Generation of deterministic multi-mode intensity squeezing in a train of ultra-short pulses by unbalanced SU(1,1) interferometers

The continuous variable quantum state generated by time-domain multiplexed optical parametric amplifier (OPA) is attractive because of the potential of enlarging the mode scale. Currently, the duration of temporal mode is longer than 100 ns since the OPA is pumped by the continuous wave laser, which restricts the scale of quantum state. Here we demonstrate multi-mode intensity squeezing localized in a train of short pulses with duration of $\sim 10$ ps by using an unbalanced SU(1,1) interferometer (USUI), where the mode-locked laser is exploited as the pump and the time-domain multiplexing is realized by the combination of optical delay and nonlinear beam splitter. Using the pulse resolved joint measurements, we reveal the correlation structure of the state is unique and fundamentally different from previous approaches. Due to the globe quantum correlation, the intensity squeezing not only depends on the gain of OPAs but also ties to the mode number $M$ of joint measurement. We experimentally perform joint measurement among 30 modes and show the intensity noise lower than shot noise level by $\sim 0.9$ dB is achievable for $M>10$. Our investigations open the door for generating ultra-large scale quantum state by pulse pumped USUI.