## Dynamic generation of robust and controlled beating signals in an asymmetric procedure of light storage and retrieval |

Optics Express, Vol. 19, Issue 12, pp. 11832-11840 (2011)

http://dx.doi.org/10.1364/OE.19.011832

Acrobat PDF (1361 KB)

### Abstract

We propose an efficient scheme for the robust and controlled generation of beating signals in a sample of stationary atoms driven into the tripod configuration. This scheme relies on an asymmetric procedure of light storage and retrieval where the two classical coupling fields have equal detunings in the storage stage but opposite detunings in the retrieval stage. A quantum probe field, incident upon such an atomic sample, is first transformed into two spin coherence wave-packets and then retrieved with two optical components characterized by different time-dependent phases. Therefore the retrieved quantum probe field exhibits a series of maxima and minima (beating signals) in intensity due to the alternative constructive and destructive interference. This interesting phenomenon involves in fact the coherent manipulation of two dark-state polaritons and may be explored to achieve the fast quantum limited measurement.

© 2011 OSA

## 1. Introduction

1. M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. **75**, 457–472 (2003). [CrossRef]

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. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. **70**, 1003–1025 (1998). [CrossRef]

4. D. A. Braje, V. Balic, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A **68**, 041801(R) (2003). [CrossRef]

7. C. Hang and G.-X. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express **18**, 2952–2966 (2010). [CrossRef] [PubMed]

8. C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic memory for correlated photon states,” Science **301**, 196–200 (2003). [CrossRef] [PubMed]

11. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature (London) **452**, 67–71 (2008). [CrossRef]

12. 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 (London) **409**, 490–493 (2001). [CrossRef]

13. M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **84**, 5094–5097 (2000). [CrossRef] [PubMed]

14. R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. **155**, 144–154 (1998). [CrossRef]

15. J.-H. Wu, C.-L. Cui, N. Ba, Q.-R. Ma, and J.-Y. Gao, “Dynamical evolution and analytical solutions for multiple degenerate dark states in the tripod-type atomic system,” Phys. Rev. A **75**, 043819 (2007). [CrossRef]

16. A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska–Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. **260**, 73–80 (2006). [CrossRef]

18. 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]

19. D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atomsin a tripod configuration,” Phys. Rev. A **70**, 023822 (2004). [CrossRef]

22. S.-J. Li, X.-D. Yang, X.-M. Cao, C.-H. Zhang, C.-D. Xie, and H. Wang, “Enhanced Cross-Phase Modulation Based on a Double Electromagnetically Induced Transparency in a Four-Level Tripod Atomic System,” Phys. Rev. Lett. **101**, 073602 (2008). [CrossRef] [PubMed]

23. L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. **101**, 170406 (2008). [CrossRef] [PubMed]

24. A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A **65**, 031802(R) (2002). [CrossRef]

25. L. Karpa, G. Nikoghosyan, F. Vewinger, M. Fleischhauer, and M. Weitz, “Frequency matching in light-storage spectroscopy of atomic Raman transitions,” Phys. Rev. Lett. **103**, 093601 (2009). [CrossRef] [PubMed]

23. L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. **101**, 170406 (2008). [CrossRef] [PubMed]

*asymmetric*procedure of light storage and retrieval. To be more specific, we first store the probe field into two different wave-packets of spin coherence by switching off the two coupling fields with

*equal*detunings, and then retrieve it after a short storage time by switching on the two coupling fields with

*unequal*detunings instead. In this case, the only retrieved probe field consists of two components characterized by different time-dependent phases so that beating signals (a series of maxima and minima in intensity) arise due to the alternate constructive and destructive interference. The generation of beating signals can be well understood in the polariton picture where a pair of DSP modes are simultaneously excited with their structures totally determined by amplitudes, phases, and detunings of the two coupling fields. Experimental examination of such beating signals may be used to acquire the frequency difference, the relative phase, and their stabilities of two classical coupling fields or to achieve the fast quantum limited measurement of magnetic field amplitudes and atomic transition frequencies between ground state sublevels.

## 2. Model and equations

*L*consisting of an ensemble of stationary atoms coherently driven into the four-level tripod configuration (see Fig. 1). The first dipole-allowed transition |

*a*〉 ↔ |

*e*〉 is coupled by one classical field with frequency

*ω*

_{c}_{1}and amplitude

**E**

_{c}_{1}and the second dipole-allowed transition |

*b*〉 ↔ |

*e*〉 is coupled by another classical field with frequency

*ω*

_{c}_{2}and amplitude

**E**

_{c}_{2}. The third dipole-allowed transition |

*c*〉 ↔ |

*e*〉, however, is probed by a weak quantum field described by where

*ε*is the polarization vector,

_{p}*ω*the carrier frequency,

_{p}*V*the quantization volume, and

*E*(

_{p}*z,t*) the slowly-varying dimensionless operator.

*N*denotes the atomic number in a small volume

_{z}*V*centered at

_{z}*z*while

*μ*〉 |

_{j}*ν*〉 with {

_{j}*μ*,

*ν*} ∈ {

*a*,

*b*,

*c*,

*e*}. For simplicity and convenience, we further introduce the slowly-varying operators

*σ*(

_{ce}*z, t*),

*σ*(

_{cb}*z, t*), and

*σ*(

_{ca}*z, t*) for three relevant coherence terms whose dynamic evolutions are governed by a set of reduced Heisenberg-Langevin equations in the weak probe and adiabatic control limits.

*σ*(Δ

_{ce}*)] and Re[*

_{p}*σ*(Δ

_{ce}*)], of a continuous-wave probe. To study the dynamic evolution of the dimensionless operator*

_{p}*E*(

_{p}*z,t*), however, we also need the wave propagation equation which is attained in the slowly-varying envelope approximation. Here

*N*refers to the total number of active atoms in the quantization volume

*V*of the weak probe field while

*c*is defined as the light speed in vacuum. Eq. (5) coupled with Eqs. (4) will be numerically solved in the next section to examine an interesting light propagation dynamics concerning the generation and control of quantum limited beating signals imposed on a probe field.

## 3. Results and discussions

*asymmetric*procedure of light storage and retrieval via the dynamic EIT technique. Without loss of generality, we will set

*γ*=

*γ*as the frequency unit,

_{ce}*E*(

_{p}*z,t*) goes slowly into the atomic sample at the velocity

*υ*= 0.25

_{g}*l*/

_{a}*t*

_{0}and is totally transformed into stationary spin coherences

*σ*(

_{ca}*z,t*) and

*σ*(

_{cb}*z,t*) at the sample center when the two coupling fields with Δ

_{c}_{1}= Δ

_{c}_{2}= 0.0

*γ*are simultaneously turned off at

*t*= 48.0

*t*

_{0}. After a short storage time of Δ

*t*= 24.0

*t*

_{0}, we switch on the two coupling fields to retrieve the quantum field from

*σ*(

_{ca}*z,t*) and

*σ*(

_{cb}*z,t*) at the same time but with opposite detunings, i.e. Δ

_{c}_{1}= −Δ

_{c}_{2}= 0.02

*γ*in (a, b), Δ

_{c}_{1}= −Δ

_{c}_{2}= 0.05

*γ*in (c, d), and Δ

_{c}_{1}= −Δ

_{c}_{2}= 0.08

*γ*in (e, f). As expected, the retrieved quantum field appears and vanishes in a periodic pattern when it propagates inside the atomic sample once again at the velocity

*υ*= 0.25

_{g}*l*/

_{a}*t*

_{0}. That is, the retrieved quantum field exhibits a series of maxima and minima (beating signals) in its average intensity, which oscillate at the frequency of Δ

*ω*= Δ

_{beat}

_{c}_{1}− Δ

_{c}_{2}when |Δ

_{c}_{1}| = |Δ

_{c}_{2}| are large enough [see Fig. 2(e, f)].

13. M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. **84**, 5094–5097 (2000). [CrossRef] [PubMed]

*z,t*) = Ψ

*(*

_{a}*z,t*) + Ψ

*(*

_{b}*z,t*) with

*z,t*) originates from the pure quantum field excitation

*E*(

_{p}*z,t*) or

*z,t*) originates from the pure atomic coherence excitation

*G*

_{c}_{1}=

*G*

_{c}_{2}for simplicity so that both DSP modes Ψ

*(*

_{a}*z,t*) and Ψ

*(*

_{b}*z,t*) can attain the same propagating velocity

*υ*=

_{g}*c*cos

^{2}

*θ*at the retrieval stage.

_{c}_{1}= Φ

_{c}_{2}= 0.0. At

*t*= 0.0

*t*

_{0}, a fast probe field

*E*(

_{p}*z,t*) enters the sample of stationary atoms and evolves into two slowly-moving DSP modes described by Eqs. (7) through its two-photon resonant interaction with both coupling fields Ω

_{c}_{1}and Ω

_{c}_{2}. In this case, the field component in Ψ

*(*

_{a}*z,t*) and that in Ψ

*(*

_{b}*z,t*) have the same vanishing phase so that no beating signals are observed in the probe intensity before

*t*= 48.0

*t*

_{0}. At

*t*= 48.0

*t*

_{0}, when both coupling fields Ω

_{c}_{1}and Ω

_{c}_{2}are switched off, the two slowly-moving DSP modes described by Eqs. (7) turn into a pair of stationary atomic excitations

_{c}_{1}= Δ

_{c}_{2}= 0.0

*γ*. This is why the probe intensity is exactly zero during the period of

*t*= 48.0

*t*

_{0}∼ 72.0

*t*

_{0}. At

*t*= 72.0

*t*

_{0}, when the two coupling fields are switched on with Δ

_{c}_{1}≠ Δ

_{c}_{2}instead, the pair of stationary atomic excitations become the origin of two slowly-moving DSP modes described by Eqs. (8). In this case, the field component in Ψ

*(*

_{a}*z,t*) and that in Ψ

*(*

_{b}*z,t*) attain, respectively, time-dependent phases Δ

_{c}_{1}

*t*and Δ

_{c}_{2}

*t*so that they interfere with each other to produce a series of beating signals in the probe intensity after

*t*= 72.0

*t*

_{0}. At the sample exit, the two DSP modes described by Eqs. (8) finally turn into a pair of fast field components

*e*

^{iΔc1t}

*E*(

_{p}*z,t*)/2 and

*e*

^{iΔc2t}

*E*(

_{p}*z,t*)/2 with beating signals perfectly reserved. It is clear that the field components of both DSP modes experience little absorptive loss even if we set Δ

_{c}_{1}≠ Δ

_{c}_{2}after

*t*= 72.0

*t*

_{0}because they are well contained in two separate EIT windows located, respectively, at Δ

*= Δ*

_{p}

_{c}_{1}and Δ

*= Δ*

_{p}

_{c}_{2}[27

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

_{c}_{2}– Δ

_{c}_{1}| in very small steps. As we can see there is only a single maximum when |Δ

_{c}_{2}– Δ

_{c}_{1}| < 0.003

*γ*while a second maximum tends to arise when |Δ

_{c}_{2}– Δ

_{c}_{1}| > 0.003

*γ*. In addition, a part of light energy is redistributed into a later time region and the destructive interference occurs between the former and later time regions when a wider EIT window is gradually split into two narrower ones by an absorption line [27

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

_{c}_{1}and Φ

_{c}_{2}of the two complex Rabi frequencies Ω

_{c}_{1}and Ω

_{c}_{2}. So one may simply modulate the relative phase ΔΦ = Φ

_{c}_{2}– Φ

_{c}_{1}to control the beating signals attained in an

*asymmetric*procedure of light storage and retrieval, which is illustrated in Fig. 4. It is found that beating signals with ΔΦ = 0.0 (

*π/*2) and beating signals with ΔΦ =

*π*(3

*π*/2) are exactly staggered by a half period, i.e. a maximum in the black-solid curves corresponds to a minimum in the red-dashed curves. In this case, it is

*e*

^{i}^{(Δc1t−Φc1)}

*E*(

_{p}*z,t*)/2 and

*e*(

^{i}^{Δc2t − Φc2)}

*E*(

_{p}*z,t*)/2 that describe the pair of field components at the sample exit.

^{3+}: Y

_{2}SiO

_{4}crystal working at the cryogenic temperature [28

28. E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A **66**, 063802 (2002). [CrossRef]

29. B. S. Ham, “Reversible quantum optical data storage based on resonant Raman optical field excited spin coherence,” Opt. Express **16**, 14304–14313 (2008). [CrossRef] [PubMed]

*γ*,

_{ca}*γ*, and

_{cb}*γ*. For the latter, we may choose the D1 line of cold

_{ce}^{87}Rb atoms to construct the tripod system with |

*a*〉, |

*b*〉, |

*c*〉, and |

*e*〉 referring to |5

^{2}

*S*

_{1/2},

*F*= 2,

*m*= +1〉, |5

_{F}^{2}

*S*

_{1/2},

*F*= 2,

*m*= −1〉, |5

_{F}^{2}

*S*

_{1/2},

*F*= 1,

*m*= +1〉, and |5

^{2}

*P*

_{1/2},

*F*′ = 1,

*m*= 0〉, respectively [30

30. H. Wang, S.-J. Li, Z.-X. Xu, X.-B. Zhao, L.-J. Zhang, J.-H. Li, Y.-L. Wu, C.-D. Xie, K.-C. Peng, and M. Xiao, “Quantum interference of stored dual-channel spin-wave excitations in a single tripod system,” Phys. Rev. A **83**, 043815 (2011). [CrossRef]

## 4. Conclusions

*asymmetric*light storage and retrieval technique. In experiment, the frequency difference

*ω*

_{c}_{2}−

*ω*

_{c}_{1}, the relative phase Φ

_{c}_{2}− Φ

_{c}_{1}, and their stabilities can be easily inferred from the beating signals imposed on a weak probe field. If the detuning difference |Δ

_{c}_{1}− Δ

_{c}_{2}| is induced by shifting hyperfine state sublevels with a magnetic field

**B**, we may have

*h̄*|Δ

_{c}_{1}− Δ

_{c}_{2}| = 2

*gμ*·

_{B}**B**with

*g*being the Lander factor and

*μ*the Bohr magneton. In this case such interferometric beating signals can be used to measure magnetic field amplitudes. If the two coupling fields have the identical frequency and differ only by

_{B}*σ*

^{+}and

*σ*

^{−}polarizations, however, we may have |Δ

_{c}_{1}− Δ

_{c}_{2}| = |

*ω*| so that atomic transition frequencies can be determined from such interferometric beating signals. In particular, when a nonclassical squeezed light is used, one can achieve the quantum limited measurement with a sub-shot noise precision because quantum properties are well conserved during light storage and retrieval [10

_{ab}10. J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. **100**, 093602 (2008). [CrossRef] [PubMed]

11. K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature (London) **452**, 67–71 (2008). [CrossRef]

23. L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. **101**, 170406 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. |

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

3. | K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. |

4. | D. A. Braje, V. Balic, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A |

5. | H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. |

6. | C.-Y. Wang, Y.-F. Chen, S.-C. Lin, W.-H. Lin, P.-C. Kuan, and I. A. Yu, “Low-light-level all-optical switching,” Opt. Lett. |

7. | C. Hang and G.-X. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express |

8. | C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic memory for correlated photon states,” Science |

9. | H.-H. Wang, X.-G. Wei, L. Wang, Y.-J. Li, D.-M. Du, J.-H. Wu, Z.-H. Kang, Y. Jiang, and J.-Y. Gao, “Optical information transfer between two light channels in a Pr |

10. | J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. |

11. | K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature (London) |

12. | 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 (London) |

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

14. | R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. |

15. | J.-H. Wu, C.-L. Cui, N. Ba, Q.-R. Ma, and J.-Y. Gao, “Dynamical evolution and analytical solutions for multiple degenerate dark states in the tripod-type atomic system,” Phys. Rev. A |

16. | A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska–Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. |

17. | A. Raczynski, J. Zaremba, and S. Zielinska–Kaniasty, “Beam splitting and Hong-Ou-Mandel interference for stored light,” Phys. Rev. A |

18. | 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 |

19. | D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atomsin a tripod configuration,” Phys. Rev. A |

20. | S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalan, “Polarization phase gate with a tripod atomic system,” Phys. Rev. A |

21. | Y.-X. Han, J.-T. Xiao, Y.-H. Liu, C.-H. Zhang, H. Wang, M. Xiao, and K.-C. Peng, “Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system,” Phys. Rev. A |

22. | S.-J. Li, X.-D. Yang, X.-M. Cao, C.-H. Zhang, C.-D. Xie, and H. Wang, “Enhanced Cross-Phase Modulation Based on a Double Electromagnetically Induced Transparency in a Four-Level Tripod Atomic System,” Phys. Rev. Lett. |

23. | L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. |

24. | A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A |

25. | L. Karpa, G. Nikoghosyan, F. Vewinger, M. Fleischhauer, and M. Weitz, “Frequency matching in light-storage spectroscopy of atomic Raman transitions,” Phys. Rev. Lett. |

26. | G. Heinze, A. Rudolf, F. Beil, and T. Halfmann, “Storage of images in atomic coherences in a rare-earth-ion-doped solid,” Phys. Rev. A |

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

28. | E. Kuznetsova, O. Kocharovskaya, P. Hemmer, and M. O. Scully, “Atomic interference phenomena in solids with a long-lived spin coherence,” Phys. Rev. A |

29. | B. S. Ham, “Reversible quantum optical data storage based on resonant Raman optical field excited spin coherence,” Opt. Express |

30. | H. Wang, S.-J. Li, Z.-X. Xu, X.-B. Zhao, L.-J. Zhang, J.-H. Li, Y.-L. Wu, C.-D. Xie, K.-C. Peng, and M. Xiao, “Quantum interference of stored dual-channel spin-wave excitations in a single tripod system,” Phys. Rev. A |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.1670) Quantum optics : Coherent optical effects

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 25, 2011

Revised Manuscript: May 20, 2011

Manuscript Accepted: May 23, 2011

Published: June 2, 2011

**Citation**

Qian-Qian Bao, Jin-Wei Gao, Cui-Li Cui, Gang Wang, Yan Xue, and Jin-Hui Wu, "Dynamic generation of robust and controlled beating signals in an asymmetric procedure of light storage and retrieval," Opt. Express **19**, 11832-11840 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11832

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### References

- M. D. Lukin, “Colloquium: trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003). [CrossRef]
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005). [CrossRef]
- K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998). [CrossRef]
- D. A. Braje, V. Balic, G. Y. Yin, and S. E. Harris, “Low-light-level nonlinear optics with slow light,” Phys. Rev. A 68, 041801(R) (2003). [CrossRef]
- H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003). [CrossRef] [PubMed]
- C.-Y. Wang, Y.-F. Chen, S.-C. Lin, W.-H. Lin, P.-C. Kuan, and I. A. Yu, “Low-light-level all-optical switching,” Opt. Lett. 31, 2350–2352 (2006). [CrossRef] [PubMed]
- C. Hang and G.-X. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express 18, 2952–2966 (2010). [CrossRef] [PubMed]
- C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, “Atomic memory for correlated photon states,” Science 301, 196–200 (2003). [CrossRef] [PubMed]
- H.-H. Wang, X.-G. Wei, L. Wang, Y.-J. Li, D.-M. Du, J.-H. Wu, Z.-H. Kang, Y. Jiang, and J.-Y. Gao, “Optical information transfer between two light channels in a Pr3+:Y2SiO5crystal,” Opt. Express 15, 16044–16050 (2007). [CrossRef] [PubMed]
- J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum memory for squeezed light,” Phys. Rev. Lett. 100, 093602 (2008). [CrossRef] [PubMed]
- K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature (London) 452, 67–71 (2008). [CrossRef]
- 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 (London) 409, 490–493 (2001). [CrossRef]
- M. Fleischhauer and M. D. Lukin, “Dark-State Polaritons in Electromagnetically Induced Transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000). [CrossRef] [PubMed]
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