Line shapes of atomic-candle-type Rabi resonances

When atoms interact with a phase-modulated field, the probability of finding the atom in the excited-state oscillates at the second harmonic of the modulation frequency, 2ω_m. The amplitude of this oscillating probability is a resonant function of the Rabi frequency Ω, and this is termed a β Rabi resonance. In this work, we examine the line shape of the β Rabi resonance both theoretically and experimentally. We find that a small-signal theory of the β-Rabi-resonance condition captures much of the line shape’s character, and, in particular, that the resonance’s “line Q” (i.e., 2δΩ_1/2/Ω) is proportional to the modulation frequency. This result can be applied to the atomic candle, where β Rabi resonances are employed to stabilize field strength. Considering our results in the context of developing an optical atomic candle, we find that a free-running diode laser’s intensity noise could be improved by orders of magnitude using the atomic candle concept.