Abstract

We have observed coherent Raman beat signals from a Λ-type three-level system in a sodium atomic vapor. The sample is first prepared in a coherent superposition state of the ground-state hyperfine levels, or a dark state, by resonant bichromatic radiation. A following sudden frequency shift of one of the excitation beams causes the beat signals. Detailed analytical calculations based on the three-level Liouville equations are presented and are compared with experimental results. This simple technique is particularly suited for the obtaining of information on the generated sublevel coherence, including magnitude, phase, and decay time.

© 2005 Optical Society of America

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References

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  1. R. G. Brewer and E. L. Hahn, "Coherent Raman beats," Phys. Rev. A 8, 464-472 (1973).
    [CrossRef]
  2. R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641-1649 (1975).
    [CrossRef]
  3. D. Suter, The Physics of Laser-Atom Interactions (Cambridge U. Press, Cambridge, UK, 1997).
    [CrossRef]
  4. K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
    [CrossRef] [PubMed]
  5. J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
    [CrossRef] [PubMed]
  6. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
    [CrossRef] [PubMed]
  7. M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
    [CrossRef] [PubMed]
  8. 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]
  9. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
    [CrossRef]
  10. C. H. van der Wal, M. D. Eisaman, A. André, 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. W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
    [CrossRef] [PubMed]
  12. S. Gu and J. A. Behr, "Off-Raman resonance effects on hyperfine coherences," Phys. Rev. A 68, 015804-015804 (2003).
    [CrossRef]
  13. E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
    [CrossRef]
  14. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
    [CrossRef]
  15. M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
    [CrossRef]
  16. K. Motomura and M. Mitsunaga, "High-resolution spectroscopy of hyperfine Zeeman components of the sodium D1 line by coherent population trapping," J. Opt. Soc. Am. B 19, 2456-2460 (2002).
    [CrossRef]
  17. H. Asahi, K. Motomura, K. Harada, and M. Mitsunaga, "Dark-state imaging for two-dimensional mapping of a magnetic field," Opt. Lett. 28, 1153-1155 (2003).
    [CrossRef] [PubMed]
  18. K. Motomura, T. Koshimizu, K. Harada, H. Ueno, and M. Mitsunaga, "Subkilohertz linewidths measured by heterodyne-detected coherent population trapping in sodium vapor," Opt. Lett. 29, 1141-1143 (2004).
    [CrossRef] [PubMed]

2004 (1)

2003 (4)

H. Asahi, K. Motomura, K. Harada, and M. Mitsunaga, "Dark-state imaging for two-dimensional mapping of a magnetic field," Opt. Lett. 28, 1153-1155 (2003).
[CrossRef] [PubMed]

S. Gu and J. A. Behr, "Off-Raman resonance effects on hyperfine coherences," Phys. Rev. A 68, 015804-015804 (2003).
[CrossRef]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

C. H. van der Wal, M. D. Eisaman, A. André, 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]

2002 (1)

2001 (1)

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]

2000 (1)

M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

1999 (2)

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

1996 (1)

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

1995 (1)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

1991 (2)

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

1975 (1)

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641-1649 (1975).
[CrossRef]

1973 (1)

R. G. Brewer and E. L. Hahn, "Coherent Raman beats," Phys. Rev. A 8, 464-472 (1973).
[CrossRef]

André, A.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Asahi, H.

Baluschev, S.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Behr, J. A.

S. Gu and J. A. Behr, "Off-Raman resonance effects on hyperfine coherences," Phys. Rev. A 68, 015804-015804 (2003).
[CrossRef]

Behroozi, C. H.

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]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Boller, K.-J.

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
[CrossRef] [PubMed]

Boozer, A. D.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Brewer, R. G.

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641-1649 (1975).
[CrossRef]

R. G. Brewer and E. L. Hahn, "Coherent Raman beats," Phys. Rev. A 8, 464-472 (1973).
[CrossRef]

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Duan, L. -M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Dutton, Z.

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]

Eisaman, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Field, J. E.

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

Gu, S.

S. Gu and J. A. Behr, "Off-Raman resonance effects on hyperfine coherences," Phys. Rev. A 68, 015804-015804 (2003).
[CrossRef]

Hahn, E. L.

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641-1649 (1975).
[CrossRef]

R. G. Brewer and E. L. Hahn, "Coherent Raman beats," Phys. Rev. A 8, 464-472 (1973).
[CrossRef]

Hahn, K. H.

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

Harada, K.

Harris, S. E.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
[CrossRef] [PubMed]

Hau, L. V.

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]

Huss, A.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Imamoglu, A.

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
[CrossRef] [PubMed]

Imoto, N.

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Kimble, H. J.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Korsunsky, E.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

Korsunsky, E. A.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Koshimizu, T.

Kuzmich, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Leinfellner, N.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

Liu, C.

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]

Lukin, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

Maichen, W.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

Mazets, I.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

Mitsunaga, M.

Motomura, K.

Phillips, D. F.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Renzoni, F.

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

Suter, D.

D. Suter, The Physics of Laser-Atom Interactions (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

Ueno, H.

van der Wal, C. H.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Walsworth, R. L.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Windholz, L.

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Zibrov, A. S.

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (London) (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 (London) 409, 490-493 (2001).
[CrossRef]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. -M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature (London) 423, 731-734 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (6)

M. Mitsunaga and N. Imoto, "Observation of an electromagnetically induced grating in cold sodium atoms," Phys. Rev. A 59, 4773-4776 (1999).
[CrossRef]

W. Maichen, F. Renzoni, I. Mazets, E. Korsunsky, and L. Windholz, "Transient coherent population trapping in a closed loop interaction scheme," Phys. Rev. A 53, 3444-3448 (1996).
[CrossRef] [PubMed]

S. Gu and J. A. Behr, "Off-Raman resonance effects on hyperfine coherences," Phys. Rev. A 68, 015804-015804 (2003).
[CrossRef]

E. A. Korsunsky, N. Leinfellner, A. Huss, S. Baluschev, and L. Windholz, "Phase-dependent electromagnetically induced transparency," Phys. Rev. A 59, 2302-2305 (1999).
[CrossRef]

R. G. Brewer and E. L. Hahn, "Coherent Raman beats," Phys. Rev. A 8, 464-472 (1973).
[CrossRef]

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641-1649 (1975).
[CrossRef]

Phys. Rev. Lett. (4)

K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2956 (1991).
[CrossRef] [PubMed]

J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991).
[CrossRef] [PubMed]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency," Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

Science (1)

C. H. van der Wal, M. D. Eisaman, A. André, 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]

Other (2)

D. Suter, The Physics of Laser-Atom Interactions (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) and (b) Energy-level diagrams of a three-level Λ atom interacting with a probe field and a coupling field. (a) Probe and coupling frequencies satisfy the two-photon resonance condition in the EIT period. (b) The probe frequency is shifted, and the two-photon resonance is not satisfied in the CRB period. (c) Expected signal waveform in the transmitted laser intensity in the EIT-CRB experiment.

Fig. 2
Fig. 2

(a) Energy-level diagram showing the generation of the Stokes beat. (b) Energy-level diagram showing the generation of the anti-Stokes beat.

Fig. 3
Fig. 3

Schematic of the CRB experiment. PBS, polarizing beam splitter; PD, photodetector; λ 2 , half-wave plate; λ 4 ; quarter-wave plate.

Fig. 4
Fig. 4

Typical experimental waveforms in the CRB experiment. Probe power I p = 50 μ W , coupling power I c = 150 μ W , and frequency shift Δ p 2 π = 200 kHz . (a) EIT-CRB sequence when ω p corresponds to the EIT resonance. (b) CRB-EIT sequence when ω p Δ p corresponds to the EIT resonance.

Fig. 5
Fig. 5

CRB signal waveforms for probe frequency shift Δ p 2 π = 100 , 200, and 400 kHz. I p = 100 μ W and I c = 150 μ W .

Fig. 6
Fig. 6

Typical CRB signal waveforms for (a) Stokes beat and (b) anti-Stokes beat. I p = 100 μ W , I c = 150 μ W , and Δ p 2 π = 200 kHz .

Fig. 7
Fig. 7

(a) Experimental CRB waveforms for I c = 310 , 140, and 33 μW. I p = 100 μ W and Δ p 2 π = 200 kHz . (b) Theoretical calculations of the anti-Stokes beat signal based on Eq. (10) for Ω c 2 π = 0.3 , 0.2, and 0.1 MHz. Other parameters are γ 2 π = 5 MHz , γ s 2 π = 2.5 kHz , and Δ p 2 π = 200 kHz .

Fig. 8
Fig. 8

CRB signal decay rates γ d 2 π as a function of coupling-beam intensity I c . Open circles, experimental results; solid line, theoretical fit.

Fig. 9
Fig. 9

(a) Expected signal waveform in the optical-data storage-type experiment. (b) CRB peak signal intensity as a function of delay time t d . I p = 50 μ W , I c = 300 μ W , and Δ p 2 π = 200 kHz .

Equations (20)

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

Ψ = 1 Ω ( Ω c 1 Ω p 2 ) ,
ρ ̇ 33 = i 2 ( Ω p * ρ 13 Ω p ρ 31 ) + i 2 ( Ω c * ρ 23 Ω c ρ 32 ) Γ ρ 33 ,
ρ ̇ 22 = i 2 ( Ω c ρ 32 Ω c * ρ 23 ) + Γ 32 ρ 33 ,
ρ ̇ 11 = i 2 ( Ω p ρ 31 Ω p * ρ 13 ) + Γ 31 ρ 33 ,
ρ ̇ 13 = i δ p ρ 13 + i 2 Ω p ( ρ 33 ρ 11 ) i 2 Ω c ρ 12 γ 31 ρ 13 ,
ρ ̇ 23 = i δ c ρ 23 + i 2 Ω c ( ρ 33 ρ 22 ) i 2 Ω p ρ 21 γ 32 ρ 23 ,
ρ ̇ 12 = i δ s ρ 12 + i 2 Ω p ρ 32 i 2 Ω c * ρ 13 γ s ρ 12 ,
ρ ̇ 13 = ( i δ p γ ) ρ 13 i 2 Ω c ρ 12 ,
ρ ̇ 12 = ( i δ s γ s ) ρ 12 i 2 Ω c * ρ 13 ,
ρ 13 ( t ) = i ρ 0 Ω c ξ exp ( γ 1 2 t ) sinh ξ 2 t ,
ρ 12 ( t ) = ρ 0 exp ( γ 1 2 t ) ( cosh ξ 2 t + γ 2 ξ sinh ξ 2 t ) ,
ρ 13 ( t ) = i ρ 0 Ω c 2 ( γ i δ p ) [ exp { ( γ i δ p ) t } exp { ( γ s i Δ p ) t Ω c 2 4 ( γ i δ p ) t } ] .
ρ 13 ( t ) = i ρ 0 Ω c 2 γ [ exp ( γ t ) exp { ( γ s + Ω c 2 4 γ ) t + i Δ p t } ] .
ρ 23 ( t ) = i ρ 0 Ω p 2 γ [ exp ( γ t ) exp { ( γ s + Ω p 2 4 γ ) t i Δ p t } ] .
I sig E p + E AS + E c + E S 2 ,
I sig E p exp ( i ω p t ) + i k p 2 ϵ 0 N p 13 ρ 31 ( t ) exp ( i ω p t ) + E c exp ( i ω c t ) + i k c 2 ϵ 0 N p 23 ρ 32 ( t ) exp ( i ω c t ) 2 ,
I AS E p 2 + β AS Ω p Ω c [ exp ( γ t ) exp { ( γ s + Ω c 2 4 γ ) t } cos ( Δ p t ) ] ,
I S E c 2 + β S Ω p Ω c [ exp ( γ t ) exp { ( γ s + Ω p 2 4 γ ) t } cos ( Δ p t ) ] ,
γ d = γ s + Ω c 2 4 γ .
ρ 12 ( t d ) = ρ 12 ( 0 ) exp ( γ s t d ) .

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