Question
A time-varying signal is applied to a collection of non-degenerate absorbing two-level atoms. This signal is tuned exactly to the transition frequency a , and
A time-varying signal is applied to a collection of non-degenerate absorbing two-level atoms. This signal is tuned exactly to the transition frequency a, and is amplitude- modulated at a low-frequency wm: W12(t) = W21(t) = Wa + Wb cos(mt). The modulation depth is small, so that Wb << Wa, and the modulation frequency is low,
so that m << 21 and wm << a. This modulation frequency wm, however, can be of the same order as the inverse relaxation rate 1/T1 = 12 + 21. (1) Insert this time-modulated signal into the two-level rate equation and solve for the time-varying population difference N(t), including saturation effects. (2) Find out how the phase lag between the signal modulation W12(t) and the population modulation N(t) will change with the modulation frequency m. Hints: Assume the population difference varying like N(t) = Na + Nb(t), with Nb << Na, and linearize the equation by neglecting cross-products of the small terms Wb and Nb.
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