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Ukrainian Journal of Physical Optics

Electromagnetically induced transparency and Autler-Townes effect in a generalized L-system: A five-level model

A. Żaba, Van Cao Long, Małgorzata Głódź, E. Paul-Kwiek, K Kowalski, Jerzy Szonert, Dariusz Woźniak, S. Gateva

Published Jan 1, 2013• 2 citations
Publisher

Abstract

We calculate electric susceptibility of a laser-dressed atomic medium.The model adopted in this work refers to the experiment with cold 85 Rb atoms, where the states F′ = 1, 2, 3 of the hyperfine manifold 5P 3/2 (F′) are strongly coupled with the ground state 5S 1/2 (F = 2), and the coupling is probed by a weak probing field from the other ground-state component 5S 1/2 (F = 3).We present a five-level model in which the states F = 2, 3 and F′ = 1, 2, 3 are taken into account, while the noncoupled state F′ = 4 is neglected.The model is used as a starting point to reproduce spectral features observed in the absorption of probe light passing through a cold sample of 85 Rb atoms in a magneto-optical trap.Basing on numerical solutions of this model, we have also studied in detail the impact on the probe spectra from the presence of the state F′ = 1 to which probing is forbidden by electric-dipole transition, but coupling is allowed [see, e.g., Proc. of SPIE 8770 (2013) 87700Q].

DOI
10.3116/16091833/14/3/135/2013

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Electromagnetically induced transparency (EIT) and Autler-Townes (A-T) effect were studied under conditions of strong coupling of the hyperfine manifold 5P3/2 (F') with the 5S 1/2 (F=2) ground state of cold 85Rb atoms in MOT. Transmission spectra of a weak probe beam, at the frequency scanned in the vicinity of the 5S1/2(F=3)→5P3/2(F') resonances were registered at various frequency settings of the coupling beam. The spectra were interpreted by applying optical Bloch equations. As a starting point, a 5-level model, accounting for F=2, 3 and F'=1, 2, 3 states was assumed (the noncoupled state F'=4 being neglected, but the F'=1 state, coupled but not directly probed, included, as its presence was found to be imprinted in the spectra). Such a model alone does not reproduce all the spectral features observed. Therefore we have considered the existence of the polarized light induced transitions between Zeeman substates, involving (F'=2, m') and (F'=3, m') upper states. In order to indirectly account for the m→m' absorption transitions to the non-coupled m' states, and to the pairs of states with incomplete coupling, we have complemented the results of the 5-level model with the ones of its reduced versions. Satisfactory agreement of the positions of respective modeled and experimental spectral peaks was achieved.

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Journal of Physics B Atomic Molecular and Optical Physics•Mar 24, 2021•8 citations
We calculate electric susceptibility of a laser-dressed atomic medium.The model adopted in this work refers to the experiment with cold 85 Rb atoms, where the states F′ = 1, 2, 3 of the hyperfine manifold 5P 3/2 (F′) are strongly coupled with the ground state 5S 1/2 (F = 2), and the coupling is probed by a weak probing field from the other ground-state component 5S 1/2 (F = 3).We present a five-level model in which the states F = 2, 3 and F′ = 1, 2, 3 are taken into account, while the noncoupled state F′ = 4 is neglected.The model is used as a starting point to reproduce spectral features observed in the absorption of probe light passing through a cold sample of 85 Rb atoms in a magneto-optical trap.Basing on numerical solutions of this model, we have also studied in detail the impact on the probe spectra from the presence of the state F′ = 1 to which probing is forbidden by electric-dipole transition, but coupling is allowed [see, e.g., Proc. of SPIE 8770 (2013) 87700Q].
Electromagnetically induced transparency (EIT) and Autler-Townes (A-T) effect were studied under conditions of strong coupling of the hyperfine manifold 5P3/2 (F') with the 5S 1/2 (F=2) ground state of cold 85Rb atoms in MOT. Transmission spectra of a weak probe beam, at the frequency scanned in the vicinity of the 5S1/2(F=3)→5P3/2(F') resonances were registered at various frequency settings of the coupling beam. The spectra were interpreted by applying optical Bloch equations. As a starting point, a 5-level model, accounting for F=2, 3 and F'=1, 2, 3 states was assumed (the noncoupled state F'=4 being neglected, but the F'=1 state, coupled but not directly probed, included, as its presence was found to be imprinted in the spectra). Such a model alone does not reproduce all the spectral features observed. Therefore we have considered the existence of the polarized light induced transitions between Zeeman substates, involving (F'=2, m') and (F'=3, m') upper states. In order to indirectly account for the m→m' absorption transitions to the non-coupled m' states, and to the pairs of states with incomplete coupling, we have complemented the results of the 5-level model with the ones of its reduced versions. Satisfactory agreement of the positions of respective modeled and experimental spectral peaks was achieved.
We have simulated spectra of weak probe absorption from one of two hyperfine structure (hfs) components of an atomic ground state, to a hfs manifold of an upper state. A stronger coupling transition was assumed to bind the other hfs component of the ground state with the same upper hfs manifold. The purpose of this simulation was to study the impact on the spectral features in probe absorption from the presence of a state to which the electric-dipole transition is allowed for coupling, but forbidden for probing. In relation to our other (experimental) work, we considered the D2-line transitions for 85Rb. With coupling from the 5S1/2(F=2) state, as in our experiment, the 5P3/2(F'=1) state is coupled but not-probed from the 5S1/2(F=3) state. In calculations we searched for steady-state solutions of optical Bloch equations assuming a 5-level model and RWA. The collisionless (cold) atoms were considered, and we assumed that decoherence was entirely due to natural decay and exciting lasers' linewidths. We investigated probe absorption spectra as a function of both coupling-field-induced Rabi frequency Ωc, and coupling field detuning from the atomic resonances. The 5-level model spectra were compared with the corresponding spectra result of 4-level model calculations performed by omission of the 5P3/2(F'=1) level. Even for small Ωc values close to the natural linewidth, for some detunings a considerable influence of the 5P3/2(F'=1) state on the spectra was observed which cannot be ignored in interpretations.
Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γ EIT ≈ A + B ( + , where Ω c and Ω p are the coupler and probe Rabi frequencies, Γ eg is the spontaneous decay rate of the intermediate 6P 3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γ ATS ≈ Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.
Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.
We report electromagnetically induced transparency (EIT) in cold 85 Rb atoms, trapped in the lower hyperfine level F = 2, of the ground state 5 2 S 1/2 (Tiwari V B et al 2008 Phys. Rev. A 78 063421). Two steady-state Λ-type systems of hyperfine energy levels are investigated using probe transitions into the levels F ′ = 2 and F ′ = 3 of the excited state 5 2 P 3/2 in the presence of coupling transitions F = 3 → F ′ = 2 and F = 3 → F ′ = 3, respectively. The effects of uncoupled magnetic sublevel transitions and coupling field's Rabi frequency on the EIT signal from these systems are studied using a simple theoretical model.
Abstract This work demonstrates an scheme in which a weak electric quadrupole ( E 2) transition with a controlled frequency detuning in a ladder configuration is used as an extremely non-perturbing probe for precisely identifying subtle details of the effects driven by AC fields coupling atomic states and the preparation of quantum states. For this purpose, we provide a precise experimental and theoretical study of the Autler Townes (AT) effect derived from a strong electric dipole transition stimulated by a resonant laser beam and probed by the E 2 interaction. The experiment was carried out for a 87 Rb atomic gas at room temperature in a velocity-selective scheme. The AT effect was monitored via the splitting of the fluorescence spectra associated with the spontaneous decay to the ground state. The theoretical description incorporates the modification of standard few-level schemes introduced by forbidden electric-dipole transitions selection rules. We develop an analytic ladder three-level scheme to approximate the cyclic 5S 1/2 F = 2 → 5P 3/2 F = 3 → 6P 3/2 F = 1, 2, 3 → 5S 1/2 F = 2 path. Other levels that could have effects on the fluorescence are included via a fourth level with effective parameters. Doppler effects and finite bandwidths of the laser beams are included in the theoretical model to closely reproduce the experimental results.