Frequency resolved optical gating using parametric amplification for characterizing ultrafast temporally multimode squeezed states

Temporally multimode squeezed states have been a topic of recent interest due to their applications in quantum communication, information processing, and sensing. Characterizing the mode shapes is crucial for effectively manipulating these states, but current mode shape and state characterization techniques necessitate constraining assumptions and complicated experimental setups. Here, we propose a characterization technique that simultaneously recovers the complex temporal mode shapes and quadrature variances of ultrafast multimode squeezed states based on frequency resolved optical gating (FROG) using an optical parametric amplifier (OPA). FROG is a promising tool for quantum state characterization due to its flexibility of implementation and high temporal resolution. Using an OPA as the nonlinear process in FROG has the benefit of amplifying weak quantum states to a detectable level while preserving quantum information. Numerical simulations demonstrate the recovery of the mode shapes and levels of squeezing and anti-squeezing of ultrafast multimode squeezed states. This scheme offers a practical experimental approach to measuring arbitrary temporal mode shapes and characterizing large-scale multimode ultrafast Gaussian quantum states.