Abstract

We show that highly efficient ultraviolet frequency up conversion can be established in a single-component quantum gas in the counter-propagating weak pump beam geometry where no frequency up conversion can occur in a normal gas. We also show that all light-wave mixing and scattering processes in quantum gases originating from elementary excitations characterized by efficient collective atomic recoil motion are stimulated Raman/hyper-Raman in nature.

© 2013 Optical Society of America

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References

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  1. D. L. Elliott, Ultraviolet Laser Technology and Applications (Academic, 1995).
  2. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  3. R. B. Miles and S. E. Harris, IEEE J Quantum Electron. QE-9, 470 (1973).
    [CrossRef]
  4. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
    [CrossRef]
  5. K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
    [CrossRef]
  6. C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
    [CrossRef]
  7. R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
    [CrossRef]
  8. W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
    [CrossRef]
  9. L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
    [CrossRef]
  10. L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
    [CrossRef]
  11. H. Uys and P. Meystre, Phys. Rev. A 75, 03385 (2007).
    [CrossRef]
  12. H. Uys and P. Meystre, Phys. Rev. A 77, 063614 (2008).
    [CrossRef]
  13. J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
    [CrossRef]
  14. N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).
  15. F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
    [CrossRef]
  16. R. P. Feynman, Phys. Rev. 94, 262 (1954).
    [CrossRef]
  17. This approximation is valid for long pulse excitation so that γτ≫1 (here τ is the pump laser pulse length).

2012 (1)

J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
[CrossRef]

2008 (1)

H. Uys and P. Meystre, Phys. Rev. A 77, 063614 (2008).
[CrossRef]

2007 (1)

H. Uys and P. Meystre, Phys. Rev. A 75, 03385 (2007).
[CrossRef]

2006 (1)

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

2000 (1)

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

1997 (2)

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

1995 (2)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

1992 (1)

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

1990 (1)

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

1973 (1)

R. B. Miles and S. E. Harris, IEEE J Quantum Electron. QE-9, 470 (1973).
[CrossRef]

1954 (1)

R. P. Feynman, Phys. Rev. 94, 262 (1954).
[CrossRef]

1947 (1)

N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Andrew, M. R.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Bogoliubov, N. N.

N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).

Bradley, C. C.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Chwedenczuk, J.

J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
[CrossRef]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Davis, K. B.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Deng, L.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

Durfee, D. S.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Elliott, D. L.

D. L. Elliott, Ultraviolet Laser Technology and Applications (Academic, 1995).

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Feynman, R. P.

R. P. Feynman, Phys. Rev. 94, 262 (1954).
[CrossRef]

Garrett, W. R.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

Harris, S. E.

R. B. Miles and S. E. Harris, IEEE J Quantum Electron. QE-9, 470 (1973).
[CrossRef]

Hart, R. C.

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

Hulet, R. G.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Ketterle, W.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Kolodynski, J.

J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
[CrossRef]

Kurn, D. M.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Mewes, M. O.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Meystre, P.

H. Uys and P. Meystre, Phys. Rev. A 77, 063614 (2008).
[CrossRef]

H. Uys and P. Meystre, Phys. Rev. A 75, 03385 (2007).
[CrossRef]

Miles, R. B.

R. B. Miles and S. E. Harris, IEEE J Quantum Electron. QE-9, 470 (1973).
[CrossRef]

Moore, M. A.

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

Payne, M. G.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

Pitaevskii, L.

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

Sackett, C. A.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Stamper-Kurn, D. M.

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

Stringari, S.

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

Uys, H.

H. Uys and P. Meystre, Phys. Rev. A 77, 063614 (2008).
[CrossRef]

H. Uys and P. Meystre, Phys. Rev. A 75, 03385 (2007).
[CrossRef]

Vandruten, N. J.

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

Wasilewski, W.

J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
[CrossRef]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Wunderlich, R. K.

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

Zambelli, F.

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

Chem. Phys. Lett. (1)

L. Deng, W. R. Garrett, M. G. Payne, and M. A. Moore, Chem. Phys. Lett. 270, 299 (1997).
[CrossRef]

IEEE J Quantum Electron. (1)

R. B. Miles and S. E. Harris, IEEE J Quantum Electron. QE-9, 470 (1973).
[CrossRef]

J. Phys. (USSR) (1)

N. N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).

Phys. Rep. (1)

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rep. 429, 123 (2006).
[CrossRef]

Phys. Rev. (1)

R. P. Feynman, Phys. Rev. 94, 262 (1954).
[CrossRef]

Phys. Rev. A (6)

F. Zambelli, L. Pitaevskii, D. M. Stamper-Kurn, and S. Stringari, Phys. Rev. A 61, 063608 (2000).
[CrossRef]

H. Uys and P. Meystre, Phys. Rev. A 75, 03385 (2007).
[CrossRef]

H. Uys and P. Meystre, Phys. Rev. A 77, 063614 (2008).
[CrossRef]

J. Kołodyński, J. Chwedeńczuk, and W. Wasilewski, Phys. Rev. A 86, 013818 (2012).
[CrossRef]

R. K. Wunderlich, W. R. Garrett, R. C. Hart, M. A. Moore, and M. G. Payne, Phys. Rev. A 41, 6345 (1990).
[CrossRef]

W. R. Garrett, M. A. Moore, R. C. Hart, M. G. Payne, and R. K. Wunderlich, Phys. Rev. A 45, 6687 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

K. B. Davis, M. O. Mewes, M. R. Andrew, N. J. Vandruten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995).
[CrossRef]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Science (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995).
[CrossRef]

Other (3)

D. L. Elliott, Ultraviolet Laser Technology and Applications (Academic, 1995).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

This approximation is valid for long pulse excitation so that γτ≫1 (here τ is the pump laser pulse length).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Energy diagram and laser couplings for THG. The dotted-dashed arrow back to the origin represents the forward THG by usual electronic excitation. The dashed arrow represents the backward emitted THG component originated from elementary excitation in a quantum gas that is resonant with a momentum state. The dotted arrow represents the off-resonance backward emitted THG component by the quantum gas. (b) Wave vector diagrams for forward generation by electronic excitation and backward emission by elementary excitation. (c) Schematics for collective atom recoil motion and generated fields.

Fig. 2.
Fig. 2.

|Ω3HG/ΩL(3)|2 as a function of normalized propagation distance z/L for normal gas (a) and quantum gas (b) in counterpropagating beams (THG propagates from 1 to 0). In (a) the large optical-wave phase mismatch is not compensated for normal, single component atomic gas, whereas in (b) the large optical wave phase mismatch is perfectly compensated by Bogoliubov dispersion of the elementary excitation.

Equations (9)

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

i(z+1ct)EM+12kM2EM=PM,
P3HG=κd41Δ4|Ψ|2[j=13(djj+1·EL)2j=12δj+1+d·E3HG],
itΨ=H^Ψ+[βeiΔk·r+iΔωt+H.c.]Ψ.
Ψ(r,t)=eiμt[Ψ0(r)+u(r,t)eiq·riωqt+v*(r,t)eiq·r+iωqt].
ut=γu+i(ωquAuBvβ*Ψ0eiξ),
vt=γv+i(ωqv+Av+Bu+β*Ψ0eiξ),
P3HG(QG)=κd14[ΩL(3)Δ4](u*+v*)Ψ0eiξ.
Λ3HGziωcΛ3HGiκ3HG|Ψ0|2S(q)ωBΔω+ω+iγΛ3HG,
GQG=κMγ|Ψ0|2S(q).

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