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Physical Review A

Absorption spectra for strong pump and probe in atomic beam of cesium atoms

T. Zigdon, A. D. Wilson‐Gordon, Harry Friedmann

Published Sep 16, 2009• 10 citations
Publisher

Abstract

We calculate the pump and probe absorption spectra for the cycling ${F}_{g}=4\ensuremath{\rightarrow}{F}_{e}=5$ transition ${D}_{2}$ line of $^{133}\text{C}\text{s}$ in an atomic beam, interacting with a strong resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and a probe of comparable intensity and either ${\ensuremath{\sigma}}_{\ensuremath{-}}$ or $\ensuremath{\pi}$ polarization. The aim is to reproduce and analyze the experiments of Dahl et al. [Opt. Lett. 33, 983 (2008)] who showed for a ${\ensuremath{\sigma}}_{+}$-polarized pump and ${\ensuremath{\sigma}}_{\ensuremath{-}}$-polarized probe that the pump absorption spectrum switches from an ``absorption within transparency'' (AWT) structure, when the probe is weaker than the pump, to a ``transparency within transparency'' (TWT) structure, when the probe is stronger than the pump. For all other polarization combinations, the pump spectrum displays AWT behavior at all probe intensities. We analyze our results by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. When the ${\ensuremath{\sigma}}_{+}$-polarized pump is stronger than the ${\ensuremath{\sigma}}_{\ensuremath{-}}$-polarized probe, the population is swept toward the ${m}_{g}\ensuremath{\rightarrow}{m}_{e}={m}_{g}+1$ transitions with the highest values of ${m}_{g}$, and the pump absorption spectrum has an AWT structure and resembles that of an $N$ system. However, when the probe is stronger than the pump, the population is swept toward the ${m}_{g}=\ensuremath{-}{F}_{g}\ensuremath{\rightarrow}{m}_{e}={m}_{g}\ensuremath{-}1$ transition when the probe is near resonance, and to the ${m}_{g}={F}_{g}\ensuremath{\rightarrow}{m}_{e}={m}_{g}+1$ transition when the probe is detuned from resonance. The pump and probe spectra are mirror images of each other and resemble those of a $V$ system where the probe has a peak at line center and the pump spectrum has a TWT structure. For a strong ${\ensuremath{\sigma}}_{+}$ pump and an even stronger $\ensuremath{\pi}$ probe, the population concentrates in the intermediate transitions, and the AWT to TWT changeover does not occur. We also show that the narrow features in the spectra at line center derive from transfer of coherence from the excited to the ground hyperfine levels.

DOI
10.1103/physreva.80.033825

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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 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 atomic four-level NNN configuration both analytically and numerically, for various pump and probe intensities, with and without transfer of coherence (TOC) and Doppler broadening, and compare the results obtained to those of realistic atomic systems. We find that TOC affects the whole spectrum, in addition to producing an electromagnetically induced absorption (EIA) peak at line center. We show that the EIA peak splits as the pump intensity increases. These results are compared with those of realistic systems. When the pump is ${\ensuremath{\sigma}}^{+}$ polarized and the probe is $\ensuremath{\pi}$ polarized, the results are similar to those of the NNN configuration. When the pump and probe polarizations are both linear with perpendicular polarizations, various NNN-like subsystems contribute to the spectrum. Consequently, the splitting of the EIA peak only occurs at very high pump intensities. We also discuss the influence of the probe on the pump absorption and refraction and find that both the pump and probe show EIA peaks when the pump intensity is low, and complementary behavior when the pump is intense. At both low and high pump intensity, the pump and probe dispersions are of opposite sign.
Pump?probe spectra of caesium D2 line are experimentally investigated in a Cs atomic vapour cell with co-propagating orthogonal linearly-polarized pump and probe laser beams. Absorption-reduction dips duo to electromagnetically induced transparency (EIT) in multi-?-type Zeeman sublevels of 6 S1/2 F=3?6 P3/2 F'=2 hyperfine transition and absorption-enhanced peaks due to electromagnetically induced absorption (EIA) in 6 S1/2 F=4?6 P3/2 F'=5 hyperfine transition are demonstrated. With detuned pump beam abnormal sign-reversed signals inside the EIT dip and the EIA peak are clearly observed.
When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.
The absorption of a resonant coupling laser driving a closed degenerate two-level system in an atomic cesium beam was investigated as a function of the detuning of a second laser probing the same transition. The measurements were performed for four different polarization combinations of the two laser beams. Except for the beams of counterrotating polarizations all coupling-laser absorption profiles showed "absorption within transparency," i.e., the absorption in the region around the two-photon resonance was smaller than the absorption corresponding to the one-photon transition induced by the coupling laser, and an extra absorption peak was observed on this curve at the two-photon resonance. With regard to the beams of counterrotating polarizations we observed a switch from absorption within transparency to "transparency within transparency" when the probe-laser power exceeded the constant coupling-laser power. In other words, the cesium ensemble became mostly transparent to the coupling-laser beam at the two-photon resonance.