We investigate coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.
We investigate coherent pump–probe spectroscopy of a medium of atoms in Λ configuration with a closely placed adjacent excited level. The presence of the additional level results in two simultaneous Λ resonances excited by the same pair of pump and probe fields. A master equation framework is used to discuss the probe absorption spectrum and dispersion in the absence/presence of inhomogeneous broadening, and the results are illustrated by using a model four-level system in the D2 transition of 85Rb. The system is observed to exhibit additional interference effects arising from two competing Λ resonances. These effects manifest in terms of linewidths of the triplet dressed state spectrum and suppression of the subnatural peak for the stationary atoms. The effect on electromagnetically induced transparency is discussed in the light of its shape, position and linewidth. The discussion is further augmented by the study of a six-level model as applicable to the D2 transition of 85Rb. The analysis presented here provides a realistic theoretical description of the pump–probe spectroscopy of hyperfine transitions of alkali atoms.
Pump–probe spectroscopy of a four-level system (FLS) consisting of a Λ system with an additional close lying excited level is investigated. The level configuration gives rise to two simultaneously excited Λ resonances driven by the same pump and probe laser beams. Two such four-level configurations, 5s1/2F=1,2→5p1/2F′=1,2 (FLS1) and 5s1/2F=1,2→5p3/2F′=1,2 (FLS2) respectively in the D1 and D2 transitions of 87Rb, are used as model systems to study theoretically the probe absorption spectrum. It is observed that the signature of the quantum interference is dependent on the nature of the FLS; FLS1 exhibits probe amplification as against probe absorption in FLS2. This contrasting behaviour is further corroborated by analytical results, which highlight the importance of transition dipole moments, atom–field interaction parameters and incoherent decays associated with the FLS. The discussion is further augmented using quantum jump formalism, which provides useful insight into the underlying mechanism responsible for probe amplification versus absorption.
We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.
Laser spectroscopy experiments are reported on rubidium atoms by using two or three external cavity diode lasers to study multiple resonance transitions in Λ- and V-type systems as well as on (Λ+V)-type system. Electromagnetically induced transparency (EIT) peaks having sub-natural line-widths are found on the Doppler broadened transmission backgrounds with velocity selective enhanced absorption dips. In the presence of a pump laser, probe spectrum shows enhancement of EIT signal by tuning the control laser frequency when the Λ- and V-type EIT signals are made to overlap. Theoretical analysis is carried out by solving the optical Bloch equations for five-level atomic model under Λ configuration. With the numerically simulated spectra, variation of EIT transmission peak with ground state decay rate and excited state spontaneous decay rate are investigated. Effect of pump Rabi frequency on the transmission peak is also shown.
Electromagnetically induced transparency (EIT) has mainly been modelled for three-level systems. In particular, a considerable interest has been dedicated to the Lambda-configuration, with two ground states and one excited state. However, in the alkali-metal atoms, which are commonly used, hyperfine interaction in the excited state introduces several levels which simultaneously participate in the scattering process. When the Doppler broadening is comparable with the hyperfine splitting in the upper state, the three-level Lambda model does not reproduce the experimental results. Here we theoretically investigate the EIT in a hot vapor of alkali-metal atoms and demonstrate that it can be strongly reduced due to the presence of multiple excited levels. Given this model, we also show that a well-designed optical pumping enables to significantly recover the transparency.
We investigate the coherent pump?probe spectroscopy of a three-level ? system, , in the hyperfine manifold of D2 transition (852?nm) of cesium with particular reference to the sub-Doppler linewidth resonance arising from Aulter?Townes (AT) splitting and the possibility of using it for realizing a scheme for tunable atomic frequency offset locking (AFOL). We discuss here the theoretical framework for a ? system interacting with a coherent pump and probe and use it to describe the process of modulation transfer in the AT and electromagnetically induced transparency regimes. We further employ an experimental scheme consisting of a strong pump and a pair of weak probes to resolve the sub-Doppler linewidth (~8?MHz) AT resonance and study its dependence on pump intensity and detuning. In order to explore the possibility of using such a sub-Doppler linewidth resonance for AFOL, we use its first derivative signal as a frequency discriminator to stabilize the probe laser. The frequency stability of the probe is characterized by means of error signal analysis. This study reveals that while the frequency stability of the AT locked laser is limited by the pump laser, the tuning range of the offset frequency lock can cover the entire Doppler profile and its immediate neighbourhood, thereby providing a simple and cost effective alternative to the external modulator. The study described in this paper contributes to the discussion on the subtle link between dressed state spectroscopy and AFOL, which is relevant for developing a master?slave-type laser system in the domain of coherent photon?atom interaction.
We present the results of a pump-probe laser spectroscopic investigation of the Doppler-broadened sodium D1 resonance line. We find 13 resonances in the resulting spectra. These observations are well described by the numerical predictions of a four-level atomic model of the hyperfine structure of the sodium D1 line. We also find that many, but not all, of these features can be understood in terms of processes originating in a two-level or three-level subset of the full four-level model. The processes we observed include forward near-degenerate four-wave mixing and saturation in a two-level system, difference-frequency crossing and nondegenerate four-wave mixing in a three-level V system, electromagnetically induced transparency and optical pumping in a three-level lambda system, cross-transition resonance in a four-level double-lambda system, and conventional optical pumping. Most of these processes lead to sub-Doppler or even subnatural linewidths. The dependence of these resonances on the pump intensity and pump detuning from atomic resonance are also studied.