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Journal of Physics B Atomic Molecular and Optical Physics

Angular momentum and two-photon detuning dependence of reflection spectrum on degenerate two-level systems in Cs vapour

Haitao Zhou, Miaojun Guo, Dan Wang, Jiangrui Gao, Junxiang Zhang, Shi-Yao Zhu

Published Nov 1, 2011• 4 citations
Publisher

Abstract

The absorption and reflection spectrum of probe light, interacting with a degenerate two-level system of any transition in the Cs D1 line driven by standing-wave, is experimentally studied. The effect that absorption changes from a transparency dip to an absorption peak when the travelling coupling field is replaced by the standing-wave field can only occur in the hyperfine transition Fg↔Fe ≤ Fg (Fg and Fe are the total angular momentum of the ground and the excited levels respectively), and in this case, a reflection of probe can be generated. It is also examined that the absorption coefficient and reflection efficiency in the transition of Fg > Fe are much higher than that in Fg = Fe. For the transition of Fg < Fe, where coherent population trapping cannot be established, the absorption does not change the sign, and there is no reflection to be observed when the coupling is switched from a travelling to a standing-wave field. As a consequence, only the degenerate two-level systems, where the population is trapped in the ground states, can exhibit steep absorption and reflection of the probe light with a standing-wave coupling. Furthermore, the reflection spectra with an asymmetric profile as the function of one- and two-photon detunings are obtained, which is theoretically explained by the phase mismatch compensation during the process of four-wave mixing in an atomic system. This shows that under the condition of coherent population trapping the nonlinear reflection can be improved with one- and two-photon detunings in a degenerate two-level system.

DOI
10.1088/0953-4075/44/22/225503

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Journal of Modern Optics•Sep 1, 2004•3 citations
The absorption and reflection spectrum of probe light, interacting with a degenerate two-level system of any transition in the Cs D1 line driven by standing-wave, is experimentally studied. The effect that absorption changes from a transparency dip to an absorption peak when the travelling coupling field is replaced by the standing-wave field can only occur in the hyperfine transition Fg↔Fe ≤ Fg (Fg and Fe are the total angular momentum of the ground and the excited levels respectively), and in this case, a reflection of probe can be generated. It is also examined that the absorption coefficient and reflection efficiency in the transition of Fg > Fe are much higher than that in Fg = Fe. For the transition of Fg < Fe, where coherent population trapping cannot be established, the absorption does not change the sign, and there is no reflection to be observed when the coupling is switched from a travelling to a standing-wave field. As a consequence, only the degenerate two-level systems, where the population is trapped in the ground states, can exhibit steep absorption and reflection of the probe light with a standing-wave coupling. Furthermore, the reflection spectra with an asymmetric profile as the function of one- and two-photon detunings are obtained, which is theoretically explained by the phase mismatch compensation during the process of four-wave mixing in an atomic system. This shows that under the condition of coherent population trapping the nonlinear reflection can be improved with one- and two-photon detunings in a degenerate two-level system.
The reflection spectrum of a probe light in a -type three-level atomic system coupled by an off-resonant standing-wave is investigated experimentally and theoretically. We show that the maximum value of reflection coefficient occurs when both of the coupling and probe lights are tuned off resonances from the atomic transitions. The nature of enhanced reflection is attributed to the phase compensation caused by the anomalous dispersion, which leads to a significant reduction of nonlinear phase mismatch in atomic four-wave mixing. At certain detuning of coupling and probe frequencies near two-photon resonance, there exits a best compensation, so the reflection efficiency reaches its maximum. The dependences of efficiency on the intensity of coupling fields and the density of atoms are also studied.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave mixing, population modulation, and Zeeman optical pumping are derived. On all these observables, subnatural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited-state population modulation in the D2{D}_{2}D2​ line of Rb vapor are presented in good agreement with the calculations.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
Abstract Optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of 85Rb D2 transition that involves the Doppler broadening effect are solved herein. The calculated spectra agree well with the experimental results obtained using the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open Fg = 3 → Fe = 2 and 3 transitions (open Fg = 2 → Fe = 2 and 3 transitions) are clearly determined to be the effect of the strong closed Fg = 3 → Fe = 4 transition line (strong closed Fg = 2 → Fe = 1 transition line) based on the comparisons of the calculated absorption profiles of a DTLS without neighboring states and those of all levels with neighboring states depending on the coupling and probe power ratios. The crucial factors established based on comparisons of the calculated absorption profiles of DTLS with and without neighboring states, which enhance or reduce coherence effects and result in transformation between electromagnetically induced absorption and electromagnetically induced transparency, are the power ratios between coupling and probe beams, openness of the excited state, and effects of the neighboring states due to the Doppler broadening in a real atomic system.
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.
We investigate the quantum coherence effects of a closed transition F e = 1 ↔ F g = 0 driven by transverse linearly polarized light field (with [sgrave] ± components) and probed by another transverse, linearly polarized light field. Owing to the competition of two-photon gain and single-photon absorption, the absorption spectrum is shown as a combination of electromagnetically induced transparency (EIT) and Mollow absorption spectrum (MAS). In the degenerate case, the MAS covers the EIT window at the pump-probe detuning centre. In the magnetic field, two single-photon absorption peaks inside the EIT windows appear when the drive Rabi frequency is smaller than the Zeeman splitting while, when the Rabi frequency is larger than the Zeeman splitting, we find four emission peaks due to the two-photon gain. A transition from positive to negative dispersion is obtained, which means a shift between the subluminal and superluminal group velocities.