Sub - Doppler resolution with double coherently driving fields

We propose a four-level model where sub-Doppler resolution as well as enhanced absorption of a weak probe field are realized by using two coherently driving fields. We show that spectral resolution can be improved by modifying the coherent fields intensity and frequencies. Multi-photon transitions are embedded in a variety of optical effects based on correlated absorption and emission of two or more photons. Step-wise and multi-photon processes can be distinguished by their frequency-correlation properties [1, 2]. Sub-Doppler resolution for an inhomogeneously broadened medium based on multi-photon processes has attracted much attention in recent decades. The physical essence for this method lies in the fact that a detuning for multi-photon transition stipulated by Doppler frequency shift can be reduced or eliminated by adopting appropriate light propagation direction, since the detuning is the sum or difference of multiple single-photon transition detunings. Sub-Doppler nonlinear optical resonance as appearance of quantum coherence and interference in the context of frequency-correlation properties of the coherent components have been proposed in [3]. A widely used method is Doppler-free two-or multi-photon absorption where the velocity dependent detuning could be removed in the case that the wave vectors of the interacting beams sum down to zero (for a review, see [4]). This type of sub-Doppler spectrum is characterized by a large detuning from the intermediate resonance, measuring the fluorescence from the upper level as well as by small cross sections for these multi-photon processes. Enhanced by intermediate resonance sub-Doppler processes based on the use of strong driving fields and on a change of frequency-correlation properties of resonant multi-photon process in strong resonant fields, have been proposed in [3] and further developed in [5, 6] (also in [2]). Substantial enhancement in absorption, gain and fluorescence controlled with the auxiliary appropriately propagating electromagnetic wave has been predicted. An interference nature of the spectrum modification has been stressed, which implies that along the growth of the absorption (gain) in certain spectral intervals, integral over the frequency may even decrease. A role of increase of intensity of a probe field as well as features of Doppler-free lasers were explored too. Control of atomic response with intense coupling lasers has been a subject of many intensive studies in the context of electromagnetically induced transparency (EIT) [7], amplification without inversion (AWI) [8, 9, 10, 11], enhancement of the refractive index without absorption [12] and so on (for review see [8, 11, 13]). Sub-Doppler resolution by …