Two-photon lock by ground state phase-modulation transfer in rubidium.

We present a method to lock on resonance the second step of the 5S$_{1/2}\rightarrow$5P$_{3/2}\rightarrow$5D$_{5/2}$ two-photon transition at 776 nm in rubidium by monitoring the changes of population of the 5S$_{1/2}$ ground state in a vapor cell. The low probability of excitation in the two-step atomic transition makes the direct observation of population in the final excited state i.e. changes in absorption of the second laser as a function of frequency, very difficult. Monitoring the ground state population instead increases the signal to noise ratio of the two-photon signal. The decrease of the stringent experimental conditions suggests combining the detection method with one of many one-photon spectroscopy techniques. A density matrix model explains well the behaviour of the signal and we show phase sensitive detection of the frequency modulated laser at 780~nm laser as a function of the frequency of the second photon to lock the modulation-free 776~nm laser.