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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., Comment: 9 pages, 7 figures

Many predictions of Doppler cooling theory of two-level atoms have never been verified in a three-dimensional geometry, including the celebrated minimum achievable temperature $\hbar \Gamma/2 k_B$, where $\Gamma$ is the transition linewidth. Here, we show that, despite their degenerate level structure, we can use Helium-4 atoms to achieve a situation in which these predictions can be verified. We make measurements of atomic temperatures, magneto-optical trap sizes, and the sensitivity of optical molasses to a power imbalance in the laser beams, finding excellent agreement with the Doppler theory. We show that the special properties of Helium, particularly its small mass and narrow transition linewidth, prevent effective sub-Doppler cooling with red-detuned optical molasses., Comment: 8 pages, 5 figures