Figure 1

Experimental setup for transmission estimation at the QCRB with a bTMSS. A continuous wave bTMSS is generated in a ⁸⁵Rb vapor cell via a FWM process in a double-Λ configuration in the D1 line, as shown in the “state generation” inset. The response of the atomic medium leads to a bTMSS from the FWM process with a bandwidth of the order of 10 MHz [42]. To generate the bTMSS, a strong pump beam (shown in purple) is combined with a weak probe beam (shown in red) to generated quantum correlated probe and conjugate (shown in green). The probe beam is used to probe the system under study, while the conjugate beam serves as the reference for the transmission estimation. We consider losses in the probe mode both before and after the system under study and losses in the conjugate mode. The “system” inset shows the configuration that is used to emulate a transmissive system. An electro-optic modulator (EOM) is used in an amplitude modulation configuration with the reflection from the polarizing beam splitter (PBS) after the EOM used to stabilize it (see Appendix A.1). After the amplitude modulation section of the system, a half waveplate and PBS are used to control the mean transmission through the system. The transmission of the system is given by the mean transmission of the EOM setup and the Set T half waveplate and PBS. An optimal intensity-difference measurement of the probe and conjugate modes, with electronic attenuation of the photocurrent of the detected conjugate mode, is used to obtain the uncertainty in the estimation of the transmission, \(\langle \Delta ^{2}T \rangle \).