth compression of single-photon pulses has been achieved using dispersive streching followed by an electro-optic sinudoidal time lens [1], [2]. An ideal time lens applies a time-dependent quadratic phase to an optical pulse, which linearly chirps the pulse [3]. However, in experimental realizations, deviations from the ideal quadratic phase leads to distortions in the output spectrum, known as temporal aberrations. Furthermore, discrepancies have been observed between theoretical predictions and experimental results for these systems [2], but never studies thoroughly. In this study, we propose a straightforward method to estimate the chirp rate introduced by a time lens implemented using an electro-optic phase modulator driven with a sinusoidal voltage. An optical pulse co-propagating with the sinusoidal drive acquires a sinusoidal phase <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A \cos(\omega_{\mathrm{m}}t)$</tex>, here <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> is the phase modulation amplitude and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega_{\mathrm{m}}$</tex> is the modulation frequency. When the pulse duration is shorter than the period of the driving signal, the extremum of the sinusoidal phase is approximately quadratic, effectively implementing a time lens.