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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 3 — Feb. 5, 2007
  • pp: 1328–1339
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On non-vanishing amplitude of Hanle electromagnetically induced absorption

M. M. Mijailović, J. Dimitrijević, A. J. Krmpot, Z. D. Grujić, B. M. Panić, D. Arsenović, D. V. Pantelić, and B. M. Jelenković  »View Author Affiliations


Optics Express, Vol. 15, Issue 3, pp. 1328-1339 (2007)
http://dx.doi.org/10.1364/OE.15.001328


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Abstract

Amplitude and linewidts of the Hanle EIA, obtained from transmission of the laser locked to closed Fg Fe = Fg + 1 transitions in 85Rb and 87Rb, have maximum values at few mW/cm2. Amplitude of the EIA reaches steady value different from zero for higher laser intensities, even for laser intensities of 40 mW/cm2. Theoretical model of EIA, for the same atomic system as in the experiment, show that the laser intensity, at which maximum of amplitudes and widths occur, depends on the laser detuning. For smaller laser detuning of a few tens of MHz, EIA has a maximum and then vanishes at higher laser intensities. For larger laser detuning of the order of hundreds MHz (but still in the range of Doppler broadening) amplitude of the EIA has very broad maximum and remains above zero for intensities above 40 mW/cm2. Such theoretical results indicate that Hanle absorption peak remains in the experimental results, regardless of the laser intensities, due to Doppler effect.

© 2007 Optical Society of America

1. Introduction

Vanishing and sign reversal of EIA, i.e., appearance of transmission peak at two photon resonance, was observed when laser light changes from linear to circular [14

14. G. Alzetta, S. Cartaleva, Y. Dancheva, Ch. Andreeva, S. Gozzini, L. Botti, and A. Rossi, “Coherent effects on the Zeeman sublevels of hyperfine states at the D1 and D2 lines of Rb,” J. Opt. B: Quantum Semiclass. Opt. 3, 181 (2001). [CrossRef]

]), and when coherence of the exited state is significantly destroyed by collisions with the buffer gas [6

6. H. Failache, P. Valente, G. Ban, V. Lorent, and A. Lezama, “Inhibition of electromagnetically induced absorption due to excited-state decoherence in Rb vapor,” Phys. Rev. A 67, 043810 (2003). [CrossRef]

]. Effect of laser intensity on Hanle EIA amplitude was predicted theoretically by Renzoni et al. [5

5. F. Renzoni, C. Zimmermann, P. Verkerk, and E. Arimondo, “Enhanced absorption Hanle effect on the Fg=F -Fe=F+1 closed transitions,” J. Opt. B: Quantum Semiclass. Opt. 3, S7 (2001). [CrossRef]

]. Theoretical studies of probe laser EIA show that the EIA also vanishes at very high pump laser intensities. Such is the work by Taichenachev et al.[4

4. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802(R), (1999). [CrossRef]

], where, using a four-state N-scheme approximation, the probe EIA diminishes at high pump laser intensity . In very detailed study of open and closed Fg = 1 → Fe = 2 transition for the D1 line of 87Rb Goren at al., [20

20. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems,” Phys. Rev. A 68, 043818 (2003). [CrossRef]

] have shown that for the same linear polarization of probe and pump lasers, probe EIA can switch to absorption dip only if Doppler broadening is not taken into account. Effect of Doppler broadening on EIA at various laser ellipticity was recently studied and it was shown that maximum of the EIA amplitude at the laser ellipticity different from zero can be explained only if Doppler effect is taken into account [21

21. D. V. Brazhnikov, A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, S. A. Zibrov, Y. O. Dudin, V. V. Vasilev, and V. L. Velichansky, “Features of magneto-optical resonances in an elliptically polarized traweling light wave,” JETP Lett. 83, 64 (2006). [CrossRef]

]. Experimental probe-pump studies of EIA have shown that a probe transmission keeps its EIA shape at high pump laser intensity [1

1. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996 (1998). [CrossRef]

,22

22. A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732 (1999). [CrossRef]

]. Using orthogonally polarized probe and pump lasers, Kim et al.[18

18. K. Kim, M. Kwon, H. D. Park, H. S. Moon, H. S. Rawat, K. An, and J. B. Kim, “Electromagnetically induced absorption spectra depending on intensities and detunings of the coupling field in Cs vapour,” J. Phys. B: At. Mol. Opt. Phys. 34, 4801 (2001). [CrossRef]

] demonstrated the switch from EIA to a transmission peak at pump laser intensity of 150 mW/cm2.

2. Experiment

The experimental set-up is shown in Fig. 1. Depending of the Rb cell we have used, the extended cavity diode laser (DL) is locked to either Fg = 3 → Fe = 4 of 85Rb or Fg = 2 → Fe = 3 of 87Rb hyperfine transitions of the D2 line using Doppler free dichroic atomic vapor laser lock technique (DDAVLL) [24

24. G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “LAser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613 (2002). [CrossRef]

]. The plane of laser polarization was determined by linear polarizer (P), while the laser power was set by rotating half-wave plate (λ/2) in front of the polarizer. Results for the Fg = 3 → Fe = 4 transition were obtained in 8 cm long Rb cell, while results for the Fg = 2 → Fe = 3 transition were obtained in 1 cm long Rb cell (with enriched 87Rb isotope). The cell was at room temperature. The cell is placed into the center of a large three pairs Helmholtz coils. Around the cell is a coaxial solenoid which provides the magnetic field Bz, parallel with the laser beam and the gas cell axis and is used to scan the magnetic field in the ±1 G range. Before entering the cell the laser light is collimated by a pair of lenses (L) to a beam waist between 1 and 15 mm. Laser intensity is obtained from measured laser power and a beam profile at the sample. The input laser intensity was between 0.05 mW/cm2 and 120 mW/cm2. Figure 2 shows absorption curves for two Rb cells. Normalized transmission, Iout/Iin, is between 35 – 60% and 60 – 75% for closed transitions in 85Rb and 87Rb, respectively. For values of laser intensities in the following discussions and figures we will state mean values of laser intensities in the cell, assuming its exponential decay in the cell.

Fig. 1. Experimental set-up. DL - diode laser, L - collimating lenses, D - detector.

3. Theory

In this section we present the model used to calculate transmission of a laser beam, resonant to the closed Fg = 3 → Fe = 4 transition of 85Rb. Optical Bloch equations were solved for density matrix elements ρi,j for the atomic system of magnetic sublevels of both the ground Fg = 3 and of the excited Fe = 4 states. Zeeman sublevels are coupled by the linearly polarized laser field propagating in a direction of the external magnetic field. The model includes spontaneous transfer of low-frequency coherence of the excited sublevels to the ground states [4

4. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802(R), (1999). [CrossRef]

]. The optical Bloch equations, assuming pure radiative relaxation and the closed system, have the form

ρ˙eiej=[29ΓL12+i(ωejωei)]ρeiej
2il=33[ρ˜eigl(μgl,ej,1μgl,ej,1)ρ˜eiej(μei,gl,1μei,gl,1)]γρeiej
ρ˜˙eigj=[ΓL912+i(ω(1)+ωgjωei)]ρ˜eigj
2i{l=44[ρeiel(μel,gj1μel,gj1)]l=33[ρglgj(μej,gl1μej,gl,1)]}γρ˜eigj
Fig. 2. Ratio of transmitted and input laser intensities as a function of the input laser beam intensity for: a)vacuum 87Rb cell of 1 cm length (the laser is locked to the Fg = 2 → Fe = 3) and b) vacuum Rb cell of 8 cm length (the laser is locked to the Fg = 3 → Fe = 4), at room temperature at B = 0. Solid lines are drawn to guide the eye.
ρ˙gigj=[2(b+(1b)δij)q=11μei+q,gi,qμej+q,gj,q*ρei+qej+qΓL+i(ωgjωgi)ρgigj]
2il=44[ρ˜giel(μel,gj,1μel,gj,1)ρ˜el,el(μgi,el1μgi,el,1)]
γ(ρgigj17δij)
(1)

where e and g refer to the ground and the excited state hyperfine levels, respectively. The diagonal elements of ρeiej(ρgigj) are populations of ρeigj(gi) sublevels, and off-diagonal elements are Zeeman coherences between ei ej (ρgigj) sublevels. Terms ρeigj represent optical coherences between ei and gj sublevels. Fast oscillations at laser frequency ω (1) in Eq.1 were eliminated by the substitution

ρeigj=ρ˜eigjeiω(1)t.
(2)

The matrix elements of the electric dipole moments in Eq. 1 were calculated from

μeme,gmg,q=1(1)me(314mgqme).
(3)

where q = 0,±1. Parameter ℊ1 is proportional to the reduced matrix element of the dipole operator between the ground and the excited states.

1~neLerngLg
(4)

Reduced matrix element is taken from [25

25. M. L. Haris, C. S. Adams, S. I. Cornish, L. C. McLeud, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006). [CrossRef]

]. In Eq. (1) ωeih̄ and ωgih̄ are energies of the atomic sublevels of the excited and ground levels,29ΓL12=Γ,Γ=2π5.89MHzis the decay rate of the excited state. 2=E(1)022h and E (1)0 is the amplitude of the laser electric field. The laser electric field written in the rotation coordinate system with unit vectors u±1u1=exiey2u+1=ex+iey2 is

Er0t=u1u+122eiω(1)tE(1)0
(5)

Laser detuning is given by Δ = ΔSR, where ΔS = ω (1) + ω g0 - ω e0 (difference between laser frequency and D2 line) is a single photon detuning, and ΔR is a Raman, two-photon detuning due to Zeeman splitting. Raman detuning is calculated from Zeeman splitting of ground and excited states using Δg(e) = 1.39962 g F g(e) MHz/Gauss, where g F g(e) is the Lande g-factor for two hyperfine levels. For 85Rb splittings of Fe = 3 and of Fe = 4 levels with magnetic field are 0.46 MHz/Gauss and 0.7 MHz/Gauss, respectively. The light Rabi frequency of the individual transition is

ΩRgkej=2μgk,ej
(6)

The first term in the expression for ρgigj in (1) corresponds to the transfer of population and of coherence from the excited to the ground level [4

4. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802(R), (1999). [CrossRef]

,26

26. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003). [CrossRef]

]. The parameter 0 ≤ b ≤ 1 is the amount of off-diagonal elements ρeiej. transferred onto coherences in ground states ρgigj. The theoretical results presented below are for b = 1. The ground state relaxation rates were taken into account by γ. In the vacuum Rb cell at room temperature γ is determined by the atom transit time through the laser beam. Under these assumption we have calculated γ from γ = vmp/r, where vmp = √2kBT/M is the most probable velocity of the atoms (equal ∼ 240 m/s for Rb atoms at room temperature [27

27. J. Alnis and M. Auzinsh, “Reverse dark resonance in Rb excited by a diode laser,” J. Phys. B: At. Mol. Opt. Phys. 34, 3889 (2001). [CrossRef]

]) and r is the radius of the laser beam. In our theoretical treatment, the change in the laser beam intensity along the Rb cell (Fig. 2) and along the laser beam diameter (usually Gaussian profile) have not been taken into account. The effect of magnetic field transversal to Bz was included by the way of quantization axis along the total magnetic field.

The system of equations given in (1) was solved assuming a steady state of an atomic system. Such approximation is correct for cold atoms, like for laser cooled atomic gas, when the interaction time between the atoms and the laser are long enough so that a steady-state is reached. Our experimental results can be compared to the steady state solution of the Eq. (1) since the estimated atom transit time through the laser beam is longer than calculated time required for atoms to reach a steady state when suddenly illuminated by light tuned to a closed transition [28

28. F. Renzoni and E. Arimondo, “Population-loss-induced narrowing of dark resonances,” Phys. Rev. A 58, 4717 (1998). [CrossRef]

]. Light absorption is calculated from the sum of populations of all magnetic substates of the excited state, i.e., diagonal density matrix elements, Σρeiei. Theoretical results shown below are in fact presented as a laser transmission, obtained after subtracting total absorption from unity. Note that measurements of total fluorescence is also a measure of the total light absorption, assuming the same decay rate for all sublevels. Calculations were performed for the same range of the laser intensities as in the experiment.

4. Discussion

4.1. Experimental results

Figure 3 shows experimental Hanle EIA for two laser intensities, 0.1 and 11 mW/cm2, for transition Fg = 2 → Fe = 3 in 87Rb and for the laser beam diameter of 2.5 mm. For intensities above these, experimental results also show characteristical EIA shape, like curves in Fig. 3. These curves were obtained by averaging more than 500 samples on the storage oscilloscope.

Fig. 3. Hanle EIA for (a) 0.1 mW/cm2 and (b) 11 mW/cm2 of the laser intensity. The laser is locked to the D2 Fg = 2 → Fe = 3 transition in 87Rb; beam diameter is 2.5 mm.

Experimental results for the Hanle EIA amplitude and width as a function of the laser intensity are given in Fig. 4 for the Fg = 2 → Fe = 3 transition in 87Rb, and in Fig. 5 for Fg = 3 → Fe = 4 transition in 85Rb. Solid lines in figures are to guide the eye. We evaluated amplitudes and widths at the interval of magnetic fields between -1 and 1 G. On these range there are no complex curves like these in Fig. 7(b) and only one peak is observed. Amplitude was evaluated like the difference between maximum of the curve and a minimum between 2 maxima. Width is a full width at half of the amplitude of the Hanle transmission curves. This method agrees with fitting the curves with double Lorentzian. Data points in these curves were also obtained after fitting transmission curves, like curves in Fig. 3 by double Lorentzian. One of Lorentzian represents a wider Hanle signal, much wither than our scanning range. Second Lorentzian represents EIA resonance which is of opposite sign than Hanle signal. Widths present domain of magnetic field in which Zeeman coherences are not yet destroyed. Note that data given in two figures were obtained using two Rb cells. For results in Fig. 4 we used 1 cm long cell with enriched 87 isotope. Both amplitude and width of the EIA have maximums. From results presented in Figs. 4 and 5 it follows that maximums for 85 and 87 isotopes appear at similar laser intensities after correction for different laser absorption (due to different absorption coefficients and different cell lengths, Fig. 2) are taken into account. Insert in Fig. 4(a) shows amplitude variations at lowest laser intensities. This interesting width narrowing of EIA at high laser intensity is in contrast to well established EIT behavior vs laser intensity. The errors for widths and amplitudes, given by error bars in Figs. 4 and 5 were estimated from experimental conditions and they are primarily due to presence of laboratory stray magnetic field, quality of polarizing optics, stability of laser intensity and frequency, and errors originating from fitting transmission curves. We like to note that we made few measurements at much higher intensities then those presented in Figs. 4 and 5. For the laser intensity of 100 mW/cm2 (obtained when using 1 mm diameter laser beam), we also had similar results in a sense that transmission minimum at Bz=0 remains at steady value, and never changed sign.

Fig. 4. (a) Amplitude of the Hanle EIA and (b) Full width at half maximum and as a function of the laser intensity for Fg = 2 → Fe = 3 transition in 87Rb. Points in the insert are experimental data for at lowest laser intensities and line is the linear fit.

Dependence of the EIA width on the inverse value of the laser beam diameter, for the laser intensity of 0.8 mW/cm2 is shown in Fig. 6. Solid line is a linear fit with a coefficient 410 ± 75 mG mm. Such dependence of the widths suggests that at these intensities inverse of atomic time of flight through the laser beam can be taken as coherence decay (like in our calculations). Dependence of Hanle EIA width is similar to the result observed in the atomic fluorescence in the pump-probe experiment [1

1. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57, 2996 (1998). [CrossRef]

].

4.2. Theoretical results

Numerical calculations for transmission of the laser were done for the atomic transition Fg = 3 → Fe = 4 in 85Rb. Detunings of the order of a few MHz simulate experimental transmission curves (Fig. 3) better than zero detuning. Results in Fig. 7 are for the laser detuning ΔS = ±3 MHz. In Fig. 7(a) the laser intensity is 0.1 mW/cm2, and in Fig. 7(b) we present calculations for higher laser intensities, from 1 to 40 mW/cm2. Small EIA, still observed at 1 mW/cm2 at the center of wide transmission gain disappears at 3 mW/cm2. Calculations of transmission of a probe laser in probe-pump studies show that probe EIA changes with a laser intensity and, similar to a Hanle EIA, switches to a transmission peak at high Rabi frequency [4

4. A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A 61, 011802(R), (1999). [CrossRef]

, 29

29. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Atomic four-level N systems,” Phys. Rev. A 69, 053818 (2004). [CrossRef]

].

Residual magnetic fields at the location of the Rb cell also influence the shape, amplitude and width of EIA. Magnetic fields transversal to Bz field, measured at the center of large Helmholtz coils, are < 5 mG. Such level of stray magnetic field should not change the amplitude or the width of the EIA, according to our calculations. Calculated EIA curve for transversal magnetic field of 20 mG (dashed line in 7(a)) shows very small difference from the curve at zero transversal magnetic field.

In a gas with Maxwell velocity distribution, total transmission is a superposition of transmissions calculated for different velocities i.e., corresponding detunings ΔS. Each of these calculeted curves has certain weigth. Maxwell-Boltzmann velocity distribution gives wide Doppler inhomogeneous broadening, but most of atoms have values of vz(z-axis components of velocities, direction of laser light propagation) such that laser detuning due to Doppler effect is in the range of a few MHz. Theoretical results for the EIA amplitudes and widths, as a function of the laser intensity, are given in Fig. 8. Curves in Fig. 8 correspond to different laser detunings ΔS ≠ 0. They show that intensities at which EIA amplitude has maximum and intensities at which EIA vanishes, strongly depend on the laser detuning. As laser detunings increase, they both move towards larger laser intensities. Moreover, at temperature T = 300 K even atomic velocities corresponding to detunings of several hunderds of MHz have a non-negligable weight. Theory indicates that at such large detunings, amplitude and width do not fall to zero at the highest experimental laser intensity or even higher. Very important conclusion then follows from theoretical results: we were not able to experimentally observe vanishing of EIA, because of Doppler broadening.

Fig. 5. (a) Amplitude of the Hanle EIA, (b) Full width at half maximum and as a function of the laser intensity for Fg = 3 → Fe = 4 transition in 85Rb.
Fig. 6. Full width at a half maximum of the EIA as a function of inverse laser beam diameter. The solid line is linear fit through the data. The laser intensity is 0.8 mW/cm2.
Fig. 7. Calculated transmission of linearly polarized input laser, detuned by Δ = 3 MHz from the Fg = 3 → Fe = 4 transition in 85Rb, as a function of the magnetic field for laser intensity (a) 0.1 mW/cm2 (transversal magnetic field zero (solid line) and 20 mG (dashed line)), and (b) 1,3,20,30 and 40 mW/cm2 for curves from top to bottom, respectively. Please note different scales for magnetic fields in (a) and (b).

Behavior of EIT amplitude and width at low and high laser intensities were studied previously. Javan at al., [23

23. A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, “Narrowing of electormagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A 66, 013805 (2002). [CrossRef]

] in their thorough analyzes gave analytical expressions for EIT widths as a function of the laser intensity. They found square-root dependence at low laser intensity (below saturation) and linear dependence at higher laser intensity. We have shown in this work that EIA amplitude and width behave quite differently with increasing laser intensity. These results can be understood from numerical results of the population, ρgi,gi, and of coherence, ρgi,gj of Zeeman sublevels of the ground state hyperfine level as a function of the laser intensities. Figure 9 shows how the populations of each Zeeman level change with the laser intensity. When we choose quantization axis parallel to the external magnetic field Bz, the laser pumps the population in the ground state Zeeman sublevels mFg = ±3. This is not the result of a strong correlation among sublevels of the same hyperfine state, instead it is the result of saturation of the Zeeman sublevels of Fe = 4, via strong coupling between mFg = 3 and mFe = 4 sublevels. With increasing laser intensity, population of ground sublevels mFg = ±3 goes through a maximum and increasing laser detuning moves this maximum towards higher laser intensities. This can explain observed behavior of EIA amplitude.

Fig. 8. Calculated (a) amplitude and (b) width of the EIA as a function of the laser intensity when input light is near-resonant to Fg = 3 → Fe = 4 transition in 85Rb. Maximum of both EIA amplitude and width shifts to higher laser intensities as the laser detuning takes values 3,5,10,15 and 20 MHz.

5. Conclusion

In this paper we presented experimental and theoretical results for amplitudes and widths of the Hanle EIA, obtained with the laser resonant to close FgFe = Fg+1 transitions in both 85Rb and 87Rb, as a function of the laser intensity. Amplitudes and widths were obtained from measured and calculated absorption resonances for the range of external magnetic field Bz = ±1 G. Effect of laboratory stray magnetic field on such resonances was evaluated theoretically and was found that measured residual, transversal (in respect to Bz) magnetic field below 5 mG does not influence the main result of the paper. Same results of EIA amplitude and width obtained with two Rb cells of very different lengths, also indicate that stray magnetic field was well compensated.

Both amplitude and width of the EIA, as a function of laser intensities, have maximums. Therefore, EIA behaves differently from well known behavior of EIT. Behavior of the theoretical EIA amplitudes and widths depends on the laser detuning - detuning influences intensity corresponding to maximums of amplitude and width. Beyond the maximum, theoretical EIA amplitude goes to zero and then switches sign to a broad transmission gain. Instead, experimental EIA amplitude and width saturates at the value different from zero. Theoretical results of the EIA amplitude and widths at different laser detunings suggest that the reason for discrepancies between theory and experiment is Doppler effect present in the experiment. Appearance of the maximum of the EIA amplitude, at particular laser intensity, can be understood from similar behavior of the loss of population of the ground state Zeeman sublevels, most coupled by the laser light.

Fig. 9. Calculated population of Zeeman sublevels of Fg = 3 in 85Rb as a function of the laser intensity; mF = ±3 (solid line), mF = ±2 (dashed line), mF = ±1 (dotted line), mF = 0 (dashed-dotted line).

Acknowledgments

This work was supported by the Ministry of science and environmental protection of the Republic of Serbia, under grant number 141003.

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A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A 59, 4732 (1999). [CrossRef]

23.

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, “Narrowing of electormagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A 66, 013805 (2002). [CrossRef]

24.

G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “LAser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B 75, 613 (2002). [CrossRef]

25.

M. L. Haris, C. S. Adams, S. I. Cornish, L. C. McLeud, E. Tarleton, and I. G. Hughes, “Polarization spectroscopy in rubidium and cesium,” Phys. Rev. A 73, 062509 (2006). [CrossRef]

26.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003). [CrossRef]

27.

J. Alnis and M. Auzinsh, “Reverse dark resonance in Rb excited by a diode laser,” J. Phys. B: At. Mol. Opt. Phys. 34, 3889 (2001). [CrossRef]

28.

F. Renzoni and E. Arimondo, “Population-loss-induced narrowing of dark resonances,” Phys. Rev. A 58, 4717 (1998). [CrossRef]

29.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Atomic four-level N systems,” Phys. Rev. A 69, 053818 (2004). [CrossRef]

OCIS Codes
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Quantum Optics

History
Original Manuscript: November 30, 2006
Revised Manuscript: December 29, 2006
Manuscript Accepted: December 29, 2006
Published: February 5, 2007

Citation
M. M. Mijailovic, J. Dimitrijevic, A. J. Krmpot, Z. D. Grujic, B. M. Panic, D. Arsenovic, D. V. Pantelic, and B. M. Jelenkovic, "On non-vanishing amplitude of Hanle electromagnetically induced absorption in Rb," Opt. Express 15, 1328-1339 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-3-1328


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References

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  16. J. Alnis, K. Blush, M. Auzinsh, S. Kennedy, N. Shafer-Ray, and E. Abraham, "The Hanle effect and level crossing spectroscopy in Rb vapour under strong laser excitation," J. Phys. B: At. Mol. Opt. Phys. 36, 1161 (2003). [CrossRef]
  17. A. Lipsich, S. Barreiro, A. M. Akulshin, and A. Lezama, "Absorption spectra of driven degenerate two-level atomic systems," Phys. Rev. A 61, 053803 (2000). [CrossRef]
  18. K. Kim, M. Kwon, H. D. Park, H. S. Moon, H. S. Rawat, K. An, and J. B. Kim, "Electromagnetically induced absorption spectra depending on intensities and detunings of the coupling field in Cs vapour," J. Phys. B: At. Mol. Opt. Phys. 34, 4801 (2001). [CrossRef]
  19. H. S. Moon, S. K. Kim, K. Kim, C. H. Lee, and J. B. Kim, "Atomic coherence changes caused by optical pumping applied to electromagnetically induced absorption," J. Phys. B: At. Mol. Opt. Phys. 36, 3721 (2003). [CrossRef]
  20. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Switching from positive to negative dispersion in transparent degenerate and near-degenerate systems," Phys. Rev. A 68, 043818 (2003). [CrossRef]
  21. D. V. Brazhnikov, A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, S. A. Zibrov, Y. O. Dudin, V. V. Vasilev, and V. L. Velichansky, "Features of magneto-optical resonances in an elliptically polarized traweling light wave," JETP Lett. 83, 64 (2006). [CrossRef]
  22. A. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999). [CrossRef]
  23. A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, "Narrowing of electormagnetically induced transparency resonance in a Doppler-broadened medium," Phys. Rev. A 66, 013805 (2002). [CrossRef]
  24. G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "LAser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613 (2002). [CrossRef]
  25. M. L. Haris, C. S. Adams, S. I. Cornish, L. C. McLeud, E. Tarleton, and I. G. Hughes, "Polarization spectroscopy in rubidium and cesium," Phys. Rev. A 73, 062509 (2006). [CrossRef]
  26. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Electromagnetically induced absorption due to transfer of coherence and to transfer of population," Phys. Rev. A 67, 033807 (2003). [CrossRef]
  27. J. Alnis and M. Auzinsh, "Reverse dark resonance in Rb excited by a diode laser," J. Phys. B: At. Mol. Opt. Phys. 34, 3889 (2001). [CrossRef]
  28. F. Renzoni and E. Arimondo, "Population-loss-induced narrowing of dark resonances," Phys. Rev. A 58, 4717 (1998). [CrossRef]
  29. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Atomic four-level N systems," Phys. Rev. A 69, 053818 (2004). [CrossRef]

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