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 ${\omega }_{\text{Rep}}$ equal to the internal quantum frequency $\omega$, the system exhibits less intuitive fractional quantum resonances at ${\omega }_{\text{Rep}}=\omega /n$, 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.

• Received 19 September 2014

DOI:https://doi.org/10.1103/PhysRevA.91.023819