Phase space sub-Planck structures: experimental realization in time-frequency domain
Ludmila Praxmeyer1*, Chi-Cheng Chen1, Shang-Da Yang1,2, Ray-Kuang Lee1,2,3
1Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, Taiwan
2Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan
3Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
* presenting author:Ludmila Praxmeyer,
We demonstrate sub-Planck structure experimentally in ​spectrograms via frequency resolved optical gating (FROG) measurement of ultrashort pulses. Through the correspondence between classical time-frequency transform limit and quantum uncertainty in phase space, superposition of quantum states is realized with four ultrashort pulses for the first time. Comparisons between theoretical results and experimental measurements show the variations in these sub-Planck structures, due to different time delays and imperfect Gaussian profiles.

Keywords: sub-Fourier/sub-Plank structure, ultrafast optics, Wigner function, FROG measuremant