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Journal of Modern Optics

Effect of neighbouring transitions on critical angle in conversion between EIA and EIT in 87 Rb atoms

Aisar-ul Hassan, Heung‐Ryoul Noh, Jin‐Tae Kim

Published May 1, 2025• 1 citation
Publisher

Abstract

The effects of neighbouring transitions (ENT) on electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and the conversion between EIA and EIT in a degenerate multi-level system of 87Rb atoms were studied in terms of the angle (θ) between the polarization axes of the coupling and probe beams. The predicted critical values of θ, in which EIT transitioned to EIA, were consistent with the experimental values. In this work these results were systematically confirmed using the calculated spectra by varying the frequency spacings in the excited state of 87Rb via a factor called the ratio. We observed that when the ratio was less than 0.1, the critical angle θc was inverted. This may be attributed to the interplay between the strengths of the EIA and EIT as the ENT varied. We also discovered that by modifying the frequency spacings in the excited state of 87Rb, it becomes feasible to predict ENT and the interplay between EIT and EIA in alkali-metal atoms.

DOI
10.1080/09500340.2025.2497438

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Journal of the Korean Physical Society•Oct 1, 2012•2 citations
The effects of neighbouring transitions (ENT) on electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and the conversion between EIA and EIT in a degenerate multi-level system of 87Rb atoms were studied in terms of the angle (θ) between the polarization axes of the coupling and probe beams. The predicted critical values of θ, in which EIT transitioned to EIA, were consistent with the experimental values. In this work these results were systematically confirmed using the calculated spectra by varying the frequency spacings in the excited state of 87Rb via a factor called the ratio. We observed that when the ratio was less than 0.1, the critical angle θc was inverted. This may be attributed to the interplay between the strengths of the EIA and EIT as the ENT varied. We also discovered that by modifying the frequency spacings in the excited state of 87Rb, it becomes feasible to predict ENT and the interplay between EIT and EIA in alkali-metal atoms.
The effects of neighboring transitions (ENT) on electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and the conversion between EIA and EIT in a degenerate multi-level system of 87Rb atoms were studied in terms of the angle (θ) between the polarization axes of the coupling and probe beams. The predicted critical values of θ, in which EIT transitioned to EIA, were consistent with the experimental values. In this work these results were systematically confirmed using the calculated spectra by varying the frequency spacings in the excited state of 87Rb via a factor called the ratio. We observed that when the ratio was less than 0.1, the critical angle θc was inverted. This may be attributed to the interplay between the strengths of the EIA and EIT as the ENT varied. We also discovered that by modifying the frequency spacings in the excited state of 87Rb, it becomes feasible to predict ENT and the interplay between EIT and EIA in alkali-metal atoms.
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.
We report here simultaneous experimental observation of Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Absorption (EIA) in a multi-level V-type system in D2 transition of Rb87, i.e., F=2→F′ with a strong pump and a weak probe beam. We studied the probe spectrum by locking the probe beam to the transition F=2→F′=2 while the pump is scanned from F=2→F′. EIA is observed for the open transition (F=2→F′=2) whereas EIT is observed in the closed transition (F=2→F′=3). Sub natural line-width is observed for the EIA. To simulate the observed spectra theoretically, Liouville equation for the three-level V-type system is solved analytically with a multi-mode approach for the density matrix elements. We assumed both the pump and the probe beams can couple the excited states. A multi-mode approach for the coherence terms facilitates the study of all the frequency contributions due to the pump and the probe fields. Since the terms contain higher harmonics of the pump and the probe frequencies, we expressed them in Fourier transformed forms. To simulate the probe spectrum, we have solved inhomogeneous difference equations for the coherence terms using the Green’s function technique and continued fraction theory. The experimental line-widths of the EIT and the EIA are compared with our theoretical model. Our system can be useful in optical switching applications as it can be precisely tuned to render the medium opaque and transparent simultaneously.
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.
We have observed a transformation from electromagnetically-induced absorption (EIA) to electromagnetically induced transparency (EIT) in open systems of the 85 Rb D 1 line by adding an incoherent optical pumping laser. This result raises a new question about recent theoretical work which does not address the degree of open. The pump beam only plays a role in transferring atoms by a spontaneous transition into the interacting system for EIT observation, which is an incoherent process. The dependence of the absorption spectra on the intensity and the polarization of each laser beam were observed. We have found the same tendencies in all transitions except the F = 2 ↔ F′ = 3 transition of the 85 Rb D 1 line, which is the system that almost satisfies conventional EIA conditions.