Susceptibility for Doppler-broadened two-level atoms in pump–probe spectroscopy: analytical solutions revisited (original) (raw)
Related papers
Pump-probe spectroscopy in degenerate two-level atoms with arbitrarily strong fields
Physical Review A, 2008
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 F g → F e = F g + 1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is σ + polarized and the probe π 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) σ + polarized pump and π polarized probe, and (ii) σ + polarized pump and σ − 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.
Applied Physics B Photophysics and Laser Chemistry, 1983
The three-level probe spectroscopy of Doppler-broadened transitions in the presence of a standing wave pump laser is investigated through a diagrammatic method. A probe-response diagram is defined where the resonance positions versus the probe laser frequency and absorber velocity are plotted. The dressed atom description provides a convenient method for deriving the probe response diagram and calculating the position of the Doppler-free structures on the absorption spectrum, including the ac Stark shifts. We have interpreted probe spectra on the basis of the probe response diagram, presenting new features and giving a detailed physical interpretation of all the coherent effects appearing in the spectra. Population effects are not included in the dressed system analysis and are calculated on the basis of a semiclassical treatment, but the probe response diagram provides a complete interpretation of the involved phenomena.
Physical Review A, 1999
A numerical method is introduced that solves the optical Bloch equations describing a two-level atom interacting with a strong polychromatic pump field with an equidistant spectrum and an arbitrarily intense monochromatic probe field. The method involves a transformation of the optical Bloch equations into a system of equations with time-independent coefficients at steady state via double harmonic expansion of the densitymatrix elements, which is then solved by the method of matrix inversion. The solutions so obtained lead immediately to the determination of the polarization of the atomic medium and of the absorption and dispersion spectra. The method is applied to the case when the pump field is bichromatic and trichromatic, and the physical interpretation of the numerically computed spectra is given. ͓S1050-2947͑99͒10409-8͔
Pump-probe spectroscopy of degenerate 2-level systems with arbitrarily strong fields (2008)
2008
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 → F e alkali-metal transition interacting with an arbitrarily intense pump and probe ͑with general Rabi frequencies ⍀ 1,2 ͒ which are perpendicularly polarized with either Ϯ or 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 Ϯ polarized and the probe 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 + polarized and the probe − 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→ F e = 3 transition in the D 2 line of 87 Rb, interacting with a resonant + -polarized pump and either aor a − -polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual m g → 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 ⍀ 1 Ն⍀ 2 Ͼ⌫, and have the same behavior at line center and complementary behavior in the wings, when ⍀ 1 Ն⍀ 2 Ͻ⌫ ͑⌫ is the rate of spontaneous decay from F e to F g ͒.
Absorption spectra of driven degenerate two-level atomic systems
PHYSICAL REVIEW A, 2000
The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 ~1999! that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.
Physical Review A, 1997
We investigate theoretically the amplification of a laser beam propagating through a collection of Dopplerbroadened two-level atoms driven by an intense counterpropagating laser beam. Large amplification of the beam is predicted when the pump-beam Rabi frequency is comparable to the Doppler width of the atomic transition, even without including the effects of atomic recoil. The microscopic origin of the gain can be attributed to the coherent driving of the atomic dipole moment, suggesting that amplification and lasing due to collective atomic recoil may be influenced by this process. ͓S1050-2947͑97͒50203-4͔
Absorption spectra for strong pump and probe in atomic beam of cesium atoms
Physical Review A, 2009
We calculate the pump and probe absorption spectra for the cycling F g =4→ F e = 5 transition D 2 line of 133 Cs in an atomic beam, interacting with a strong resonant +-polarized pump and a probe of comparable intensity and either − or polarization. The aim is to reproduce and analyze the experiments of Dahl et al. ͓Opt. Lett. 33, 983 ͑2008͔͒ who showed for a +-polarized pump and −-polarized probe that the pump absorption spectrum switches from an "absorption within transparency" ͑AWT͒ structure, when the probe is weaker than the pump, to a "transparency within transparency" ͑TWT͒ 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 → m e transitions. When the +-polarized pump is stronger than the −-polarized probe, the population is swept toward the m g → 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 =−F g → m e = m g − 1 transition when the probe is near resonance, and to the m g = F g → 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 + pump and an even stronger 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.
Pump-probe absorption in Cesium atomic beam.
We calculate the pump and probe absorption spectra for the cycling F g =4→ F e = 5 transition D 2 line of 133 Cs in an atomic beam, interacting with a strong resonant + -polarized pump and a probe of comparable intensity and either − or polarization. The aim is to reproduce and analyze the experiments of Dahl et al. ͓Opt. Lett. 33, 983 ͑2008͔͒ who showed for a + -polarized pump and − -polarized probe that the pump absorption spectrum switches from an "absorption within transparency" ͑AWT͒ structure, when the probe is weaker than the pump, to a "transparency within transparency" ͑TWT͒ 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 → m e transitions. When the + -polarized pump is stronger than the − -polarized probe, the population is swept toward the m g → 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 =−F g → m e = m g − 1 transition when the probe is near resonance, and to the m g = F g → 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 + pump and an even stronger 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.
Absorption spectra for strong pump and probe in atomic beam of cesium atoms (2009)
2009
We calculate the pump and probe absorption spectra for the cycling F g =4→ F e = 5 transition D 2 line of 133 Cs in an atomic beam, interacting with a strong resonant + -polarized pump and a probe of comparable intensity and either − or polarization. The aim is to reproduce and analyze the experiments of Dahl et al. ͓Opt. Lett. 33, 983 ͑2008͔͒ who showed for a + -polarized pump and − -polarized probe that the pump absorption spectrum switches from an "absorption within transparency" ͑AWT͒ structure, when the probe is weaker than the pump, to a "transparency within transparency" ͑TWT͒ 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 → m e transitions. When the + -polarized pump is stronger than the − -polarized probe, the population is swept toward the m g → 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 =−F g → m e = m g − 1 transition when the probe is near resonance, and to the m g = F g → 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 + pump and an even stronger 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.
2011
In this work the quantum interference effect on the weak probe absorption in a closed three-level V atomic system driven by a coherent driving field is shown to result from the twoquantum processes, constructive for the amplification channels and destructive for the absorption channel. A fourth state in the atom is coupled incoherently to the V system and acts as both an incoherent pumping reservoir and as a stationary, final state in perturbation theory. The application refers to Be-like carbon ions where non-linear pump process of the 1s 2 2s5s(1 S e)-1s 2 2p5s(1 P 0) transition is combined with the absorption or emission of a single probe photon corresponding to 1s 2 2s5s(1 S e)-1s 2 2p7s(1 P 0) transition. The system is analyzed within the Rmatrix Floquet theory and codes results.