Abstract

This work presents an analytical calculation of the time-dependent radiation forces on a two-level atom interacting with a single-mode laser field. Such a closed and compact expression of the radiation forces is derived by solving the optical Bloch equations analytically. It is confirmed, in particular, that the radiation force consists of reactive as well as dissipative components, whose explicit analytical forms of the temporal solutions can be explicitly obtained. The succinct analytical solutions of the radiation forces may be helpful for a convenient and intuitive description of the complex atomic dynamics such as interaction with various laser fields.

© 2010 Optical Society of America

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  1. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).
    [CrossRef]
  2. V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms,” Rep. Prog. Phys. 63, 1429–1510 (2000).
    [CrossRef]
  3. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
    [CrossRef] [PubMed]
  4. C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
    [CrossRef] [PubMed]
  5. J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
    [CrossRef]
  6. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
    [CrossRef]
  7. J. I. Cirac and P. Zoller, “New frontiers in quantum information with atoms and ions,” Phys. Today 57(3), 38–44 (2004).
    [CrossRef]
  8. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).
  9. C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, J.Dalibard, J.M.Raimond, and J.Zinn-Justin, eds. (North-Holland, 1992), pp. 1–164.
  10. R. J. Cook, “Atomic motion in resonant radiation: An application of Ehrenfest’s theorem,” Phys. Rev. A 20, 224–228 (1979).
    [CrossRef]
  11. J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
    [CrossRef]
  12. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).
  13. L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
    [CrossRef] [PubMed]
  14. A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
    [CrossRef]
  15. H. C. Torrey, “Transient nutations in nuclear magnetic resonance,” Phys. Rev. 76, 1059–1068 (1949).
    [CrossRef]
  16. A. V. Alekseev and N. V. Sushilov, “Analytic solutions of Bloch and Maxwell–Bloch equations in the case of arbitrary field amplitude and phase modulation,” Phys. Rev. A 46, 351–355 (1992).
    [CrossRef] [PubMed]
  17. P. K. Madhu and A. Kumar, “Bloch equations revisited: New analytical solutions for the generalized Bloch equations,” Concepts Magn. Reson. 9, 1–12 (1997).
    [CrossRef]
  18. A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
    [CrossRef] [PubMed]
  19. S. Bougouffa and S. Al-Awfi, “Transient optical regime of two level atom in laser light,” Int. J. Theor. Phys. 46, 920–934 (2007).
    [CrossRef]
  20. S. Bougouffa and S. Al-Awfi, “Analysis of transient effects of two-level atom in laser light,” J. Mod. Opt. 55, 473–489 (2008).
    [CrossRef]
  21. H. R. Noh and W. Jhe, “Analytic solutions of the optical Bloch equations,” Opt. Commun. 283, 2353–2355 (2010).
    [CrossRef]
  22. A. Al-Hilfy and R. Loudon, “Rate-equation and Bloch-equation theories of radiation pressure on two-level atoms,” Opt. Acta 32, 995–1013 (1985).
  23. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]

2010 (1)

H. R. Noh and W. Jhe, “Analytic solutions of the optical Bloch equations,” Opt. Commun. 283, 2353–2355 (2010).
[CrossRef]

2009 (1)

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[CrossRef]

2008 (1)

S. Bougouffa and S. Al-Awfi, “Analysis of transient effects of two-level atom in laser light,” J. Mod. Opt. 55, 473–489 (2008).
[CrossRef]

2007 (1)

S. Bougouffa and S. Al-Awfi, “Transient optical regime of two level atom in laser light,” Int. J. Theor. Phys. 46, 920–934 (2007).
[CrossRef]

2006 (1)

A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
[CrossRef] [PubMed]

2005 (1)

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

2004 (1)

J. I. Cirac and P. Zoller, “New frontiers in quantum information with atoms and ions,” Phys. Today 57(3), 38–44 (2004).
[CrossRef]

2000 (1)

V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms,” Rep. Prog. Phys. 63, 1429–1510 (2000).
[CrossRef]

1999 (2)

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).
[CrossRef]

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

1997 (1)

P. K. Madhu and A. Kumar, “Bloch equations revisited: New analytical solutions for the generalized Bloch equations,” Concepts Magn. Reson. 9, 1–12 (1997).
[CrossRef]

1996 (2)

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

1992 (4)

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, J.Dalibard, J.M.Raimond, and J.Zinn-Justin, eds. (North-Holland, 1992), pp. 1–164.

A. V. Alekseev and N. V. Sushilov, “Analytic solutions of Bloch and Maxwell–Bloch equations in the case of arbitrary field amplitude and phase modulation,” Phys. Rev. A 46, 351–355 (1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1987 (1)

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

1985 (1)

A. Al-Hilfy and R. Loudon, “Rate-equation and Bloch-equation theories of radiation pressure on two-level atoms,” Opt. Acta 32, 995–1013 (1985).

1980 (1)

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

1979 (1)

R. J. Cook, “Atomic motion in resonant radiation: An application of Ehrenfest’s theorem,” Phys. Rev. A 20, 224–228 (1979).
[CrossRef]

1949 (1)

H. C. Torrey, “Transient nutations in nuclear magnetic resonance,” Phys. Rev. 76, 1059–1068 (1949).
[CrossRef]

Al-Amri, M.

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

Al-Awfi, S.

S. Bougouffa and S. Al-Awfi, “Analysis of transient effects of two-level atom in laser light,” J. Mod. Opt. 55, 473–489 (2008).
[CrossRef]

S. Bougouffa and S. Al-Awfi, “Transient optical regime of two level atom in laser light,” Int. J. Theor. Phys. 46, 920–934 (2007).
[CrossRef]

Alekseev, A. V.

A. V. Alekseev and N. V. Sushilov, “Analytic solutions of Bloch and Maxwell–Bloch equations in the case of arbitrary field amplitude and phase modulation,” Phys. Rev. A 46, 351–355 (1992).
[CrossRef] [PubMed]

Al-Hilfy, A.

A. Al-Hilfy and R. Loudon, “Rate-equation and Bloch-equation theories of radiation pressure on two-level atoms,” Opt. Acta 32, 995–1013 (1985).

Allen, L.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

Andrews, D. L.

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

Ashkin, A.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Babiker, M.

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

Bagnato, V. S.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Balykin, V. I.

V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms,” Rep. Prog. Phys. 63, 1429–1510 (2000).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bougouffa, S.

S. Bougouffa and S. Al-Awfi, “Analysis of transient effects of two-level atom in laser light,” J. Mod. Opt. 55, 473–489 (2008).
[CrossRef]

S. Bougouffa and S. Al-Awfi, “Transient optical regime of two level atom in laser light,” Int. J. Theor. Phys. 46, 920–934 (2007).
[CrossRef]

Brumer, P.

A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
[CrossRef] [PubMed]

Carter, A. R.

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

Cesar, C. L.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Cirac, J. I.

J. I. Cirac and P. Zoller, “New frontiers in quantum information with atoms and ions,” Phys. Today 57(3), 38–44 (2004).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, J.Dalibard, J.M.Raimond, and J.Zinn-Justin, eds. (North-Holland, 1992), pp. 1–164.

Cook, R. J.

R. J. Cook, “Atomic motion in resonant radiation: An application of Ehrenfest’s theorem,” Phys. Rev. A 20, 224–228 (1979).
[CrossRef]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

Cronin, A. D.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[CrossRef]

Doyle, J. M.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

Fried, D. G.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Greytak, T. J.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).

Han, H.

A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
[CrossRef] [PubMed]

Jhe, W.

H. R. Noh and W. Jhe, “Analytic solutions of the optical Bloch equations,” Opt. Commun. 283, 2353–2355 (2010).
[CrossRef]

Julienne, P. S.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Killian, T. C.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Kleppner, D.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Kumar, A.

P. K. Madhu and A. Kumar, “Bloch equations revisited: New analytical solutions for the generalized Bloch equations,” Concepts Magn. Reson. 9, 1–12 (1997).
[CrossRef]

Lai, W. K.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

Lembessis, V. E.

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

Letokhov, V. S.

V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms,” Rep. Prog. Phys. 63, 1429–1510 (2000).
[CrossRef]

Loudon, R.

A. Al-Hilfy and R. Loudon, “Rate-equation and Bloch-equation theories of radiation pressure on two-level atoms,” Opt. Acta 32, 995–1013 (1985).

Madhu, P. K.

P. K. Madhu and A. Kumar, “Bloch equations revisited: New analytical solutions for the generalized Bloch equations,” Concepts Magn. Reson. 9, 1–12 (1997).
[CrossRef]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

Metcalf, H. J.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).
[CrossRef]

Minogin, V. G.

V. I. Balykin, V. G. Minogin, and V. S. Letokhov, “Electromagnetic trapping of cold atoms,” Rep. Prog. Phys. 63, 1429–1510 (2000).
[CrossRef]

Noh, H. R.

H. R. Noh and W. Jhe, “Analytic solutions of the optical Bloch equations,” Opt. Commun. 283, 2353–2355 (2010).
[CrossRef]

Polcyn, A. D.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[CrossRef]

Sandberg, J. C.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Sanz, A. S.

A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
[CrossRef] [PubMed]

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Sushilov, N. V.

A. V. Alekseev and N. V. Sushilov, “Analytic solutions of Bloch and Maxwell–Bloch equations in the case of arbitrary field amplitude and phase modulation,” Phys. Rev. A 46, 351–355 (1992).
[CrossRef] [PubMed]

Torrey, H. C.

H. C. Torrey, “Transient nutations in nuclear magnetic resonance,” Phys. Rev. 76, 1059–1068 (1949).
[CrossRef]

van der Straten, P.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).
[CrossRef]

Weiner, J.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Yu, I. A.

C. L. Cesar, D. G. Fried, T. C. Killian, A. D. Polcyn, J. C. Sandberg, I. A. Yu, T. J. Greytak, D. Kleppner, and J. M. Doyle, “Two-photon spectroscopy of trapped atomic hydrogen,” Phys. Rev. Lett. 77, 255–258 (1996).
[CrossRef] [PubMed]

Zilio, S.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Zoller, P.

J. I. Cirac and P. Zoller, “New frontiers in quantum information with atoms and ions,” Phys. Today 57(3), 38–44 (2004).
[CrossRef]

Concepts Magn. Reson. (1)

P. K. Madhu and A. Kumar, “Bloch equations revisited: New analytical solutions for the generalized Bloch equations,” Concepts Magn. Reson. 9, 1–12 (1997).
[CrossRef]

Int. J. Theor. Phys. (1)

S. Bougouffa and S. Al-Awfi, “Transient optical regime of two level atom in laser light,” Int. J. Theor. Phys. 46, 920–934 (2007).
[CrossRef]

J. Chem. Phys. (1)

A. S. Sanz, H. Han, and P. Brumer, “Aspects of quantum coherence in the optical Bloch equations,” J. Chem. Phys. 124, 214106 (2006).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

S. Bougouffa and S. Al-Awfi, “Analysis of transient effects of two-level atom in laser light,” J. Mod. Opt. 55, 473–489 (2008).
[CrossRef]

Opt. Acta (1)

A. Al-Hilfy and R. Loudon, “Rate-equation and Bloch-equation theories of radiation pressure on two-level atoms,” Opt. Acta 32, 995–1013 (1985).

Opt. Commun. (1)

H. R. Noh and W. Jhe, “Analytic solutions of the optical Bloch equations,” Opt. Commun. 283, 2353–2355 (2010).
[CrossRef]

Phys. Rev. (1)

H. C. Torrey, “Transient nutations in nuclear magnetic resonance,” Phys. Rev. 76, 1059–1068 (1949).
[CrossRef]

Phys. Rev. A (6)

A. V. Alekseev and N. V. Sushilov, “Analytic solutions of Bloch and Maxwell–Bloch equations in the case of arbitrary field amplitude and phase modulation,” Phys. Rev. A 46, 351–355 (1992).
[CrossRef] [PubMed]

L. Allen, M. Babiker, W. K. Lai, and V. E. Lembessis, “Atom dynamics in multiple Laguerre–Gaussian beams,” Phys. Rev. A 54, 4259–4270 (1996).
[CrossRef] [PubMed]

A. R. Carter, M. Babiker, M. Al-Amri, and D. L. Andrews, “Transient optical angular momentum effects in light-matter interactions,” Phys. Rev. A 72, 043407 (2005).
[CrossRef]

R. J. Cook, “Atomic motion in resonant radiation: An application of Ehrenfest’s theorem,” Phys. Rev. A 20, 224–228 (1979).
[CrossRef]

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Map describing the behavior of the radiation forces. The solutions show the oscillatory (monotonic decaying) behavior outside (inside) the boundary. The cusp points ( C ± ) are given by δ + θ ̇ = ( 3 / 18 ) Γ and Ω 1 = ( 6 / 9 ) Γ .

Fig. 2
Fig. 2

Time-dependence of the dissipative radiation forces at δ k v = 2 Γ and Ω 1 = 0.5 Γ [curve (A)] and at δ k v = 0.05 Γ and Ω 1 = 0.2 Γ [curve (B)].

Equations (38)

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E ( r , t ) = e ̂ E 0 ( r ) cos [ ω t + θ ( r ) ] ,
F ( r , t ) = H int ( r , t ) .
H int ( r , t ) = 1 2 Ω 1 ( r ) e i [ ω t + θ ( r ) ] | b a | + H .c . ,
F ( r , t ) = Tr   ρ H int = 2 e i ( ω t + θ ) ρ a b ( Ω 1 i Ω 1 θ ) 2 e i ( ω t + θ ) ρ b a ( Ω 1 + i Ω 1 θ ) ,
F = U Ω 1 Ω 1 V θ .
F react = U Ω 1 ,
F dissip = Ω 1 V θ .
ρ ̇ = i [ H 0 + H int , ρ ] + ρ ̇ sp ,
ρ ̇ sp = ( Γ ρ a a ( Γ / 2 ) ρ a b ( Γ / 2 ) ρ b a Γ ρ b b ) ,
U ̇ = Γ 2 U + ( δ + θ ̇ ) V ,
V ̇ = Γ 2 V ( δ + θ ̇ ) U + Ω 1 2 W ,
W ̇ = Γ W 2 Ω 1 V + Γ ,
F react = Ω 1 [ U s + A u e a t + ( B u   cos   q t + Γ C u q sin   q t ) e p t ] ,
F dissip = Ω 1 θ [ V s + A v e a t + ( B v   cos   q t + Γ C v q sin   q t ) e p t ] ,
a = Γ ( 2 3 2 S + ) ,     p = Γ ( 2 3 + S + ) ,     q = 3 Γ S ,
S ± = 1 2 [ ( R + R 2 + Q 3 ) 1 / 3 ± ( R R 2 + Q 3 ) 1 / 3 ] ,
Q = ( δ + θ ̇ ) 2 + Ω 1 2 3 Γ 2 1 36 ,
R = 2 ( δ + θ ̇ ) 2 Ω 1 2 12 Γ 2 1 216 ,
U s = 2 ( δ + θ ̇ ) Ω 1 4 ( δ + θ ̇ ) 2 + Γ 2 + 2 Ω 1 2 ,
V s = Ω 1 4 ( δ + θ ̇ ) 2 + Γ 2 + 2 Ω 1 2 .
A u = 1 Δ { ( δ + θ ̇ ) Ω 1 2 Γ 2 [ ( S + + 2 3 ) 2 + 3 S 2 ] U s } ,
B u = 1 Δ { ( δ + θ ̇ ) Ω 1 2 Γ 2 + 4 9 ( 3 S + 1 ) ( 6 S + + 1 ) U s } ,
C u = 1 Δ { 3 ( δ + θ ̇ ) Ω 1 2 Γ 2 S + + 2 3 ( 3 S + 1 ) ( 3 S + 2 + 2 S + 3 S 2 ) U s } ,
A v = 1 Δ { ( S + + 5 12 ) Ω 1 Γ [ ( S + + 2 3 ) 2 + 3 S 2 ] V s } ,
B v = 1 Δ { ( S + + 5 12 ) Ω 1 Γ + 4 9 ( 3 S + 1 ) ( 6 S + + 1 ) V s } ,
C v = 1 Δ { Ω 1 4 Γ ( 6 S + 2 5 S + + 6 S 2 ) 2 3 ( 3 S + 1 ) ( 3 S + 2 + 2 S + 3 S 2 ) V s } ,
F react = Ω 1 [ U s + A u e a t + ( B u   cosh   β t + Γ C u β sinh   β t ) e p t ] ,
F dissip = Ω 1 θ [ V s + A v e a t + ( B v   cosh   β t + Γ C v β sinh   β t ) e p t ] ,
c 1 + c 2 e a t + ( c 3 + c 4 t ) e p t .
c 5 + ( c 6 + c 7 t + c 8 t 2 ) e ( 2 / 3 ) Γ t .
F dissip = Ω 1 k { V s + A v e a t + [ B v   cos   q t + Γ C v q sin   q t ] e p t } .
F dissip = Γ Ω 1 2 k Γ 2 + 4 ( δ k v ) 2 { 1 + [ cos ( δ k v ) t + 2 ( δ k v ) sin ( δ k v ) t ] e Γ t / 2 } .
E ( r , t ) = e ̂ E 0   cos ( k r ) cos   ω t ,
F react = Ω 0   sin ( k r ) k { U s + A u e a t + [ B u   cos   q t + Γ C u q sin   q t ] e p t } ,
F dissip = 2 Γ Ω 1 2 θ Γ 2 + 4 Ω 1 2 { 1 e 3 Γ t / 2 [ cos   Ω t + Γ 2 + 4 Ω 1 2 4 Γ Ω sin   Ω t ] } ,
Ω = | Ω 1 2 ( Γ / 4 ) 2 | 1 / 2 .
Ω 1 ( r ) = N l u Ω 0 ( 1 + z 2 / z R 2 ) 1 / 2 ( 2 r w ( z ) ) | l | L u | l | ( 2 r 2 w ( z ) 2 ) e r 2 / w 2 ( z ) ,
θ ( r ) = k r 2 z 2 ( z 2 + z R 2 ) l ϕ ( 2 u + l + 1 ) tan 1 ( z / z R ) k z ,

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