PHYSICAL REVIEW A 100, 023808 (2019) Influence of coherent population trapping on Raman scattering Pooja Singh , 1, 2 Anil K. Patnaik, 3, 4 Sukesh Roy, 3 James R. Gord, 5 and Yuri V. Rostovtsev 1 1 Center for Nonlinear Sciences and Department of Physics, University of North Texas, Denton, Texas 76203, USA 2 Division of Sciences and Mathematics, Louisiana State University at Eunice, Eunice, Louisiana 70535, USA 3 Spectral Energies LLC, 5100 Springfield Street, Suite 301, Dayton, Ohio 45431,USA 4 Department of Physics, Wright State University, Dayton, Ohio 45435, USA 5 Air Force Research Laboratory, Aerospace Systems Directorate, Wright-Patterson Air Force Base, Ohio 45433, USA (Received 15 November 2018; published 8 August 2019) We have considered the Raman scattering in molecular media. Applying two laser fields in a two-photon resonance with vibrational transition, we have studied the role of rotational levels for excitation of vibrational coherence. It is shown that the molecular vibrational coherence strongly depends on the effect of coherent pop- ulation trapping for rotational levels. The obtained results are important for applications of Raman spectroscopy to molecular detection in engineering, chemical, and biological applications. DOI: 10.1103/PhysRevA.100.023808 I. INTRODUCTION Raman spectroscopy [1–3] is one among many power- ful techniques that has been widely used in engineering, chemical, and biological applications. Raman spectroscopy is based on a two-photon optical resonance with vibrational molecular levels (see Fig. 1) when two optical pulses excite the molecular vibrational coherence. In an effort to optimize Raman spectroscopy, techniques have been developed that introduce modified optical pulses and models. Applying the femtosecond adaptive technique allows researchers to excite maximal vibrational coherence to improve the sensitivity of coherent Raman spectroscopy and to perform real-time identification of bacterial spores and biomolecules [4–8]. The femtosecond-laser-based coherent anti-Stokes Raman spec- troscopy (CARS) has been used extensively in time-resolved nonlinear spectroscopy research in recent years [9]. It is used in several fields of study, such as identifying molecules in chemistry, measuring temperature in solid-state physics, and noninvasive monitoring of muscle tissue, among other things. It is the quantum coherent effects that have strong influence on the Raman scattering. Quantum coherence effects, such as coherent population trapping (CPT) [10] and electromag- netically induced transparency (EIT) [11–14], have been the focus of broad research activity for the past decades, as they drastically change optical properties of media. For example, for EIT in continuous-wave(CW) regimes [12–16], absorption practically vanishes. The medium with excited quantum coherence [11] shows ultradispersive properties [17] and has several orders of mag- nitude higher spectral dispersion than natural materials [18]. The corresponding steep dispersion results in the ultraslow or ultrafast propagation of light pulses [19–23], which can be used for drastic modification of the phase-matching condi- tions for Brillouin scattering [24] and four-wave mixing [25]. It has been shown that the optical 0π pulses [26] under the condition of EIT [27,28] are very sensitive to resonant inter- action and have advantages for use in Raman spectroscopy. Recently, the saturation of vibrational Raman coherence and coherent anti-Stokes Raman scattering (CARS) using femtosecond optical pulses has been investigated theoretically [29]. It was demonstrated that the vibrational coherence and also the vibrational CARS with femtosecond excitation dis- play saturation-like behavior once the rotational coherence is saturated. A generalized formulation is developed for deter- mining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse [30] and for different pulse shapes [31]. The condition was derived for the saturation threshold of a probe pulse in an ultrafast electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman spectroscopy (CARS) configuration [32]. Further, femtosecond fully resonant electronically enhanced CARS (FREE-CARS) has been demonstrated with orders of magnitude enhancement of the CARS signal, where all three input pump, Stokes, and probe pulses are resonant to electronic states of the molecules [33,34]. In this paper, we study excitation of the molecular coher- ence in a -type molecular media (see Fig. 2). In order to analyze the interaction and gain new insights into a rotational- vibrational system, we restrict ourselves to a simplistic model of a single rotational split of a ground level. Thus, we consider a four-level molecular medium interact- ing with the probe and coupling fields (see the Appendix for more details of the simplified system). We have considered the three- and four-level molecules [Figs. 2(a)–2(c)]. The dressed- state basis approach is employed, which provides deep physi- cal insights showing interaction of “bright” and “dark” states with radiation. For the four-level model, we find two sets of the bright and dark states that show the important role of coherent population trapping between split ground states on Raman scattering in such molecular systems. The level structure of the model is common for the molecular media, where the split ground states can be viewed as rotational levels in addition to the vibrational levels with much higher frequency. We demonstrate the importance of formation of dark states between rotational levels on Raman and stimulated 2469-9926/2019/100(2)/023808(9) 023808-1 ©2019 American Physical Society