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

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  1. H. R. Gray, R. M. Whitley, and C. R. StroudJr., "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), and references are there in.
    [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]
  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]
  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]
  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]
  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]
  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. 93, 183601 (2004).
    [CrossRef] [PubMed]
  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. 88, 143902 (2002).
    [CrossRef] [PubMed]
  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]
  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. 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]
  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]
  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]
  21. A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, "Photon echoes produced by switching electric fields," Phys. Rev. Lett. 96043602 (2006).
    [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]
  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. 87, 173601 (2001).
    [CrossRef] [PubMed]
  24. K. Holiday, M. Croci, E. Vauthey, U. P. Wild, "Spectral hole burning and holography in an Y2SIO5:Pr3+ crystal," Phys. Rev. B 47, 14741-14752 (1993).
    [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]
  26. M. Sargent III, M. O. Scully, and W. E. Lamb Jr., Laser Physics (Addison-Wesley, 1974), Chap. 7.
  27. R. W. Equall, R. L. Cone, R. M. Macfarlane, "Homogeneous broadening and hyperfine structure of optical transitions in Pr3+:Y2SiO5," Phys. Rev. B 52, 3963-3969 (1995).
    [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, R2583-2586 (1999).
    [CrossRef]

2008 (1)

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]

2006 (5)

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]

A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, "Photon echoes produced by switching electric fields," Phys. Rev. Lett. 96043602 (2006).
[CrossRef] [PubMed]

F. Xia, L. Sekaric, and L. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).
[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]

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

2005 (2)

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]

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]

2004 (1)

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]

2003 (3)

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]

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]

2002 (3)

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]

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]

2001 (2)

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]

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. 87, 173601 (2001).
[CrossRef] [PubMed]

2000 (1)

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]

1999 (3)

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, R2583-2586 (1999).
[CrossRef]

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

1998 (1)

S. E. Harris and Y. Yamamoto, "Quantum switching by quantum interference," Phys. Rev. Lett. 81, 3611-3614 (1998).
[CrossRef]

1997 (1)

1995 (1)

R. W. Equall, R. L. Cone, R. M. Macfarlane, "Homogeneous broadening and hyperfine structure of optical transitions in Pr3+:Y2SiO5," Phys. Rev. B 52, 3963-3969 (1995).
[CrossRef]

1993 (1)

K. Holiday, M. Croci, E. Vauthey, U. P. Wild, "Spectral hole burning and holography in an Y2SIO5:Pr3+ crystal," Phys. Rev. B 47, 14741-14752 (1993).
[CrossRef]

1978 (1)

Nat. Photonics (1)

F. Xia, L. Sekaric, and L. Vlasov, "Ultracompact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2006).
[CrossRef]

Nature (2)

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]

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]

Opt. Lett. (2)

Phys. Rev. A (6)

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]

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]

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]

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

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, R2583-2586 (1999).
[CrossRef]

Phys. Rev. B (2)

R. W. Equall, R. L. Cone, R. M. Macfarlane, "Homogeneous broadening and hyperfine structure of optical transitions in Pr3+:Y2SiO5," Phys. Rev. B 52, 3963-3969 (1995).
[CrossRef]

K. Holiday, M. Croci, E. Vauthey, U. P. Wild, "Spectral hole burning and holography in an Y2SIO5:Pr3+ crystal," Phys. Rev. B 47, 14741-14752 (1993).
[CrossRef]

Phys. Rev. Lett. (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. 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]

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]

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. 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]

A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, "Photon echoes produced by switching electric fields," Phys. Rev. Lett. 96043602 (2006).
[CrossRef] [PubMed]

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]

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. 87, 173601 (2001).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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]

Science (1)

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]

Other (2)

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]

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

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Figures (16)

Fig. 1.
Fig. 1.

(a). Energy level diagram and (b). Pulse sequence: ΩPC=20kHz; γ3132=50kHz; Γ3132=0.5kHz; γ21=0.2kHz; Γ21=0; Δspin inh=50kHz.

Fig. 2.
Fig. 2.

Spin inhomogeneous broadening.

Fig. 3.
Fig. 3.

Coherence vs. (a) optical population difference, and (b) spin population difference.

Fig. 4.
Fig. 4.

Coherence vs. interaction time for two-photon resonance (δ2=0). Dotted line: ρ2211; pink (red) curve: ρ1122=0.5:0.5 (1:0); blue curve: r12).

Fig. 5.
Fig. 5.

(a). Spin population difference, and (b) Spin coherence

Fig. 6.
Fig. 6.

Spin coherence (r(ρ12)) evolution vs. two-photon detuning δ2.

Fig. 7.
Fig. 7.

(a). Spin coherence vs. interaction time for initial condition of ρ11=1 and ρ22=0. (b) Spin coherence vs (c) spin population difference. ΩPP=20 kHz.

Fig. 8.
Fig. 8.

Coherence excitation vs. interaction time (a) for all atoms, and (b) only for δ2=0: ΩPP=20 kHz; ρ1122=0.5; γ3132=50kHz; Γ3132=0.5kHz; γ21=0.2kHz; Γ21=0.

Fig. 9.
Fig. 9.

Coherence vs. interaction time: ΩP=10 kHz; ΩC=200 kHz; ρ1122=0.5; γ3132=50kHz; Γ3132=0.5kHz; γ21=0.2kHz; Γ21=0.

Fig. 10.
Fig. 10.

(a). Pulse sequence, (b) overall spin coherence, and (c) two-photon resonant spin coherence.

Fig. 11.
Fig. 11.

Coherence excitation in a lambda-type three-level system of Fig. 1(a).

Fig. 12.
Fig. 12.

Spin coherence retrieval to optical coherence.

Fig. 13.
Fig. 13.

Coherence transfer from spin coherence to optical coherence.

Fig. 14.
Fig. 14.

3D simulations for optical absorption and spin coherence.

Fig. 15.
Fig. 15.

Coherent control at strong field limit: ρ1122.

Fig. 16.
Fig. 16.

Dynamic coherence transfer to optical emission.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

d ρ dt = i ħ [ H , ρ ] 1 2 { Γ , ρ } ,
H = ħ { δ 1 1 1 δ 2 2 2 δ 3 3 3 1 2 ( Ω 1 1 3 + Ω 2 2 3 ) + H . c . } ,
d ρ 12 dt = i 2 Ω C ρ 13 + i 2 Ω P ρ 32 i ( δ 1 δ 2 ) ρ 12 γ 12 ρ 12 ,
d ρ 13 dt = i 2 Ω P ( ρ 11 ρ 33 ) i 2 Ω C ρ 12 i δ 1 ρ 13 γ 13 ρ 13 ,
d ρ 23 dt = i 2 Ω P ρ 21 i 2 Ω C ( ρ 22 ρ 33 ) i δ 2 ρ 23 γ 23 ρ 23 .
E ( t ) d dt [ r ( ρ 12 ( t ) ) ]

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