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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Pump-probe spectra modeled with inclusion of a dipole-coupled but not dipole-probedF'state, for the case of85Rb 5S1/2(F)↔5P3/2(F') transitions

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

Published Mar 15, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2015078

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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 (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 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].
We study the pump and probe absorption spectra, as a function of the probe detuning, in a degenerate two-level atomic system, for the case where the probe intensity is high enough to affect the pump absorption. The theory is valid for any ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ alkali-metal transition interacting with an arbitrarily intense pump and probe (with general Rabi frequencies ${\ensuremath{\Omega}}_{1,2}$) which are perpendicularly polarized with either ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ or $\ensuremath{\pi}$ polarization. We have constructed a computer program that can calculate the spectra without requiring one to write out the Bloch equations explicitly. We show that, when the pump is ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polarized and the probe $\ensuremath{\pi}$ polarized, or vice versa, the pump and probe absorptions depend on the Zeeman coherences between the nearest-neighboring ground or excited Zeeman sublevels, whereas when the pump is ${\ensuremath{\sigma}}_{+}$ polarized and the probe ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized, or vice versa, the Zeeman coherences that directly determine the absorption are between next-nearest neighbors. We report calculations of the pump and probe absorption spectra for the cycling ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition in the D2{D}_{2}D2​ line of 87Rb^{87}\text{R}\text{b}87Rb, interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from Fe{F}_{e}Fe​ to Fg{F}_{g}Fg​).
We investigated the multi-photon process of each hyperfine-structure dependence on the probe and coupling laser intensities in the closed and open ladder-type atomic configurations in the 5S1/2–5P3/2–5D5/2 transition of 87Rb atoms. When the intensity of the probe laser was comparable to that of the coupling laser, a variation of the closed atomic configuration of the 5S1/2 (F = 2)–5P3/2 (F′ = 3)–5D5/2 (F″ = 4) cycling transition from transmittance to absorption was observed clearly. The spectral features due to multi-photon effects were understood intuitively by using diagrammatic analysis. The observed spectra as functions of the probe and coupling laser intensities were in good agreement with the numerical results calculated with full density matrix equations that included all the degenerate magnetic sublevels of the 5S1/2–5P3/2–5D5/2 transition.
We experimentally study the absorption spectroscopy from a collection of gaseous 87Rb atoms at room temperature irradiated with three fields. Two of these fields are in a pump–probe saturation absorption configuration. The third field co-propagates with the pump field. The three fields address Zeeman degenerate transitions between hyperfine levels 5S1/2, F = 1 and 5P3/2, F = 0, F = 1 around the D2 line. We find a sub-natural absorption resonance in the counter-propagating probe field for equal detunings of all three fields. This absorption arises in conjunction with the appearance of increased transmission due to electro-magnetically induced transparency in the co-propagating fields. The novel feature of this absorption is its onset only for the blue of 5P3/2, F = 0, as the laser frequency is scanned through the excited states 5P3/2, F = 0, F = 1 and F = 2. The absorption rapidly rises to near maximum values within a narrow band of frequency near 5P3/2, F = 0. Our experimental results are compared with a dressed atom model. We find the threshold absorption to be a result of coherent interaction between the dressed states of our system.
Abstract The absorption features of a probe field propagating through a four-level N-type atomic system in the presence of two coherent radiation fields is studied analytically by using a density matrix formulation. The system has two ground levels and two excited levels. A weak probe laser couples the upper ground level to the lower excited level whereas a strong control field connects the lower ground level to the lower excited level. The coupling field acts between the upper ground level and the upper excited level. The transition parameters of the 87 Rb D 1 line have been used to simulate the probe response. The simulated probe absorption shows a gain-like structure depending on the relative field intensities. The spectral features of the probe response exhibit substantial differences under thermal averaging as compared to a Doppler-free condition. The splitting of simulated probe absorption can be explained by the dressed state model. Electromagnetically induced absorption (EIA) is observed in the simulated probe response curve when the spontaneous decay of the population from the uppermost excited state to the lower ground state is absent.