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Unravelling the Mechanisms of Electromagnetically Induced Absorption and Transparency in Open Degenerate Multilevel System: Effects of Neighboring Transitions

Zeeshan Ali Safdar Jadoon, Heung‐Ryoul Noh, Jin‐Tae Kim

Published Jul 15, 2021• 0 citations
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Abstract

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.

DOI
10.21203/rs.3.rs-701938/v1

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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.
In this study, optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of [Formula: see text]Rb D2 transition, which involves the Doppler broadening effect, are solved. The calculated spectra agree well with the experimental results obtained based on 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 [Formula: see text] and 3 transitions (open [Formula: see text] and 3 transitions) are determined to be the effect of the strong closed [Formula: see text] transition line (strong closed [Formula: see text] transition line); this finding is based on a comparison between the calculated absorption profiles of the DTLS without neighboring states and those of all levels with neighboring states, depending on the coupling and probe power ratios. Furthermore, based on the aforementioned comparison, the crucial factors that enhance or reduce the coherence effects and lead to the transformation between electromagnetically induced absorption and electromagnetically induced transparency, are (1) the power ratios between the coupling and probe beams, (2) the openness of the excited state, and (3) effects of the neighboring states due to Doppler broadening in a real atomic system.
Effects of neighboring transitions through Doppler broadening on electromagnetically induced absorption (EIA) and electromagnetically induced transparency (EIT) of the degenerate two-level system at the F g =2→ F e =1,2, and 3 transitions of the 87 Rb D2 line have been investigated. Two different polarization configurations, such as linear parallel and linear perpendicular polarizations of coupling and probe lasers, have been studied. We study the significant variation of EIT and EIA due to the effect of the neighboring transitions via artificial variation of the hyperfine spacings of the 5 P 3/2 state. We have a new observation such as EIT instead of EIA due to the neighboring effect, even in the case of closed systems such as F g =2→ F e =3 of 87 Rb for the linear parallel configuration, for the first time to our best knowledge. The observed spectra match well with theoretically calculated spectra. EIAs for the open F g =2→ F e =1 and 2 transitions at the linear perpendicular polarization are observed due to neighboring effects. This system may be applied to optical switching systems for future quantum processing application.
The effects of neighboring transitions through Doppler broadening on electromagnetically induced absorption (EIA) and electromagnetically induced transparency (EIT) for the D2 transition line in Rb atoms with respect to the same circular polarization configurations ( σ + − σ + ) of coupling and probe lasers have been investigated. Spectra for the open F g = 2 → F e = 2 transition of 87 Rb and the F g = 3 → F e = 2 and 3 transitions of 85 Rb exhibit EIA, resulting from the neighboring effect of F g = 2 → F e = 3 and F g = 3 → F e = 4 transitions, respectively. In contrast, EIT is observed for the open F g = 2 → F e = 1 transition of 87 Rb, which indicates greater hyperfine energy splittings of 87 Rb and weaker neighboring effects than those of 85 Rb. Based on the theoretical results, we can confirm that EIT in the case of F g > F e for 87 Rb and circular parallel polarization transforms into EIA due to the magnitude of the neighboring effects with a decrease in the hyperfine energy splittings.
Spontaneous transfer of coherence has proven to be a good interpretative scheme for the explantation of the spectra of a probe laser probing a closed degenerate two-level systems. With its aid it was possible to give an explanation for the emergence of electromagnetically induced absorption and also to make predictions on the associated coupling laser spectra. Here we extend our work on the role of the coupling laser in electromagnetically induced absorption presenting new measurements of the probe and coupling laser absorption and dispersion spectra - taken in the D2 line of caesium - which reassert the importance of spontaneous transfer of coherence in the generation of electromagnetically induced absorption spectra. All measurements were performed with linearly polarised coupling and probe laser of orthogonal polarisation, acting on a perpendicularly propagating caesium atomic beam to minimise the Doppler broadening of the lines. For sake of completeness we compared the electromagnetically induced absorption spectra with electromagnetically induced transparency spectra obtained in another two-level system within the same line. The measured probe spectra were used to calculate the refractive index of caesium in the presence of electromagnetically induced transparency and absorption. On that basis we could calculate the effect of Kerr nonlinearities and measure nonlinear Kerr coefficients of the order of n2 ≈ 10-5 cm2/mW with absorption coefficients of the order of &agr; ≈ 0.1 cm-1.
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.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.