Quantum resonances by sequential pulsed excitation with pulse repetition rate at fractional atomic frequencies

We propose a concept of fractional quantum resonances based on an idea of driving a quantum system by an external field in the form of a repetitive pulse sequence. We show that, in addition to intuitively expected resonance at repetition rate ωRep equal to the internal quantum frequency ω, the system exhibits less intuitive fractional quantum resonances at ωRep=ω/n, with n being an integer. It is a nonintuitive phenomenon since the external repetition rate has no quantum character, yet the atom responds to it, if the rate is equal to 1/n of its eigenfrequency. This result is in good agreement with recent magnetometer experiments. It is also found that other resonances are possible at pulse-repetition-rate frequencies equal to 1/n of combination frequencies involving the internal system frequencies and Rabi frequencies. We show that quantum-interference-related phenomena of gain without population inversion and absorption with inversion are observed at these unique resonances. Fractional quantum resonances provide a spectroscopy tool, allowing us to measure optical frequency on one transition through detection of resonances on another transition. We believe that our results will have implications in other quantum-related processes, such as laser-assisted resonant enhancement of chemical reactions and biological processes.