## On non-vanishing amplitude of Hanle electromagnetically induced absorption

Optics Express, Vol. 15, Issue 3, pp. 1328-1339 (2007)

http://dx.doi.org/10.1364/OE.15.001328

Acrobat PDF (460 KB)

### Abstract

Amplitude and linewidts of the Hanle EIA, obtained from transmission of the laser locked to closed *F _{g}
* →

*F*=

_{e}*F*+ 1 transitions in

_{g}^{85}Rb and

^{87}Rb, 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/cm

^{2}. 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/cm

^{2}. 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

9. M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **84**, 5094 (2000). [CrossRef] [PubMed]

10. A. M. Akulshin, A. Lezama, A. I. Sidorov, R. J. Mclean, and P. Hannaford, “Storage of light in an atomic medium using electromagnetically induced absorption,” J. Phys. B: At. Mol. Opt. Phys. **38**, L365 (2005). [CrossRef]

*is scanned near zero value, due to the alignment of atoms induced by the laser at B*

_{z}*= 0 and destroyed at B*

_{z}*> 0. More specifically for our configuration, a single optical field, parallel to the external magnetic field is used and coherent effects are induced by its two counter-rotating circular polarization components. Theoretically Hanle effects were analyzed on a closed*

_{z}*F*→

_{g}*F*=

_{e}*F*+ 1 transition, by calculating a steady-state population of excited states at different laser intensities [5

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

12. F. Renzoni, S. Cartaleva, G. Alzetta, and E. Arimondo, “Enhanced absorption Hanle effect in the configuration of crossed laser beam and magnetic field,” Phys. Rev. A **63**, 065401, (2001). [CrossRef]

12. F. Renzoni, S. Cartaleva, G. Alzetta, and E. Arimondo, “Enhanced absorption Hanle effect in the configuration of crossed laser beam and magnetic field,” Phys. Rev. A **63**, 065401, (2001). [CrossRef]

13. Y. Dancheva, G. Alzetta, S. Cartaleva, M. Taslakov, and Ch. Andreeva, “Coherent effects on the Zeeman sublevels of hyperfine states in optical pumping of Rb by monomode diode laser,” Opt. Commun. **178**, 103 (2000). [CrossRef]

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]

15. E. Alipieva, S. Gateva, E. Taskova, and S. Cartaleva, “Narrow structure in the coherent population trapping resonance in rubidium,” Opt. Lett. **28**, 1817 (2003). [CrossRef] [PubMed]

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]

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]

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]

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]

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]

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]

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

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]

*N*-scheme approximation, the probe EIA diminishes at high pump laser intensity . In very detailed study of open and closed

*F*= 1 →

_{g}*F*= 2 transition for the D1 line of

_{e}^{87}Rb 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]

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]

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

^{2}.

*F*= 3 →

_{g}*F*= 4 transition in

_{e}^{85}Rb and

*F*= 2 →

_{g}*F*= 3 in

_{e}^{87}Rb. We covered a wide range of laser intensities, below and above the saturation level. Our theoretical analyzes was done for the full atomic system of 16 Zeeman sublevels and for laser intensities used in the experiment. We also investigate, theoretically, effect of small stray laboratory magnetic field of a few mG on the shape of Hanle absorption spectra and on EIA amplitudes and widths. Amplitudes and widths of EIT as a function of laser intensity was thoroughly studied in homogeneously and inhomogenously broadened medium [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]

^{2}[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]

## 2. Experiment

*F*= 3 →

_{g}*F*= 4 of

_{e}^{85}Rb or

*F*= 2 →

_{g}*F*= 3 of

_{e}^{87}Rb 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]

*λ*/2) in front of the polarizer. Results for the

*F*= 3 →

_{g}*F*= 4 transition were obtained in 8 cm long Rb cell, while results for the

_{e}*F*= 2 →

_{g}*F*= 3 transition were obtained in 1 cm long Rb cell (with enriched

_{e}^{87}Rb 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

*B*, 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/cm

_{z}^{2}and 120 mW/cm

^{2}. Figure 2 shows absorption curves for two Rb cells. Normalized transmission,

*I*/

_{out}*I*, is between 35 – 60% and 60 – 75% for closed transitions in

_{in}^{85}Rb and

^{87}Rb, 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.

## 3. Theory

*F*= 3 →

_{g}*F*= 4 transition of

_{e}^{85}Rb. Optical Bloch equations were solved for density matrix elements

*ρ*for the atomic system of magnetic sublevels of both the ground

_{i,j}*F*= 3 and of the excited

_{g}*F*= 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

_{e}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]

*e*and

*g*refer to the ground and the excited state hyperfine levels, respectively. The diagonal elements of

*ρ*(

_{ei}_{ej}*ρ*) are populations of

_{gi}_{gj}*ρ*(gi) sublevels, and off-diagonal elements are Zeeman coherences between

_{ei}_{gj}*e*

_{i}*e*(

_{j}*ρ*) sublevels. Terms

_{gi}_{gj}*ρ*represent optical coherences between

_{ei}_{gj}*e*and

_{i}*g*sublevels. Fast oscillations at laser frequency

_{j}*ω*

_{(1)}in Eq.1 were eliminated by the substitution

*q*= 0,±1. Parameter ℊ

_{1}is proportional to the reduced matrix element of the dipole operator between the ground and the excited states.

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]

*ω*h̄ and

_{ei}*ω*h̄ are energies of the atomic sublevels of the excited and ground levels,

_{gi}*E*

_{(1)0}is the amplitude of the laser electric field. The laser electric field written in the rotation coordinate system with unit vectors

*+Δ*

_{S}*, where Δ*

_{R}*=*

_{S}*ω*

_{(1)}+

*ω*

_{g0}-

*ω*

_{e0}(difference between laser frequency and D2 line) is a single photon detuning, and Δ

*is a Raman, two-photon detuning due to Zeeman splitting. Raman detuning is calculated from Zeeman splitting of ground and excited states using Δ*

_{R}_{g(e)}= 1.39962

*g*

*F*

_{g(e)}MHz/Gauss, where

*g*

*F*

_{g(e)}is the Lande

*g*-factor for two hyperfine levels. For

^{85}Rb splittings of

*F*= 3 and of

_{e}*F*= 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

_{e}*ρ*in (1) corresponds to the transfer of population and of coherence from the excited to the ground level [4

_{gigj}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. 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]

*b*≤ 1 is the amount of off-diagonal elements

*ρ*. transferred onto coherences in ground states

_{eiej}*ρ*. The theoretical results presented below are for

_{gigj}*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 =

*v*/

_{mp}*r*, where

*v*= √2

_{mp}*k*/

_{B}T*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]

*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

*B*was included by the way of quantization axis along the total magnetic field.

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

*ρ*. 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.

_{eiei}## 4. Discussion

### 4.1. Experimental results

^{2}, for transition

*F*= 2 →

_{g}*F*= 3 in

_{e}^{87}Rb 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.

*F*= 2 →

_{g}*F*= 3 transition in

_{e}^{87}Rb, and in Fig. 5 for

*F*= 3 →

_{g}*F*= 4 transition in

_{e}^{85}Rb. 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/cm

^{2}(obtained when using 1 mm diameter laser beam), we also had similar results in a sense that transmission minimum at B

*=0 remains at steady value, and never changed sign.*

_{z}^{2}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

**57**, 2996 (1998). [CrossRef]

### 4.2. Theoretical results

*F*= 3 →

_{g}*F*= 4 in

_{e}^{85}Rb. 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 Δ

*= ±3 MHz. In Fig. 7(a) the laser intensity is 0.1 mW/cm*

_{S}^{2}, and in Fig. 7(b) we present calculations for higher laser intensities, from 1 to 40 mW/cm

^{2}. Small EIA, still observed at 1 mW/cm

^{2}at the center of wide transmission gain disappears at 3 mW/cm

^{2}. 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

**61**, 011802(R), (1999). [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]

*B*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.

_{z}*. Each of these calculeted curves has certain weigth. Maxwell-Boltzmann velocity distribution gives wide Doppler inhomogeneous broadening, but most of atoms have values of*

_{S}*v*(

_{z}*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 Δ

*≠ 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*

_{S}*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.

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]

*ρ*, and of coherence,

_{gi,gi}*ρ*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

_{gi,gj}*B*, the laser pumps the population in the ground state Zeeman sublevels

_{z}*m*= ±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

_{Fg}*F*= 4, via strong coupling between

_{e}*m*= 3 and

_{Fg}*m*= 4 sublevels. With increasing laser intensity, population of ground sublevels

_{Fe}*m*= ±3 goes through a maximum and increasing laser detuning moves this maximum towards higher laser intensities. This can explain observed behavior of EIA amplitude.

_{Fg}## 5. Conclusion

*F*→

_{g}*F*=

_{e}*F*+1 transitions in both

_{g}^{85}Rb and

^{87}Rb, 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

*B*= ±1 G. Effect of laboratory stray magnetic field on such resonances was evaluated theoretically and was found that measured residual, transversal (in respect to

_{z}*B*) 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.

_{z}## Acknowledgments

## References and links

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 |

2. | E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. XXXV, 257 (1996). [CrossRef] |

3. | F. Renzoni, W. Maichen, L. Windholz, and E. Arimondo, “Coherent population trapping with losses observed on the Hanle effect of the D1 sodium line,” Phys. Rev. A |

4. | A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, “Electromagnetically induced absorption in a four-state system,” Phys. Rev. A |

5. | F. Renzoni, C. Zimmermann, P. Verkerk, and E. Arimondo, “Enhanced absorption Hanle effect on the F |

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 |

7. | J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients: simple theoretical model,” J. Opt. Soc. Am. |

8. | A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity selective coherent population trapping,” Phys. Rev. Lett. |

9. | M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. |

10. | A. M. Akulshin, A. Lezama, A. I. Sidorov, R. J. Mclean, and P. Hannaford, “Storage of light in an atomic medium using electromagnetically induced absorption,” J. Phys. B: At. Mol. Opt. Phys. |

11. | Giovanni Moruzzi and Franco Strumia, “The Hanle effect and level crossing spectroscopy,” Plenum Press 1991. |

12. | F. Renzoni, S. Cartaleva, G. Alzetta, and E. Arimondo, “Enhanced absorption Hanle effect in the configuration of crossed laser beam and magnetic field,” Phys. Rev. A |

13. | Y. Dancheva, G. Alzetta, S. Cartaleva, M. Taslakov, and Ch. Andreeva, “Coherent effects on the Zeeman sublevels of hyperfine states in optical pumping of Rb by monomode diode laser,” Opt. Commun. |

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. |

15. | E. Alipieva, S. Gateva, E. Taskova, and S. Cartaleva, “Narrow structure in the coherent population trapping resonance in rubidium,” Opt. Lett. |

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. |

17. | A. Lipsich, S. Barreiro, A. M. Akulshin, and A. Lezama, “Absorption spectra of driven degenerate two-level atomic systems,” Phys. Rev. A |

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. |

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. |

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 |

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. |

22. | A. Lezama, S. Barreiro, and A. M. Akulshin, “Electromagnetically induced absorption,” Phys. Rev. A |

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 |

24. | G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, “LAser frequency stabilization by Doppler-free magnetic dichroism,” Appl. Phys. B |

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 |

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 |

27. | J. Alnis and M. Auzinsh, “Reverse dark resonance in Rb excited by a diode laser,” J. Phys. B: At. Mol. Opt. Phys. |

28. | F. Renzoni and E. Arimondo, “Population-loss-induced narrowing of dark resonances,” Phys. Rev. A |

29. | C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Atomic four-level N systems,” Phys. Rev. A |

**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

- 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]
- E. Arimondo, "Coherent population trapping in laser spectroscopy," Prog. Opt. 35, 257 (1996). [CrossRef]
- F. Renzoni, W. Maichen, L. Windholz, and E. Arimondo, "Coherent population trapping with losses observed on the Hanle effect of the D1 sodium line," Phys. Rev. A 55, 3710 (1997). [CrossRef]
- A. V. Taichenachev, A. M. Tumaikin, and V. I. Yudin, "Electromagnetically induced absorption in a four-state system," Phys. Rev. A 61, 011802 (1999). [CrossRef]
- 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 Semiclassical Opt. 3, S7 (2001). [CrossRef]
- 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]
- J. Dalibard and C. Cohen-Tannoudji, "Laser cooling below the Doppler limit by polarization gradients: simple theoretical model," J. Opt. Soc. Am. B 6, 2023 (1989).
- A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste and C. Cohen-Tannoudji, "Laser cooling below the onephoton recoil energy by velocity selective coherent population trapping," Phys. Rev. Lett. 61, 826 (1988). [CrossRef] [PubMed]
- M. Fleischhauer and M. D. Lukin, "Dark-State Polaritons in Electromagnetically Induced Transparency," Phys. Rev. Lett. 84, 5094 (2000). [CrossRef] [PubMed]
- A. M. Akulshin, A. Lezama, A. I. Sidorov, R. J. Mclean, and P. Hannaford, "Storage of light in an atomic medium using electromagnetically induced absorption," J. Phys. B: At. Mol. Opt. Phys. 38, L365 (2005). [CrossRef]
- Giovanni Moruzzi and Franco Strumia, "The Hanle effect and level crossing spectroscopy," (Plenum Press 1991).
- F. Renzoni, S. Cartaleva, G. Alzetta, and E. Arimondo, "Enhanced absorption Hanle effect in the configuration of crossed laser beam and magnetic field," Phys. Rev. A 63, 065401, (2001). [CrossRef]
- Y. Dancheva, G. Alzetta, S. Cartaleva, M. Taslakov, and Ch. Andreeva, "Coherent effects on the Zeeman sublevels of hyperfine states in optical pumping of Rb by monomode diode laser," Opt. Commun. 178, 103 (2000). [CrossRef]
- 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 Semiclassical Opt. 3, 181 (2001). [CrossRef]
- E. Alipieva, S. Gateva, E. Taskova, and S. Cartaleva, "Narrow structure in the coherent population trapping resonance in rubidium," Opt. Lett. 28, 1817 (2003). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- A. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption," Phys. Rev. A 59, 4732 (1999). [CrossRef]
- 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]
- G. Wasik, W. Gawlik, J. Zachorowski, and W. Zawadzki, "LAser frequency stabilization by Doppler-free magnetic dichroism," Appl. Phys. B 75, 613 (2002). [CrossRef]
- 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]
- 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]
- 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]
- F. Renzoni and E. Arimondo, "Population-loss-induced narrowing of dark resonances," Phys. Rev. A 58, 4717 (1998). [CrossRef]
- 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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