  We demonstrate a technique based on optical heterodyne detection to measure
Rydberg population in thermal atomic vapour. The technique used a probe beam
far off resonant to the D2 line of rubidium along with a reference beam with
frequency offset by 800 MHz in the presence of a coupling laser that couples to
Rydberg state via two-photon resonance. The polarizations of the probe,
reference and coupling beams are suitably chosen such that only the probe beam
goes through a non-linear phase shift due to two-photon process which is
measured relative to the phase shift of the reference beam using optical
heterodyne detection technique. We show that the technique has a sensitivity to
measure the minimum phase shift of the order of few $\mu$rad. We have used a
suitable model of two-photon excitation of a 3-level atom to show that the
minimum phase shift measured in our experiment corresponds to Rydberg
population of the order of $10^{-5}$. The corresponding probe absorption for
the given laser parameters is of the order of $10^{-7}$. We demonstrate that
this technique is insensitive to polarization impurity or fluctuations in the
beams. The technique is particularly useful in measuring Rydberg population via
two-photon excitation in thermal vapour where multi channel plates (MCP) could
be relatively difficult to impliment. It can also be used in ultra-cold atomic
sample with suitable laser parameters.
