## Resonant gain suppression and superluminal group velocity in a multilevel system |

Optics Express, Vol. 20, Issue 10, pp. 10712-10720 (2012)

http://dx.doi.org/10.1364/OE.20.010712

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### Abstract

We investigate the interaction of an open (N + 1)-level extended V-type atomic system (i.e. a closed (N + 2)-level atomic system) with N coherent laser fields and one incoherent pumping field through both analytical and numerical calculations. Our results show that the system can exhibit multiple resonant gain suppressions via perfect quantum destructive interference, which is usually believed to be absent in closed three-level V system and its extended versions involving more atomic levels, with at most N – 1 transparency windows associated with very steep anomalous dispersions occurring in the system. The superluminal group velocity of the probe-laser pulse with at most N – 1 negative values can also be generated and controlled with little gain or absorption.

© 2012 OSA

## 1. Introduction

1. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science **326**, 1074–1077 (2009). [CrossRef] [PubMed]

5. L. Thevenaz, “Slow and fast light in optical fibres,” Nat. Photonics **2**, 474–481 (2008). [CrossRef]

2. A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. **12**, 104001 (2010). [CrossRef]

6. S. Chu and S. Wang, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. **48**, 738–741 (1982). [CrossRef]

7. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science **301**, 200–202 (2003). [CrossRef] [PubMed]

8. M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. **87**, 081113 (2005). [CrossRef]

9. K. Y. Song, K. S. Abedin, and K. Hotate, “Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering,” Opt. Express **16**, 225–230 (2008). [CrossRef] [PubMed]

8. M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. **87**, 081113 (2005). [CrossRef]

9. K. Y. Song, K. S. Abedin, and K. Hotate, “Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering,” Opt. Express **16**, 225–230 (2008). [CrossRef] [PubMed]

10. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature **406**, 277–279 (2000). [CrossRef] [PubMed]

11. C. Zhu and G. Huang, “High-order nonlinear Schrodinger equation and weak-light superluminal solitons in active Raman gain media with two control fields,” Opt. Express **19**, 1963–1974 (2011). [CrossRef] [PubMed]

7. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science **301**, 200–202 (2003). [CrossRef] [PubMed]

12. F. Arrieta-Yanez, O. G. Calderon, and S. Melle, “Slow and fast light based on coherent population oscillations in erbium-doped fibres,” J. Opt. **12**, 104002 (2010). [CrossRef]

13. C.-L. Cui, J.-K. Jia, J.-W. Gao, Y. Xue, G. Wang, and J.-H. Wu, “Ultraslow and superluminal light propagation in a four-level atomic system,” Phys. Rev. A **76**, 033815 (2007). [CrossRef]

14. A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. **83**, 4277–4280 (1999). [CrossRef]

15. K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A **68**, 013810 (2003). [CrossRef]

16. C.-L. C., J.-K. Jia, Y. Zhang, Y. Xue, H.-L. Xu, and J.-H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B: At. Mol. Opt. Phys. **44**, 215504 (2011). [CrossRef]

*c*as required by the causality, although the pulse center may attain a group velocity much larger than

*c*in an anomalous dispersive medium [17–19

19. M. D. Crisp, “Concept of group velocity in resonant pulse propagation,” Phys. Rev. A **4**, 2104–2108 (1971). [CrossRef]

16. C.-L. C., J.-K. Jia, Y. Zhang, Y. Xue, H.-L. Xu, and J.-H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B: At. Mol. Opt. Phys. **44**, 215504 (2011). [CrossRef]

20. E. Paspalakis and P. L. Knight, “Electromagnetically induced transparency and controlled group velocity in a multilevel system,” Phys. Rev. A **66**, 015802 (2002). [CrossRef]

*N*+ 2)-level atomic system and then the resulted superluminal light propagation. The system we considered may be regarded as a (

*N*+ 1)-level open system, the extended version of a three-level open V system [16

16. C.-L. C., J.-K. Jia, Y. Zhang, Y. Xue, H.-L. Xu, and J.-H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B: At. Mol. Opt. Phys. **44**, 215504 (2011). [CrossRef]

*N*– 1 strong coherent fields (couplings). Similar as in Ref. [16

**44**, 215504 (2011). [CrossRef]

*perfect*quantum

*destructive*interference, which has not been proved to exist in the (

*N*+1)-level extended V-type system, the lower level in the open (

*N*+1)-level system should have a spontaneous decay rate much larger than those of the

*N*upper levels. This specific situation may be realized when all

*N*upper levels in the open (

*N*+1)-level system are chosen to be highly excited Rydberg states of radiative lifetimes up to tens of microseconds [21–23

23. D. Yan, J.-W. Gao, Q.-Q. Bao, H. Yang, H. Wang, and J.-H. Wu, “Electromagnetically induced transparency in a five-level Λ system dominated by two-photon resonant transitions,” Phys. Rev. A **83**, 033830 (2011). [CrossRef]

*N*– 1 narrow and deep transparency windows, which are in fact the signatures of

*perfect*quantum

*destructive*interference, may be obtained in the open (

*N*+ 1)-level system, and that the probe field is superluminal at the transparency frequencies with at most

*N*– 1 different group velocities. Then we consider a few examples with realistic parameters for cold

^{87}Rb atoms. Full numerical calculations based on the coupled Maxwell-Bloch equations well confirm our analytical conclusions.

## 2. Model and equations

*N*+ 2)-level atomic system as illustrated in Fig. 1, in which level |1〉, level |2〉, ..., and level |

*N*〉 may refer to

*N*Rydberg states with very high principal quantum numbers while level |

*g*〉 and level |0〉 belong, respectively, to the ground state and the first excited state with the same principal quantum number. In this situation, spontaneous decay rate (Γ

*) of level |*

_{i}*i*〉 (

*i*= 1, 2,...,

*N*) is expected to be much smaller than that (Γ

_{0}) of level |0〉. As far as cold

^{87}Rb atoms are concerned, Γ

*(*

_{i}*i*= 1, 2,...,

*N*) is about 10 kHz for a highly excited Rydberg state with principal quantum number

*n*≈ 70 while Γ

_{0}is equal to 6.0 MHz for the 5

*P*

_{3/2}state. A monochromatic probe field coherently drives the atomic transition between level |1〉 and level |0〉 with the complex Rabi frequency Ω

*=*

_{p}*E⃗*·

_{p}*d⃗*

_{10}/2

*h̄*and the real frequency detuning Δ

*=*

_{p}*ω*−

_{p}*ω*

_{10}. The

*n*th monochromatic coupling field coherently drives the atomic transition between level |

*n*+ 1〉 and level |0〉 with the complex Rabi frequency Ω

*=*

_{n}*E⃗*·

_{n}*d⃗*

_{n}_{+1,0}/2

*h̄*and the real frequency detuning Δ

*=*

_{n}*ω*−

_{n}*ω*

_{n}_{+1,0}(

*n*= 1, 2,...,

*N*− 1). A broadband laser [24

24. M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pumpfields,” Phys. Lett. A **357**, 66–71 (2006). [CrossRef]

26. D. Bullock, J. Evers, and C. H. Keitel, “Modifying spontaneous emission via interferences from incoherent pump fields,” Phys. Lett. A **307**, 8–12 (2003). [CrossRef]

*g*〉 into level |1〉 at the rate Λ without introducing atomic coherence between level |

*g*〉 and other levels. It is clear that level |

*g*〉 is coherently decoupled from the other

*N*+ 1 levels and therefore we can envision here an open (

*N*+ 1)-level system consisting of only levels |1〉, |2〉, ..., |

*N*〉, and |0〉, the extended version of a three-level open V system [16

**44**, 215504 (2011). [CrossRef]

*N*+ 1)-level system can be written as which allows us to attain the following Bloch equations for density matrix elements

*γ*

_{1}

*= (Γ*

_{n}_{1}+ Γ

*+ Λ)/2,*

_{n}*γ*

_{10}= (Γ

_{1}+ Γ

_{0}+ Λ)/2,

*γ*= (Γ

_{mn}*+ Γ*

_{m}*) /2 and*

_{n}*γ*

_{n}_{0}= (Γ

*+ Γ*

_{n}_{0}) /2 are defined as the decay rates of atomic coherence

*ρ*

_{1}

*,*

_{n}*ρ*

_{10},

*ρ*, and

_{mn}*ρ*

_{n}_{0}respectively (

*m*≠

*n*,

*m,n*= 2 ∼

*N*).

*<< Γ*

_{p}_{0}) and weak pump (Λ << Γ

_{0}) limits, we can analytically solve Eqs. (2) in the steady state to attain

*but in all order of Ω*

_{p}*(*

_{n}*n*= 1 ∼

*N*− 1), which is proportional to the linear probe susceptibility with

*N*being the atomic volume density,

*d*

_{10}the dipole moment on transition |1〉 ↔ |0〉,

*δ*= Δ

_{n}*− Δ*

_{p}*the two-photon Raman detuning between the probe and the*

_{n}*n*th coupling field, and

*ω*. Calculating imaginary and real parts of the linear probe susceptibility with realistic parameters, it is straightforward to examine the absorption and dispersion spectra on transition |1〉 ↔ |0〉 in the next section. Considering Λ ≈ Γ

_{p}*<< Γ*

_{i}_{0}(

*i*= 1, 2,...,

*N*), the probe field is amplified if

*Im*(

*χ*) < 0 in a certain spectral region. In addition, the susceptibility goes to zero when

*δ*= 0 with

_{n}*n*= 1 ∼

*N*− 1. Therefore, if all the coupling detunings are different then this open (

*N*+1)-level system will become transparent at

*N*− 1 different frequencies of the probe field.

*M*out of the

*N*− 1 coupling detunings Δ

*are equal to Δ and the remaining*

_{n}*N*−

*M*− 1 are different than Δ (for simplification, we take Δ

_{1}= Δ

_{2}= ... = Δ

*= Δ), the susceptibility then approximates which means that*

_{M}*N*−

*M*transparency windows will appear in the probe gain spectrum. Finally, if all the coupling detunings Δ

*are equal to Δ then the susceptibility reduces to Thus, all these*

_{n}*N*− 1 transparency windows will degenerate into a single one.

*ω*is concerned, the following Maxwell wave equation in the slowly-varying-envelope approximation is also required: where

_{p}*f*(

*z,t*) is the dimensionless pulse envelope (i.e.,

*E⃗*=

_{p}*⃗f*(

*z,t*)). In particular, we have

*f*(

*z,t*) ≡ 1 and

*E⃗*≡

_{p}*⃗*in the limit of a cw field. For the convenience of both quantitative calculation and qualitative analysis, we further transform Eq. (6) into the retarded local frame where

*τ*=

*t − z/c*and

*ξ*=

*z*, with

*α*=

*N*|

*d*

_{10}|

^{2}

*ω*/

_{p}*ε*

_{0}

*h̄c*Γ

_{0}being the propagation constant and

*N*+ 1)-level system into with Eq. (3) taken into account under the two-photon resonant condition Δ

*= Δ*

_{p}*(Δ*

_{n}*≠ Δ*

_{n}*,*

_{m}*m,n*= 1, 2,...,

*N*− 1). Therefore, if none of the coupling detunings are the same, the probe field can propagate with

*N*− 1 different group velocities in the medium. The group velocity

*υ*at the

_{g}*n*th transparency window center can be controlled via the intensity of the

*n*th coupling laser field. Obviously, it is always larger than the light speed in vacuum

*c*and a critical Rabi frequency

_{0}represents a specific value of the coupling Rabi frequency Ω

*(*

_{n}*υ*is negative when Ω

_{g}*< Ω*

_{n}_{0}whereas positive when Ω

*> Ω*

_{n}_{0}). Note that one may control Ω

_{0}by changing the atomic volume density

*N*or the incoherent pumping rate Λ. However, the definition of Ω

_{0}is valid only for a nonzero Λ although it could be very small. If we set Λ = 0, all atoms under consideration will be located at the coherently decoupled level |

*g*〉 so that the probe and coupling fields interact with nothing, i.e., propagate as in vacuum.

*M*out of the

*N*− 1 coupling detunings Δ

*are equal (for simplification, we take Δ*

_{n}_{1}= Δ

_{2}= ... = Δ

*= Δ), the group velocity of the probe pulse then becomes the same as Eq. (9) at the*

_{M}*n*th transparency window center with

*n*=

*M*+ 1,...,

*N*− 1, and around detuning Δ. Finally, if all

*N*fields are on two-photon resonance, the group velocity then becomes at the single transparency window center. To deduce Eq. (10) and Eq. (11), we have assumed that

*γ*

_{1}

*=*

_{n}*γ*

_{1}

*(*

_{m}*n*,

*m*= 2 ∼

*N*) without the loss of generality.

## 3. Results and discussion

*N*+ 1)-level system with realistic parameters for cold

^{87}Rb atoms. We plot in Fig. 2 the imaginary (solid curves) and real (dashed curves) parts of the probe susceptibility

*χ*as a function of the probe detuning Δ

*for an open four-level system (*

_{p}*N*= 3). It is clear that the weak probe field is always amplified around its resonant frequencies and two narrow transparency windows will arise between three gain lines in the case of Δ

_{1}≠ Δ

_{2}. In addition, the transparency windows are accompanied by very steep anomalous dispersions as determined by the Kramers-Kronig relation, which is essential for attaining the superluminal light propagation with

*υ*>

_{g}*c*or even

*υ*< 0. The narrow and deep transparency windows are in fact the signatures of

_{g}*perfect*quantum

*destructive*interference and can be observed only when the lower level has a spontaneous decay rate much larger than those of all the upper levels Γ

*<< Γ*

_{i}_{0}(

*i*= 1

^{∼}

*N*). In a closed (

*N*+ 1)-level extended V-type system, however, one will find quantum

*constructive*interference instead. These remarks can be verified by the same method as in Ref. [16

**44**, 215504 (2011). [CrossRef]

*g*〉 and level |1〉 has non-vanishing populations because the probe field is very weak, level |0〉 has a much larger decay rate than level |1〉, and the coupling field Ω

*will not excite atoms into level |*

_{n}*n*〉 in the presence of

*perfect*quantum

*destructive*interference. In addition, as we can see from Fig. 4, the middle gain line between Δ

*= Δ*

_{p}_{1}and Δ

*= Δ*

_{p}_{2}can become very narrow if we increase the coupling Rabi frequencies Ω

_{1}and Ω

_{2}[see Fig. 4(a)] or decrease the coupling detuning difference |Δ

_{1}− Δ

_{2}| [see Fig. 4(b)], while the outboard one near Δ

*= Δ*

_{p}_{1}(Δ

*= Δ*

_{p}_{2}) can become very narrow if we choose a large detuning Δ

_{1}(Δ

_{2}) of the respective coupling field Ω

_{1}(Ω

_{2}) [see Fig. 4(c)]. Such dynamically controlled narrow gain lines may have potential applications in the accurate spectroscopic measurement.

*N*= 4) (see Fig. 5) and open six- (

*N*= 5) (see Fig. 6) level systems. As we can see, at most three and four transparency windows appear between four and five gain lines, respectively. Accordingly, we can attain the superluminal light signals when their frequencies fall into these transparency windows accompanied by the anomalous dispersion.

*N*+ 1)-leve system with realistic parameters for cold

^{87}Rb atoms. As an example, we consider here an open four-level system (

*N*= 3). We suppose that the probe pulse is bichromatic

*E*

_{p}_{1}(

*E*

_{p}_{2}) is on Raman resonance with the monochromatic coupling field Ω

_{1}(Ω

_{2}). Both envelopes of the two components are supposed to be in the Gaussian shape. In Fig. 7 we show the magnitude squared of two-color pulse envelopes at different penetration positions in the medium as a function of the time delay with Δ

_{1}≠ Δ

_{2}. It is clear that, as predicted by Eq. (9) with

*N*= 3, both pulse components could be much more advanced than their counterparts propagating in the vacuum, and their group velocities can be controlled by manipulating intensities of the respective coupling fields on Raman resonance. In particular, the group time delay and the group velocity of the first pulse component in Fig. 7(a) are Δ

*τ*≈ −3.24

*μ*s and

*υ*≈ −1.85 × 10

_{g}^{4}m/s, while those of the second pulse component in Fig. 7(b) are Δ

*τ*≈ −1.24

*μ*s and

*υ*≈ −4.84×10

_{g}^{4}m/s. Similar results will also be obtained in the open five- (

*N*= 4), six- (

*N*= 5) level systems and so on, which are not shown here.

*F*= −

*c/υ*to denote how fast a superluminal light signal is, we have quite promising results:

_{g}*F*= 1.62 × 10

^{4}in Fig. 7(a) and

*F*= 0.62 × 10

^{4}in Fig. 7(b). Note that the figure of merit in [10

10. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature **406**, 277–279 (2000). [CrossRef] [PubMed]

*F*= 310 and cannot be easily improved because the two gain lines should be well separated to generate a wide and deep transparency window in the absence of quantum

*destructive*interference. Note also that the figure of merit in [15

15. K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A **68**, 013810 (2003). [CrossRef]

*F*= 1.44 × 10

^{4}. But the superluminal light signal experiences remarkable absorptive loss because the underlying physics of a steep anomalous dispersion is electromagnetically induced absorption (EIA) [27

27. 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]

*∂Re*(

*χ*)/

*∂*Δ

*> 0 while the fast light is attained with*

_{p}*∂Re*(

*χ*)/

*∂*Δ

*< 0. So there is no fundamental difference between the slow light and the fast light as far as the underlying physics is concerned. They both originates from the Kramers-Kronig relation between real and imaginary parts of the probe susceptibility. Thus the group velocity of a light pulse contributed by all carrier frequencies can take a value either smaller than*

_{p}*c*due to the normal dispersion or larger than

*c*due to the anomalous dispersion. Note, however, that the information carried by a light pulse can never propagate with a velocity exceeding

*c*and, according to many models, always propagates with the vacuum light speed

*c*[1

1. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science **326**, 1074–1077 (2009). [CrossRef] [PubMed]

## 4. Conclusions

*N*+ 1)-level extended V-type atomic system and the superluminal propagation dynamics of a weak probe pulse. The open (

*N*+ 1)-level system is driven by

*N*coherent fields (the probe and the

*N*− 1 couplings) to generate quantum interference and simultaneously interacts with an incoherent field (the pump) to accumulate necessary population from the external ground state. All

*N*upper levels in the open (

*N*+ 1)-level system are chosen to be highly excited Rydberg states of radiative lifetimes up to tens of microseconds, so that they could have spontaneous decay rates much smaller than that of the lower level. In this situation, the quantum interference is both

*destructive*and

*perfect*, which is however absent in the closed (

*N*+ 1)-level extended V-type system. Our analytical and numerical results show that, due to the

*perfect*quantum

*destructive*interference, at most

*N*− 1 narrow and deep transparency windows accompanied by very steep anomalous dispersions can be observed between

*N*gain lines. And the

*destructive*and

*perfect*quantum interference is therefore essential to attain superluminal light propagation with at most

*N*− 1 different negative group velocities with high figures of merit, which can be controlled by varying the Rabi frequencies of the coupling laser fields on Raman resonance.

## Acknowledgments

## References and links

1. | R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science |

2. | A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt. |

3. | J. Mork, F. Ohman, M. Van Der Poel, Y. Chen, P. Lunnemann, and K. Yvind, “Slow and fast light: Controlling the speed of light using semiconductor waveguides,” Laser Photon. Rev. |

4. | J. Mork, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol. |

5. | L. Thevenaz, “Slow and fast light in optical fibres,” Nat. Photonics |

6. | S. Chu and S. Wang, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. |

7. | M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science |

8. | M. Gonzalez-Herraez, K.-Y. Song, and L. Thevenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. |

9. | K. Y. Song, K. S. Abedin, and K. Hotate, “Gain-assisted superluminal propagation in tellurite glass fiber based on stimulated Brillouin scattering,” Opt. Express |

10. | L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature |

11. | C. Zhu and G. Huang, “High-order nonlinear Schrodinger equation and weak-light superluminal solitons in active Raman gain media with two control fields,” Opt. Express |

12. | F. Arrieta-Yanez, O. G. Calderon, and S. Melle, “Slow and fast light based on coherent population oscillations in erbium-doped fibres,” J. Opt. |

13. | C.-L. Cui, J.-K. Jia, J.-W. Gao, Y. Xue, G. Wang, and J.-H. Wu, “Ultraslow and superluminal light propagation in a four-level atomic system,” Phys. Rev. A |

14. | A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. |

15. | K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A |

16. | C.-L. C., J.-K. Jia, Y. Zhang, Y. Xue, H.-L. Xu, and J.-H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B: At. Mol. Opt. Phys. |

17. | L. Brillouin, |

18. | C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A |

19. | M. D. Crisp, “Concept of group velocity in resonant pulse propagation,” Phys. Rev. A |

20. | E. Paspalakis and P. L. Knight, “Electromagnetically induced transparency and controlled group velocity in a multilevel system,” Phys. Rev. A |

21. | T. F. Gallagher, |

22. | D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Cote, E. E. Eyler, and P. L. Gould, “Local blockade of Rydberg excitation in an ultracold gas,” Phys. Rev. Lett. |

23. | D. Yan, J.-W. Gao, Q.-Q. Bao, H. Yang, H. Wang, and J.-H. Wu, “Electromagnetically induced transparency in a five-level Λ system dominated by two-photon resonant transitions,” Phys. Rev. A |

24. | M. Mahmoudi, M. Sahrai, and H. Tajalli, “Subluminal and superluminal light propagation via interference of incoherent pumpfields,” Phys. Lett. A |

25. | M. Fleischhauer, C. H. Keitel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. |

26. | D. Bullock, J. Evers, and C. H. Keitel, “Modifying spontaneous emission via interferences from incoherent pump fields,” Phys. Lett. A |

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

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.1670) Quantum optics : Coherent optical effects

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 16, 2012

Revised Manuscript: April 4, 2012

Manuscript Accepted: April 4, 2012

Published: April 24, 2012

**Citation**

Cui-Li Cui, Chang-Bao Fu, Hong Yang, Qian-Qian Bao, Huai-Liang Xu, and Jin-Hui Wu, "Resonant gain suppression and superluminal group velocity in a multilevel system," Opt. Express **20**, 10712-10720 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10712

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### References

- R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science326, 1074–1077 (2009). [CrossRef] [PubMed]
- A. M. Akulshin and R. J. McLean, “Fast light in atomic media,” J. Opt.12, 104001 (2010). [CrossRef]
- J. Mork, F. Ohman, M. Van Der Poel, Y. Chen, P. Lunnemann, and K. Yvind, “Slow and fast light: Controlling the speed of light using semiconductor waveguides,” Laser Photon. Rev.3, 30–44 (2009). [CrossRef]
- J. Mork, P. Lunnemann, W. Xue, Y. Chen, P. Kaer, and T. R. Nielsen, “Slow and fast light in semiconductor waveguides,” Semicond. Sci. Technol.25, 083002 (2010). [CrossRef]
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