  Photon number-resolving detectors (PNRDs) are the ultimate optical sensors.
Superconducting-nanostrip photon detectors (SNSPDs), traditionally known as
ON-OFF detectors, have recently been found to have photon number resolving
capability without multiplexing. This discovery positions them to become true
PNRDs. However, their practical use is limited by the need to precisely detect
tiny signal differences with low signal-to-noise ratios within sub-nanosecond
time frames. We overcome this challenge using optical sampling with a
dual-output Mach Zehnder modulator (DO-MZM) and ultra-short pulsed laser. By
adjusting the DO-MZM's bias voltage to nearly balance the outputs, this method
enables sensitive detection of picosecond-order signal differences, achieving a
temporal resolution of 1.9 ps and facilitating real-time photon number
resolution. We applied this method to produce various non-classical quantum
states, enhancing their non-classicality through photon number resolution. This
advancement marks a significant shift from principle verification to practical
application for SNSPD-type PNRDs in diverse quantum optics fields.
