## Investigation of quantum coherence excitation and coherence transfer in an inhomogeneously broadened rare-earth doped solid

Optics Express, Vol. 16, Issue 8, pp. 5350-5361 (2008)

http://dx.doi.org/10.1364/OE.16.005350

Acrobat PDF (671 KB)

### Abstract

Quantum coherence excitation onto spin ensembles by resonant Raman optical fields and coherence transfer back to an optical emission are discussed in a three-level optical system composed of inhomogeneously broadened spins, where the spin decay time is much slower than the optical decay time. Dynamic quantum coherent control of the spin excitations and coherence conversion are also discussed at a strong coupling field limit for practical applications of optical information processing.

© 2008 Optical Society of America

## 1. Introduction

1. H. R. Gray, R. M. Whitley, and C. R. Stroud, Jr., “Coherent trapping of atomic
populations,” Opt. Lett. **3**, 218–220
(1978). [CrossRef] [PubMed]

2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced
transparency: Optics in coherent media,”
Rev. Mod. Phys. **77**, 633–673
(2005). [CrossRef]

3. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters
per second in an ultracold atomic gas,”
Nature **397**, 594–598
(1999). [CrossRef]

7. F. Xia, L. Sekaric, and L. Vlasov, “Ultracompact optical buffers on a
silicon chip,” Nat. Photonics **1**, 65–71
(2006). [CrossRef]

8. A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary
pulses of light,” Phys. Rev. Lett. **94**, 063902 (2005). [CrossRef] [PubMed]

9. S. E. Harris and L. V. Hau, “Nonlinear Optics at Low Light
Levels,” Phys. Rev. Lett. **82**, 4611 (1999). [CrossRef]

13. D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by
atoms with Zeeman-split ublevels,” Phys.
Rev. A **65**, 033833 (2002). [CrossRef]

13. D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by
atoms with Zeeman-split ublevels,” Phys.
Rev. A **65**, 033833 (2002). [CrossRef]

14. M. Paternostro, M. S. Kim, and B. S. Ham, “Generation of entangled coherent
states via cross-phase-modulation in a double electromagnetically induced
transparency regime,” Phys. Rev. A **67**, 023811 (2003). [CrossRef]

16. S. E. Harris and Y. Yamamoto, “Quantum switching by quantum
interference,” Phys. Rev. Lett. **81**, 3611–3614
(1998). [CrossRef]

17. B. S. Ham and P. R. Hemmer, “Coherence switching in a four-level
system: Quantum switching,” Phys. Rev.
Lett. **84**, 4080–4083
(2000). [CrossRef] [PubMed]

10. Y. Zhang, A. W. Brown, and M. Xiao, “Matched ultraslow propagation of
highly efficient four-wave mixing in a closely cycled double-ladder
system,” Phys. Rev. A **74**, 053813 (2006). [CrossRef]

18. S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color
stationary light: Quantum wavelength conversion,”
Phys. Rev. A **73**, 033812 (2006). [CrossRef]

4. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of Ultraslow and Stored
Light Pulses in a Solid,” Phys. Rev.
Lett. **88**, 023602 (2002). [CrossRef] [PubMed]

17. B. S. Ham and P. R. Hemmer, “Coherence switching in a four-level
system: Quantum switching,” Phys. Rev.
Lett. **84**, 4080–4083
(2000). [CrossRef] [PubMed]

19. B. S. Ham, M. S. Shshriar, and P. R. Hemmer, “Frequency-selective time-domain
optical data storage by electromagnetically induced transparency in a
rare-earth-doped solid,” Opt. Lett. **22**, 1849–1851
(1997). [CrossRef]

24. K. Holiday, M. Croci, E. Vauthey, and U. P. Wild, “Spectral hole burning and holography
in an Y_{2}SIO_{5}:Pr^{3+}
crystal,” Phys. Rev. B **47**, 14741–14752
(1993). [CrossRef]

4. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of Ultraslow and Stored
Light Pulses in a Solid,” Phys. Rev.
Lett. **88**, 023602 (2002). [CrossRef] [PubMed]

17. B. S. Ham and P. R. Hemmer, “Coherence switching in a four-level
system: Quantum switching,” Phys. Rev.
Lett. **84**, 4080–4083
(2000). [CrossRef] [PubMed]

19. B. S. Ham, M. S. Shshriar, and P. R. Hemmer, “Frequency-selective time-domain
optical data storage by electromagnetically induced transparency in a
rare-earth-doped solid,” Opt. Lett. **22**, 1849–1851
(1997). [CrossRef]

20. L. Rippe, M. Nilsson, S. Kroll, R. Klieber, and D. Suter, “Experimental demonstration of
efficient and selective population transfer and qubit distillation in a
rare-earth-metal-ion-doped crystal,”
Phys. Rev. A **71**, 062328 (2006). [CrossRef]

4. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of Ultraslow and Stored
Light Pulses in a Solid,” Phys. Rev.
Lett. **88**, 023602 (2002). [CrossRef] [PubMed]

19. B. S. Ham, M. S. Shshriar, and P. R. Hemmer, “Frequency-selective time-domain
optical data storage by electromagnetically induced transparency in a
rare-earth-doped solid,” Opt. Lett. **22**, 1849–1851
(1997). [CrossRef]

**88**, 023602 (2002). [CrossRef] [PubMed]

**84**, 4080–4083
(2000). [CrossRef] [PubMed]

22. G. He′tet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for
light using two-level atoms,” Phys. Rev.
Lett. **100**, 023601 (2008). [CrossRef]

25. B. S. Ham, “Observations of delayed all-optical
routing in a slow light regime,” Phys.
Rev. Lett. (To be published); *ibid.*
arXiv:0801.3501 (2008). [PubMed]

## 2. Theory

_{P}and Ω

_{C}(see Fig. 1(a)), the time-dependent density matrix equation is denoted by [26]:

_{1}=ω

_{31}-ω

_{P}, δ

_{2}=ω

_{32}-ω

_{C}, ω

_{ij}=ω

_{i}-ω

_{j}, and ω

_{P}and ω

_{C}are the frequencies of the probe (Ω

_{P}) and coupling (Ω

_{C}) fields, respectively. In Fig. 1(a), the thick line on level |2> stands for spin inhomogeneous broadening between |1> and |2>.

## 3. Results and discussions

_{C}and the probe field Ω

_{P}temporally overlap each other. Initially equal population distribution between two low lying levels |1> and |2> are assumed: ρ

_{11}=1/2; ρ

_{22}=ρ

_{33}=1/2. Even if optical transitions Ω

_{P}for (|1>-|3>) and Ω

_{C}for (|2>-|3>) satisfy the resonant two-photon condition, the spin inhomogeneous broadening between |1>-|2> makes an intrinsic detuning. We choose only δ

_{2}as an intrinsic detuning for the inhomogeneously broadened spins to the two-photon optical fields (in this case only to the coupling field Ω

_{C}) for the following numerical calculations.

_{2}=-90 kHz to δ

_{2}=+90 kHz at a step of 2 kHz.

^{3+}doped Y

_{2}SiO

_{5}are used [19

**22**, 1849–1851
(1997). [CrossRef]

24. K. Holiday, M. Croci, E. Vauthey, and U. P. Wild, “Spectral hole burning and holography
in an Y_{2}SIO_{5}:Pr^{3+}
crystal,” Phys. Rev. B **47**, 14741–14752
(1993). [CrossRef]

27. R. W. Equall, R. L. Cone, and R. M. Macfarlane, “Homogeneous broadening and hyperfine
structure of optical transitions in
Pr^{3+}:Y_{2}SiO_{5},”
Phys. Rev. B **52**, 3963–3969
(1995). [CrossRef]

_{P}and Ω

_{C}is 20 kHz for a weak field limit, where the optical phase decay rate is γ

_{31}=γ

_{32}=50 kHz. The atom-field interaction time of 60 µs) is identified as much longer than the optical phase decay time T

_{2}(T

_{2}=1/(πγ

_{32}=6.4 µs).

*i*(ρ

_{13})) and spin coherence (

*r*(ρ

_{12})) are presented. For the calculations all groups of atoms (spins) with different detuning δ

_{2}are considered. As seen in Figs. 3(a) and 3(b), the probe field absorption (

*i*(ρ

_{13})) and spin coherence (

*r*(ρ

_{12})) are affected by both population differences between levels |3> and |1> and between |2> and |1>. According to the theory of coherent population trapping (in a weak field limit) the maximum spin coherence (

*r*(ρ

_{12})) is -0.5, where the current coherence magnitude in Fig. 3 should be reduced by a higher optical decay rate γ and the spin inhomogeneous broadening.

_{P}and Ω

_{C}. Unlike Fig. 3 discussed for population-dependent coherence excitations, here the spin coherence is independent of the population difference between levels |2> and |1>. This is because the optical system in Fig. 1(a) is population shelved, in which the optical population decay rate is much weaker than the applied optical Rabi frequencies. Moreover, both optical Rabi frequencies are exactly the same in magnitude and phase. Thus, the two optical fields incur population difference only between levels either |1> and |3>, or |2> and |3>, under perfect resonance condition (δ

_{2}=0).

_{12}, optical coherence ρ

_{13}, and optical coherence ρ

_{23}), where the population difference should not be a factor. However for the optical coherence the population difference must be considered as shown in Fig. 3. This means that the population difference between two low-lying ground levels is not a necessary condition to induce the spin coherence excitation by resonant two-optical fields.

_{22}-ρ

_{11}) via those between optical transitions as discussed in Fig. 4.

_{2}as a function of interaction time (see Fig. 6): The more detuning it has, the faster oscillation it experiences. Of course its amplitude becomes weaker as the detuning gets wider. As is well known in the area of optical transient phenomena such as free induction decay as shown in Fig. 3, the overall coherence decay time becomes shorter than the spin phase decay time T

_{2}

^{Spin}as the detuning becomes wider: Here T

_{2}

^{Spin}is 1/(πγ

_{21})=1,590 µs. Thus, Figs. 3 and 6 prove a spin coherence transient effect induced by two optical fields under the spin broadened system: nutation. This optical field-induced spin coherence transient effect is important in analyzing the EIT-based nonlinear Kerr effect such as nondegenerate four-wave mixing processes as experimentally demonstrated already [4

**88**, 023602 (2002). [CrossRef] [PubMed]

**84**, 4080–4083
(2000). [CrossRef] [PubMed]

**22**, 1849–1851
(1997). [CrossRef]

28. B. S. Ham, M. S. Shahriar, and P. R. Hemmer, “Efficient phase conjugate via
two-photon coherence in an optically dense
crystal,” Phys. Rev. A **59**, R2583– R2586
(1999). [CrossRef]

3. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters
per second in an ultracold atomic gas,”
Nature **397**, 594–598
(1999). [CrossRef]

5. 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]

6. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical
information storage in an atomic medium using halted light
pulses,” Nature **409**, 490–493,
(2001). [CrossRef] [PubMed]

10. Y. Zhang, A. W. Brown, and M. Xiao, “Matched ultraslow propagation of
highly efficient four-wave mixing in a closely cycled double-ladder
system,” Phys. Rev. A **74**, 053813 (2006). [CrossRef]

_{2}[28

28. B. S. Ham, M. S. Shahriar, and P. R. Hemmer, “Efficient phase conjugate via
two-photon coherence in an optically dense
crystal,” Phys. Rev. A **59**, R2583– R2586
(1999). [CrossRef]

_{P}=Ω

_{C}) or equal population distributions on the low lying two ground levels (ρ

_{11}=ρ

_{22}) are not provided. Figure 7 shows a general case of coherence excitation induced by two optical fields whose Rabi frequency is the same, where initial population distribution is unbalanced: ρ

_{11}=1; ρ

_{22}=ρ

_{33}=0. As seen in Fig. 7, the spin coherence excitation strongly depends on the population difference (see also Eqs. 3(b) and 3(c)).

_{11}=ρ

_{22}). All other parameters are the same as above. As seen in Figs. 8, spin coherence excitation (

*r*(ρ

_{12})) results from optical absorption (

*i*(ρ

_{13})) with a phase delay. The phase delay is a common characteristic of the response function in a physical system. For example, the absorption and dispersion relation is characterized as the Kramers-Kronig relation, where the absorption and dispersion are coupled to each other resulting in a response function. Here the relation between linear absorption (

*i*(ρ

_{13})) and two-photon dispersion (

*r*(ρ

_{12})) mimics the Kramers-Kronig relation as a response function. Surprisingly time evolution of the spin coherence (

*r*(ρ

_{12})) matches that of the population difference between the excited and ground levels (ρ

_{33}-ρ

_{11}). This is because the atom population on both levels must be Rabi flopping, and then the coherence excitation directly results from the population difference: See Eqs. (3). Thus, spin coherence excitation can be controlled only by adjusting one of the optical fields’ Rabi frequencies. Figure 8(a) depicts overall atoms, and 8b only two-photon resonant atoms (δ

_{2}=0). As seen in Fig. 8(b), the ground levels population difference is negligible for the spin coherence excitation.

_{C}) can be used to control the spin coherence excitation, the following is considered: Ω

_{P}≪γ; Ω

_{P}≪Ω

_{C}; γ≪Ω

_{C}.

_{P}, each atomic population on levels |2> and |3> strongly depends on the coupling field Ω

_{C}: Rabi flopping. The Rabi flopping-induced coherence oscillation at a frequency of 200 kHz is the same as the coupling Rabi frequency in Fig. 9. So is the population difference between levels |3> and |1> as wells as between |2> and |1>: See the blue dotted and red curves, respectively. Unlike the weak coupling limit (Ω

_{C}≪γ) discussed Figs. 1–8, spin coherence excitation now strongly depends on the population on level |2> via the coupling field interaction. Region A in Fig. 9 shows spin free-induction decay, where the decay time is 1/Δ

_{spin}: Δ

_{spin}=50 kHz.

_{32}(=50 kHz), where the optical phase decay time is T

_{2}=1/(πγ

_{32})=6.4 µs. In Fig. 10(b) and 10(c) the dotted exponential curve is for the best fit to the coherence envelope: Fig. 10(b) shows overall inhomogeneous spins, while Fig. 10(c) shows only two-photon resonance spins at line center in Fig. 2. As seen in Fig. 10, the spin coherence (

*r*(ρ

_{12})) evolution nearly perfectly follows the population change on level |2> (ρ

_{22}). For the calculations in Fig. 10(c), both optical and spin population decay rates are set to zero for analysis purposes. From these results, we conclude that the spin coherence excitation depends on both optical phase decay rate and Rabi flopping by the coupling field Ω

_{C}.

_{A}immediately following the excitation pulse composed of Ω

_{P}and Ω

_{C}, in which Ω

_{A}has the same transition as Ω

_{C}.

_{A}is 10 µs for all cases. From Figs. 12, we conclude that the spin coherence is transferred to optical coherence resulting in optical emission by the action of the retrieval pulse Ω

_{A}, and the strength of the optical coherence (magnitude of emission) is proportional to that of the spin coherence (denoted by dotted arrows). This phenomenon is actually EIT-based nondegenerate four-wave mixing experimentally demonstrated in Pr

^{3+}doped Y

_{2}SiO

_{5}[28

28. B. S. Ham, M. S. Shahriar, and P. R. Hemmer, “Efficient phase conjugate via
two-photon coherence in an optically dense
crystal,” Phys. Rev. A **59**, R2583– R2586
(1999). [CrossRef]

_{A}is denoted by blue-colored “o,” which is a perfect match to the optical coherence (red curve) obtained in Fig. 12(b) for the zero detuned spins (δ

_{2}=0, green curve). For overall spins spanned over 50kHz, the coherence transfer induced optical emission lags a little bit behind (see the black curve).

*i*(ρ

_{13})) and the spin coherence (

*r*(ρ

_{12})) for all inhomogeneous spins. As seen in Fig. 14, the overall one-photon optical coherence (emission; red area in Fig. 14(a)) is from the retrieval of the overall two-photon spin coherence (blue area in Fig. 14(b)) as discussed in Fig. 13. This phenomenon has already been studied experimentally in Pr

^{3+}doped Y

_{2}SiO

_{5}[28

**59**, R2583– R2586
(1999). [CrossRef]

_{A}. Figure 15 shows coherence oscillation at a strong coupling limit. Surprisingly, without population inversion between the ground level |1> and the excited level |3>, Figs. 15(b) and 15(e) show photon emission: ι(ρ

_{13})>0; (ρ

_{33}-ρ

_{11})<0. This is due to the coupling induced Rabi flopping on level |3>, so that the slopes of population differences for both transitions are negative (see Fig. 15(c)), which means photon emission. As discussed in Fig. 12, the retrieval pulse whose Rabi frequency is 100 kHz follows the two-photon excitation pulse composed of Ω

_{P}and Ω

_{C}with no time delay (see Fig. 16). To demonstrate a dynamic coherence transfer of the excited spin coherence to optical one-photon coherence, we choose three different moments at t=12, 15, and 20 µs (see the green dashed line in Fig. 15(b)). For the coherence transfer at t=15 µs and t=20 µs (see respectively Figs. 16(b)/(e)/(h) and (c)/(f)/(i)), the photon emission at t=20 µs is bigger because of a stronger spin coherence excited. Moreover, there are extra photon emission peaks as a result of Fig. 15(c): see pink shaded area in Fig. 15(c). This kind of dynamic coherence control is important in a population shelved system to avoid unwanted signals.

## 4. Conclusion

**88**, 023602 (2002). [CrossRef] [PubMed]

**22**, 1849–1851
(1997). [CrossRef]

## Acknowledgment

## References and links

1. | H. R. Gray, R. M. Whitley, and C. R. Stroud, Jr., “Coherent trapping of atomic
populations,” Opt. Lett. |

2. | M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced
transparency: Optics in coherent media,”
Rev. Mod. Phys. |

3. | L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters
per second in an ultracold atomic gas,”
Nature |

4. | A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of Ultraslow and Stored
Light Pulses in a Solid,” Phys. Rev.
Lett. |

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

6. | C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical
information storage in an atomic medium using halted light
pulses,” Nature |

7. | F. Xia, L. Sekaric, and L. Vlasov, “Ultracompact optical buffers on a
silicon chip,” Nat. Photonics |

8. | A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary
pulses of light,” Phys. Rev. Lett. |

9. | S. E. Harris and L. V. Hau, “Nonlinear Optics at Low Light
Levels,” Phys. Rev. Lett. |

10. | Y. Zhang, A. W. Brown, and M. Xiao, “Matched ultraslow propagation of
highly efficient four-wave mixing in a closely cycled double-ladder
system,” Phys. Rev. A |

11. | D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using
electromagnetically induced transparency in cold
atoms,” Phys. Rev. Lett. |

12. | L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing
channels with giant enhancement using ultraslow pump
waves,” Phys. Rev. Lett. |

13. | D. Petrosyan and G. Kurizki, “Symmetric photon-photon coupling by
atoms with Zeeman-split ublevels,” Phys.
Rev. A |

14. | M. Paternostro, M. S. Kim, and B. S. Ham, “Generation of entangled coherent
states via cross-phase-modulation in a double electromagnetically induced
transparency regime,” Phys. Rev. A |

15. | M. G. Payne and L. Deng, “Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing,” Phys. Rev. Lett.91, 123602 (2003); S. A. Moiseev and B. S. Ham, Phys. Rev. A 71, 053802 (2006). [CrossRef] [PubMed] |

16. | S. E. Harris and Y. Yamamoto, “Quantum switching by quantum
interference,” Phys. Rev. Lett. |

17. | B. S. Ham and P. R. Hemmer, “Coherence switching in a four-level
system: Quantum switching,” Phys. Rev.
Lett. |

18. | S. A. Moiseev and B. S. Ham, “Quantum manipulation of two-color
stationary light: Quantum wavelength conversion,”
Phys. Rev. A |

19. | B. S. Ham, M. S. Shshriar, and P. R. Hemmer, “Frequency-selective time-domain
optical data storage by electromagnetically induced transparency in a
rare-earth-doped solid,” Opt. Lett. |

20. | L. Rippe, M. Nilsson, S. Kroll, R. Klieber, and D. Suter, “Experimental demonstration of
efficient and selective population transfer and qubit distillation in a
rare-earth-metal-ion-doped crystal,”
Phys. Rev. A |

21. | A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, “Photon echoes produced by switching
electric fields,” Phys. Rev. Lett. |

22. | G. He′tet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for
light using two-level atoms,” Phys. Rev.
Lett. |

23. | S. A. Moiseev and S. Kroll, “Complete reconstruction of the
quantum state of a single-photon wave packet absorbed by a Doppler-broadened
transition,” Phys. Rev. Lett. |

24. | K. Holiday, M. Croci, E. Vauthey, and U. P. Wild, “Spectral hole burning and holography
in an Y |

25. | B. S. Ham, “Observations of delayed all-optical
routing in a slow light regime,” Phys.
Rev. Lett. (To be published); |

26. | M. Sargent III, M. O. Scully, W. E. Lamb, Jr., and Laser Physics, (Addison-Wesley, 1974), Chap. 7. |

27. | R. W. Equall, R. L. Cone, and R. M. Macfarlane, “Homogeneous broadening and hyperfine
structure of optical transitions in
Pr |

28. | B. S. Ham, M. S. Shahriar, and P. R. Hemmer, “Efficient phase conjugate via
two-photon coherence in an optically dense
crystal,” Phys. Rev. A |

**OCIS Codes**

(030.1670) Coherence and statistical optics : Coherent optical effects

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(270.1670) Quantum optics : Coherent optical effects

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 15, 2008

Revised Manuscript: March 30, 2008

Manuscript Accepted: March 30, 2008

Published: April 2, 2008

**Citation**

Byoung S. Ham, "Investigation of quantum coherence excitation and coherence transfer in an inhomogeneously broadened rare-earth doped solid," Opt. Express **16**, 5350-5361 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5350

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### References

- H. R. Gray, R. M. Whitley, and C. R. StroudJr., "Coherent trapping of atomic populations," Opt. Lett. 3, 218-220 (1978). [CrossRef] [PubMed]
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Rev. Mod. Phys. 77, 633-673 (2005), and references are there in. [CrossRef]
- L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999). [CrossRef]
- A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, "Observation of Ultraslow and Stored Light Pulses in a Solid," Phys. Rev. Lett. 88, 023602 (2002). [CrossRef] [PubMed]
- 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]
- C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses," Nature 409, 490-493 (2001). [CrossRef] [PubMed]
- F. Xia, L. Sekaric, and L. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006). [CrossRef]
- A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Nonlinear optics with stationary pulses of light," Phys. Rev. Lett. 94, 063902 (2005). [CrossRef] [PubMed]
- S. E. Harris and L. V. Hau, "Nonlinear Optics at Low Light Levels," Phys. Rev. Lett. 82, 4611 (1999). [CrossRef]
- Y. Zhang, A. W. Brown, and M. Xiao, "Matched ultraslow propagation of highly efficient four-wave mixing in a closely cycled double-ladder system," Phys. Rev. A 74, 053813 (2006). [CrossRef]
- D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004). [CrossRef] [PubMed]
- L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, "Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves," Phys. Rev. Lett. 88, 143902 (2002). [CrossRef] [PubMed]
- D. Petrosyan and G. Kurizki, "Symmetric photon-photon coupling by atoms with Zeeman-split ublevels," Phys. Rev. A 65, 033833 (2002). [CrossRef]
- M. Paternostro, M. S. Kim, and B. S. Ham, "Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime," Phys. Rev. A 67, 023811 (2003). [CrossRef]
- M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003);S. A. Moiseev and B. S. Ham, Phys. Rev. A 71, 053802 (2006). [CrossRef] [PubMed]
- S. E. Harris and Y. Yamamoto, "Quantum switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998). [CrossRef]
- B. S. Ham and P. R. Hemmer, "Coherence switching in a four-level system: Quantum switching," Phys. Rev. Lett. 84, 4080-4083 (2000). [CrossRef] [PubMed]
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