Ta shg pro

The probe field couples |g〉 and |e〉 states with wavelength of 780 nm, generated from an external cavity diode laser. The coupling field drives atoms from |e〉 to |r〉 states with wavelength of 480 nm, produced from a frequency doubled diode laser system (Toptica TA SHG pro). These two beams are sent into a counter-propagation direction to diminish the Doppler effect due to the atomic motion. We applied a dichroic mirror (DM) to separate the mixed probe field from the coupling beam after the vapor cell. The full width at e⁻² maximum of the probe and coupling beams were 1.4 mm and 2.2 mm, respectively. The vapor cell is filled with the admixture of ⁸⁷Rb and ⁸⁵Rb atoms at the temperature of 300 K.

Numerical calculations: In Figs. 2, 3, 4, home-made Matlab programs are used for Eq. (4) and numerically calculated, where the random phase noise is obtained from the rand(1) commend. In Figs. 2, 3, 4, various phase noise range for ${\zeta }^{″}$ and $\mathrm{\zeta }$ was controlled by multiplying a certain number to the output of rand(1).
Experiments: In Fig. 4, the wavelength of the input light was 606 nm from Toptica TA-SHG pro. The optical power of the input light was ~ 1 mW. After splitting by the first beam splitter in Fig. 1, each channel was controlled by each AOM driven by synchronized rf generators (PTS 160/250; Tektronix AFG3102), resulting in the same initial phase (see ref. 29 for details). The data was captured in the screen of an oscilloscope (Tektronix DPO 5204B) via avalanche photodiodes (Hamamatsu C12703). The experimental layout is for Fig. 1(b), where the transmission length of each MZI is ~ 70 cm, and independent (random) phase noise occurs in both MZIs, satisfying non-zero phase noise.