We theoretically study a scheme to develop an atomic based micro-wave (MW) interferometry using the Rydberg states in Rb. Unlike the traditional MW interferometry, this scheme is not based upon the electrical circuits, hence the sensitivity of the phase and the amplitude/strength of the MW field is not limited by the Nyquist thermal noise. Further, this system has great advantage due to its much higher frequency range in comparision to the electrical circuit, ranging from radio frequency (RF), MW to terahertz regime. In addition, this is two orders of magnitude more sensitive to field strength as compared to the prior demonstrations on the MW electrometry using the Rydberg atomic states. Further, previously studied atomic systems are only sensitive to the field strength but not to the phase and hence this scheme provides a great opportunity to characterize the MW completely including the propagation direction and the wavefront. The atomic based MW interferometry is based upon a six-level loopy ladder system involving the Rydberg states in which two sub-systems interfere constructively or destructively depending upon the phase between the MW electric fields closing the loop. This work opens up a new field i.e. atomic based MW interferometry replacing the conventional electrical circuit in much superior fashion.

In this paper, we present the spectroscopy of the 6P 1/2 state in 87 Rb using a double-resonance technique at 780 nm and 421 nm. The double-resonance technique is implemented using electromagnetically induced transparency (EIT) and optical pumping methods. Using these spectroscopy methods, we have measured the hyperfine splitting of the 6P 1/2 state with precision of <400 kHz, which agrees well with other spectroscopy methods such as electrical discharge and saturated absorption spectroscopy at 421 nm.

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