  Fundamentally, the dynamics of micro-macro transitions is instrumental to
understanding the process of quantum-to-classical transitions; technologically,
it can also facilitate the detection of the microscopic signals in quantum
experiments via convenient detectors. Here, we demonstrate a scheme to
characterize micro-macro transitions based on a four-wave mixing linear optical
amplification process in a hot rubidium vapor. The linear optical amplifier
provides a large optical gain of $10^7$ for injected single-photon-level
pulses, enabling photon-number-resolving detection by average via
non-single-photon counting detectors with a large dynamic range. The scheme
exhibits strong dispersion which is sensitive to the input's change at the
single-photon level, resulting in the group-velocity delay time scaling with
$1/\sqrt{N}$, where $N$ is the average input photon number. The output probe
and conjugate modes have different coefficients of this $1/\sqrt{N}$ scaling,
indicating the coefficient can serve as an efficient parameter to characterize
the specified micro-macro transitions. The demonstrated results are generally
applicable for quantum detection and optical signal processing in light-atom
interfaces. Furthermore, the present system is suitable for the study of
relevant time-resolved dynamics of the quantum-to-classical transitions.
