We have experimentally studied electromagnetically induced transparency (EIT) and absorption (EIA) in hot 85Rb atomic vapor using probe and coupling light with comparable power levels. We have shown that strong-probe EIT has different linewidth and appears in fewer configurations than does usual, weak probe EIT. In V-scheme, where optical pumping and saturation are dominant mechanisms, narrow EIT is possible only when a probe is tuned to a closed transition. The width of the EIT resonance increases with laser intensity with non-linear dependence, similar to the weak-probe EIT in Λ- scheme. The EIT in Λ- scheme was observed when two transitions had balanced population losses. The EIA was modified for the case of a strong probe as well: in four-level N-scheme with Zeeman sublevels the EIA was observed only for a cycling transition when F’=F+1, where F and F’ are the angular momenta of the 5 2S1/2 (ground) and 5 2P3/2 (excited) state hyper-fine levels, respectively. The combination of strong probe and strong coupling laser beam intensities allows observation of an absorption dip due to three-photon resonance in a four-level scheme that involves the Raman transitions via virtual level.
©2005 Optical Society of America
Coherent population trapping (CPT) is a nonlinear process associated with coherent excitation of atomic transitions and formation of a superposition of atomic levels by strong resonant laser fields [1, 2]. Formation of CPT leads to two effects: electromagnetically induced transparency (EIT) due to destructive interference and electromagnetically induced absorption (EIA) due to constructive interference of atomic transitions.
After the first experimental work on the EIT  and its theoretical explanation [4, 5], the EIT became a subject of intense study, due to its different applications: lasing without inversion , high resolution spectroscopy , enhancement of refractive index , high-precision magnetometry  and slow light generation . EIA was observed in experiments [11, 12] and explained by Taichenachev et al.  as a coherence transfer from the excited to the ground states, due to spontaneous emission. It has been recently shown that, for a closed transition when F’=F+1, and for lasers of the same linear polarization, the EIA is due to transfer of population . Continuing interest in EIA is related to its potential applications in high-speed optical modulation  and optical switching in a solid sample .
Usually EIT and EIA resonances are studied with a strong pump (drive) and a weak probe, i.e., when a strong pump laser couples two of the atomic energy levels, and a weak probe laser couples one of the two levels with the third one. However, recent theoretical studies [17, 18] have shown that both EIT and EIA in systems with comparable probe and pump laser beam intensities have novel features. Studies of atomic systems interacting with a probe that has intensity comparable to the pump intensity have shown that the EIT resonances become weaker for both V- and Λ- schemes . The analyses of a system with degenerate Zeeman sublevels show that when pump Rabi frequency increases system goes from a peak in laser transmission to peak in laser absorption , and that three-photon EIA splits into three parts: Autler-Townes absorption peaks with the central transparency peak in between .
Interaction with strong laser fields allows observation of a three-photon resonance via virtual level with the pump laser far detuned from the resonance [18, 20]. For a cascade scheme, not investigated here, the calculations and experiment have shown different probe absorption spectra depending on whether the probe is weak or strong, and also on whether the strong probe is weaker, comparable or stronger then the pump .
In this work we have studied interaction of two strong laser fields with 85Rb vapor by measuring the transmission of the fixed-frequency coupling laser while tuning the frequency of the probe laser. The probe laser intensity is comparable to the coupling laser intensity and the probe itself is modifying the atomic system. Since in this case both lasers can dress the atoms, the goal of the work is to compare the behavior of three and two level systems in this configuration with the more familiar behavior of these systems when in the configuration where the transmission of a weak probe is measured. In the V- scheme the strong probe makes the population losses large and observation of EIT difficult. We have found that narrow EIT in the V-scheme is possible when one laser couples a closed transition and population losses, induced by other laser, are moderate. The width of this EIT increases with the laser field when the laser intensity is in the range of 5 to 35 mW/cm2. We are not aware of other measurements of EIT linewidth in a V- scheme when the width is affected by the decay rate of the excited state. In the Λ- scheme, due to a repumping role of the probe laser, narrow EIT (similar to weak probe result ) can be seen only if population losses induced by the probe are not large. When the two lasers were tuned to closed transition F→F’=F+1, EIA was observed. While Ye et al.  were able to see the EIA in open transitions in 87Rb, we could observe the EIA only when the lasers coupled a closed transition. With high probe intensity and the detuning of two lasers close to the splitting of the 85Rb ground state hyperfine levels, the transmission spectra exhibits a characteristic dip. This may be due to a three-photon resonance absorption peak, similar to a three-photon enhanced absorption of the moderate power probe in the experiment with D1 light .
The experimental set-up and the energy levels of 85Rb relevant to this work’s D2 line are presented in Fig. 1. Two linear and orthogonally polarized laser beams at ~780 nm couple hyperfine levels of the ground 2S1/2 and excited 2P3/2 state. The coupling laser was locked to a transition between two hyperfine levels by using saturation absorption spectroscopy with two fully overlapped counter-propagating laser beams. The frequency stabilization is digital and performed by a PC: the signal from the differential amplifier is digitized, the lock-in signal is obtained from its first derivative and the active feedback loop is turned on at the zero-crossing of the lock-in signal.
The two laser beams co-propagate through the 10-cm-long room-temperature Rb cell with natural abundance of Rb isotopes. The lasers are overlapped before entering the Rb cell by a polarizing cube, and separated with another polarizing beam splitter after leaving the cell. Co-propagating beams eliminate cross-over resonances and, because of similar wave-vectors k and k’ of two fields, the residual two-photon linewidth v(k-k′)  (v is atom velocity) is much smaller than the typical sub-Doppler width of the absorption lines. When the two lasers are detuned from each other by the hyperfine splitting of the ground state, this residual width is of the order of several kHz.
The transmission of the coupling laser is detected with the photo diode while the probe frequency was swept across the 2P3/2 levels from the hyperfine level F. Detecting transmission of the frequency-fixed coupling vs tunable-probe frequency eliminates underlying Doppler-broadened profile . The Rb cell is shielded by two layers of a µ metal. A solenoid inside the magnetic shield provides a controllable axial magnetic field. The laser intensity ranges from 5–80 mW/cm2 and is controlled by half-wave plates and polarizers. The cross sections of the unfocused coupling and probe beams were elliptical. Lengths of the ellipse axis are 0.7 and 1.8 mm for the coupling laser beam and 0.5 and 1.3 for the probe laser beam so that the areas of the two beams are ~4mm2 and ~2mm2.
3. Results and Discussion
We have investigated the EIT in a three-level system by using V and Λ- schemes. EIT observed in weak probe experiments requires a strong pump laser beam to reduce dephasing of the coherence. Here, we investigate behavior of EIT when both pump and probe lasers have higher intensity. When both lasers are tuned to the same cycling transition we observe enhanced absorption which can be explained by the four-level N-scheme [17,18].
3.1 V-type scheme
Usually EIT can not be isolated from several processes that also affect laser transmission in the V-scheme. The contribution to laser transmission from different mechanisms is expected to be more pronounced at high probe intensity. As an example of the transmission spectrum, we present the spectrum with peaks that are due to different mechanisms in the V-scheme: pumping, saturation and EIT. Due to the short life-time of the 2P3/2 levels, optical pumping is faster than the build-up of coherence in the upper levels and thus in the presence of large pumping EIT can not be observed. Figure 2 shows the transmission spectrum of the coupling laser locked at the F=2→F’=3 transition while the probe scans across transitions F=2→5 2P3/2. For the middle and upper curves, the intensities of the lasers were ~7 mW/cm2 and ~18 mW/cm2, respectively. The bottom curve is the coupling laser transmission when the probe is blocked, or when the probe is far detuned from the resonance. The peaks 1–3 are Doppler-free peaks, obtained when the probe is tuned to the hyperfine levels F’=1, 2 and 3. Different widths of the peaks indicate different excitation mechanisms present in the V-system . For peak 3 both lasers are tuned to the F=2→F’=3 transition and this peak is predominantly broadened by the field saturation. The transparency of peak 3 reaches ~90% of the coupling laser transmission without the Rb cell (transmission equals to 7 on the arbitrary scale of Fig. 2). The transmission peak 2 is due to the large population loss to the non-coupled hyper-fine level of the ground state: nearly two times more population is transferred from F’=2 to F=3 then back to F=2 . When the probe is tuned to the F=2→F’=1 transition, pumping by the probe to the F=3 level is prevented by transition rules. The EIT process competes then with saturation and with pumping into magnetic sub-levels of one of the ground state hyperfine levels. The narrow width of the peak of a few MHz indicates that the peak is predominantly due to the EIT. The reduced background of peak 1 might be due to the probe pumping the magnetic sublevels of F=2 level to levels with lower magnetic number.
In Fig. 3(a), the EIT (peak 1 from Fig. 2) with an expanded frequency scale is shown for different probe laser intensities. The two absorption peaks around the EIT peak, so called Autler-Townes peaks, are expected at sufficiently high intensity of the laser field and when two-photon detuning is close to laser the Rabi frequency, Ω/2π [4, 26]. The EIT width in this case is defined by the splitting of the absorption peaks  and the atom velocities . It is not straightforward to relate unambiguously the Rabi frequency to laser intensity in this experiment. Estimates can be obtained from Ω=2πγ(I/8)1/2 where I is the laser intensity in mW/cm2, and γ is the decay rate of the excited state . The laser intensities for the three curves in Fig. 3 (a), 8, 15 and 25 mW/cm2 correspond to Rabi frequencies of ~γ, 1.5γ and 2γ, respectively. The γ for 2P3/2 is ~6MHz.
In V- scheme, the EIT width depends strongly on the spontaneous decay rate, and, at higher laser intensity, is affected by power broadening. According to Fig. 3(a), the spacing of the absorption peaks and the EIT linewidth increases with laser intensity. Also, with higher laser power the symmetry of the EIT peaks decreases, which makes determination of the dependence of the line width on laser intensity difficult. Nevertheless, fitting transmission peaks with Gaussian curves we obtained estimated linewidths at several laser intensities. In Fig. 3(b) we plot the EIT linewidth vs Rabi frequency, estimated from measured laser intensity using the above approximation . The solid line is drawn as a guide to the eye. In the Λ- scheme, with a strong pump (Rabi frequency much higher than the relaxation rate of the lower level coherences and the decay rate of the excited state) and a weak probe, the EIT width is expected to increase linearly with laser intensity .
Strong probe in V- scheme masks EIT except when the probe is tuned to the cycling transition, F=2→F’=1. When the probe is coupling another cycling transition, the F=3→F’=4 transition and coupling laser locked to the same F=3→F’=3 transition (the result not presented here) the transmission peak is broadened due to saturation. When both lasers are tuned to the F=2→F’=3 transition we observe a broad transmission maximum, while Ye et al., in the transmission spectra of the weak probe laser for the same open transition observed the EIA with the similar (narrow) width as in closed transitions.
3.2 Λ-type scheme
We have investigated the behavior of the atomic system in a Λ- scheme with the coupling laser beam locked to an open transition and to an closed transition. Figure 4 shows two traces of the coupling laser transmission when the probe laser scans across different F’ levels. For the upper curve, the coupling laser is locked on the F=2→F’=3 resonance and probe scans the F=3→2P3/2 transition. Laser intensities are ~20 mW/cm2. The absorption peaks 2 and 3 are due to optical pumping by the probe laser and correspond to the probe tuned to the transitions with F’=2 and F’=3, respectively. The condition for EIT is met only for peak 3 when the two lasers share a common upper level and this peak is due to optical pumping and EIT. When the coupling and probe laser beams are tuned to the F=3→F’=2 transition, the narrow EIT is missing from the transmission spectrum because of extremely high population losses for the F=2→F’=2 transition.
For the lower curve in Fig. 4, the coupling laser is resonant with the F=3→F’=4 transition and peaks 2 and 3 correspond to the probe scanning across the F=2→F’=2 and 3 transitions. There are no Λ-schemes for zero velocity atoms in this configuration. The coupling laser is Doppler shifted into the F=3→F’=3 and F=3→F’=2 resonances by positive velocity atoms with velocities v’ such that kv’1=Δ43 and kv’2=Δ42 where Δ43 or Δ42 are hyperfine splittings between the F’=4 and F’=3 and 2 levels, respectively. As the probe frequency increases above the value for peak 3 the probe interacts with atoms from the same velocity groups which then tunes both lasers to two Λ- schemes (3→2’, 2→2’ and 3→3’,2→3’) simultaneously. At this probe frequency we see the absorption peak V’ and, due to two Λ-type schemes, a transmission peak that splits the V’ absorption peak into the EIT doublet. The peak V”, in the upper trace, is also due to Doppler tuning of the coupling laser to the F=2→F’=2 transition and probe to the F=3→F’=3 transition.
The EIT peak in the Λ-scheme (probe on the F=2→F’=3 transition, pump on the F=3→F’=3 transition) with a weak probe laser beam was observable with pump power above 1 mW . When probe intensity is increasing we continue to see this EIT with upper level F’=3, but not if the upper level is F’=2 presumably due to very high population losses associated with the F=2→F’=2 transition .
3.3 N-type scheme
There are two N-schemes analyzed in this work, one in a four-(sub)level degenerate two-level system and the other in a four-level system composed of three hyperfine levels and one virtual level. Analyses of atomic four-state N-configuration systems can explain the behavior of a realistic two-level atom with degenerate Zeeman sublevels [17,29]. The N- scheme with four states is characterized by absorption of two photons from one laser field (stronger pump) and one photon from the second laser field (weaker probe).
The transmission spectrum of the coupling laser locked to the F=3→F’=4 transition shows (Fig. 5(a)) enhanced absorption at the center of the transmission peak 4, obtained when the probe laser has the same frequency as the coupling laser. Both lasers have similar intensities of ~17 mW/cm2. The EIA background for two lasers coupled to the same F=3→F’=4 transition in Fig. 5(a) is different from that shown in [11, 29] which was obtained with a standard, weak probe. Here the background is the transmission peak 4, which is due to saturation of the transition and pumping atoms with atoms whose velocities Doppler-tune frequencies of both lasers to F=3→F’=3 transitions. The intensity of peak 4 can be compared to intensity of peaks 2 and 3 obtained when the probe couples F=3 and F’=2 and 3, respectively, for atoms with zero velocity.
The EIA peak is shown again, on an expanded scale, in Fig. 5(b). Calculations have predicted  that the probe absorption for this transition is the Mollow triplet, i.e., two absorption peaks with a transmission peak in between. The observed EIA peak is due to coherence induced among the Zeeman sub-levels and therefore depends on the ambient magnetic field. As shown in Fig. 5(b), the transmission spectrum of the coupling laser when the probe laser is near the F=3→F’=4 transition changes when the magnetic field B changes from B=0 to 300mG. The magnetic field lifts the degeneracy of the Zeeman sublevels, shifting them by Δz=1.39962·106 gFB, where Δz is the level splitting in Hz, gF is the Landé factor, and B is the magnetic field, in Gauss. At 300mG the splitting of sublevels of the F=3 level is 0.139 MHz, which seems to be enough to eliminate the atomic dark state, into which atoms are pumped when B=0. Decreasing absorption with increasing magnetic field, shown by the three curves in Fig. 5(b), represents a study of the Hanle effect on the F→F’=F+1 cycling transition. This, the variation of the EIA amplitude vs magnetic field, is presented in the insert in Fig. 5(b). The FWHM of this curve is much larger than that of the Hanle curve obtained in fluorescence of the single laser coupling the F=3→F’=4 transition .
Calculated pump laser transmission in the N- scheme with degenerate sublevels in the cycling F=3→F’=4 transition  shows that as the pump intensity increases, the EIA observed at low intensity changes to a transmission peak at moderate intensity. With a further increase of laser intensity, so that the pump Rabi frequency is equal to two times the spontaneous emission rate from the excited state, the absorption peak reappears along with two transmission peaks that are due to Autler-Townes effect. Using the same formula  to estimate laser intensity from the Rabi rates, for the F=3→F’=4 transition, I=7.56(Ω/2πγ)2, we found that the intensities of both lasers in our experiment are above the value required for the re-appearance of EIA.
In our set-up, we were not able to observe EIA in any F’=F+1 transition of 85Rb other then the closed transition. This is similar to results presented in , but differs from results given in  where EIA was observed for an open F’=F+1 transition for weak probe intensity. In Ref. , with two high-power lasers, the EIA in a Cs vapor was observed only in closed transition. With laser power comparable to ours, the EIA shape in Ref.  is similar to EIA feature in Fig. 5(b) at zero magnetic field.
A different N- scheme arises when the two lasers are frequency shifted with respect to each other by the hyperfine splitting of the ground state. The trace in Fig. 6(a) was obtained when the coupling laser was locked to the F=2→F’=3 transition and the probe laser scanned across a broad frequency range of several GHz. The coupling laser intensity was 20 mW/cm2. The Λ and V peaks in Fig. 6(a) occur when the probe laser is coupling F=3 and 2 levels, respectively, to 2P3/2. The third peak, 3p, is at the probe detuning corresponding to the ground state hyperfine splitting of 3.03 GHz. This peak can result from three-photon resonance, similar to observations in Ref. . This process is schematically shown by the energy level diagram in Fig. 6(a). The coupling-laser photon allows for the transition from F=3 to an intermediate virtual level, the probe-laser photon induces stimulated emission from the virtual level to F=2, and then, the second coupling laser photon excites the atom to a hyper-fine level of 2P3/2. In Fig. 6(b), two shapes of this peak are shown for two probe laser powers, 70 mW/cm2 and 80 mW/cm2. Three-photon resonances, observed in  show similar splitting of absorption peak into two components when the laser power increases. That absorption peak, of the fixed-frequency laser obtained in the experiment with the D1 line , is considerably narrower then peak 3p in Fig. 6(b).
We have discussed observation of the EIT and EIA resonances in the absorption spectrum of a coupling laser, when the coupling and probe laser beams have similar intensities and co-propagate through Doppler-broadened 85Rb vapor. In comparison with the weak-probe case, there are fewer atomic configurations for which narrow resonances can be observed in both the V and Λ- schemes. In the V-type scheme, if population losses due to optical pumping can be induced by both lasers, the EIT is completely masked. The width of the EIT in the V-scheme, affected by spontaneous emission and power broadening, is of the order of a few MHz and increases as the laser intensity increases. Although in the Λ- scheme a stronger probe laser beam intensity has less negative effect on the EIT, the observation of EIT is still partially or fully masked by saturation and pumping. The EIT was observed with lasers coupling two ground hyperfine levels to F’=3 for both zero and non zero velocity atoms. We have found that absorption features corresponding to two-photon resonance in atoms within different velocity groups can be readily observed by increasing the probe intensity. EIA was observed only when both lasers are tuned to a closed transition that increases the angular momentum by one, F→F’=F+1. High power for both lasers allows detection of the absorption peaks in the transmission spectrum of the coupling laser when one laser is detuned from the F→2P3/2 resonance and the frequency difference between two lasers is close to the hyperfine splitting of the ground state. We have found that the laser power window for the observation of this particular absorption feature is narrow because the absorption profile changes quickly (with power) from a single absorption peak to two transmission peaks.
The authors are thankful to A. Matsko and D. Rostohar for reading the manuscript and for useful suggestions. This work was supported by the Ministry of science and environmental protection of the Republic of Serbia, under grant number 1443.
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