## Calculations of laser induced dipole-quadrupole collisional energy transfer in Sr-Ca |

Optics Express, Vol. 18, Issue 20, pp. 21062-21073 (2010)

http://dx.doi.org/10.1364/OE.18.021062

Acrobat PDF (1407 KB)

### Abstract

A three-state model for calculating the cross section of laser-induced dipole-quadrupole collisional energy transfer in Sr-Ca system is presented. The motion equations for the probability amplitudes of the three intermediate states are obtained. The expression of the cross section is derived. Various factors including field intensity, relative speed, system temperature which influence the collisional cross section are discussed to illustrate the features of the dipole-quadrupole laser-induced collisional energy transfer (LICET)process. Calculating results show that the peak of the LICET profiles moves to the red, the tuning range of the profiles obviously becomes narrower with the laser field intensity increasing and a cross section of 1.25 × 10^{−13}cm^{2} at a laser intensity of 8.29 × 10^{9}W/cm^{2} is obtained. Our results indicate that dipole-quadrupole LICET process can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

© 2010 OSA

## 1. Introduction

1. R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A **15**(3), 1333–1335 (1977). [CrossRef]

2. A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B **16**(3), 431–436 (1983). [CrossRef]

3. C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A **21**(6), 1969–1974 (1980). [CrossRef]

4. F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A **37**(7), 2441–2447 (1988). [CrossRef] [PubMed]

5. B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. **42**(2), 109–112 (1982). [CrossRef]

10. A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A **16**(6), 2413–2431 (1977). [CrossRef]

11. A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A **35**(9), 3753–3757 (1987). [CrossRef] [PubMed]

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A **45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

14. A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A **50**(6), 5081–5091 (1994). [CrossRef] [PubMed]

18. W. R. Green, M. D. Wright, J. Lukasik, J. F. Young, and S. E. Harris, “Observation of a laser-induced dipole-quadrupole collision,” Opt. Lett. **4**(9), 265–267 (1979). [CrossRef] [PubMed]

19. J. C. White, “Observation of dipole - quadrupole radiative collisional fluorescence,” Opt. Lett. **5**(6), 239–241 (1980). [CrossRef] [PubMed]

18. W. R. Green, M. D. Wright, J. Lukasik, J. F. Young, and S. E. Harris, “Observation of a laser-induced dipole-quadrupole collision,” Opt. Lett. **4**(9), 265–267 (1979). [CrossRef] [PubMed]

7. M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A **36**(3), 1471–1473 (1987). [CrossRef] [PubMed]

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. **13**(12), 972–978 (1977). [CrossRef]

14. A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A **50**(6), 5081–5091 (1994). [CrossRef] [PubMed]

*m*= 0 substates. In this paper, the three-level dipole-quadrupole LICET model considering the relative velocity distribution function and including all the degenerate

*m*states which may give more accurate details of the line shape is presented. Laser induced dipole-quadrupole collision process in Sr-Ca system is numerically calculated through immediate integration. Various factors including field intensity, relative speed, temperature which influence the collisional cross section are discussed to illustrate the features of the dipole-quadrupole LICET process. And our results indicate that dipole-quadrupole LICET process can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

## 2. Theory

*v*along the z axis. The unprimed system is fixed in space, while in the primed system, the z’ axis points the interatomic axis, and therefore rotates with respect to the unprimed system during the collision, i.e., where cos

*θ*=

*b*/

*R*(

*t*),and

*θ*varies form -π/2 to π/2。

*R*(

*t*) = (

*b*

^{2}+

*v*

^{2}

*t*

^{2})

^{1/2}, where

*b*is an impact parameter and

*v*is the relative velocity. Assuming the

**E**(t) =

*E*

_{0}

**a**

_{y}cos(

*ωt*) is the laser field with frequency

*ω*, then the interaction Hamiltonian can be written The interaction

*V*can be represented by the multipole expansion [20] where Here is the lesser of

_{AB}*l*and

*j*-1-

*l*,

*F*(

*j*,

*l*,

*m*) is given by [20,21]

*C*(

*j*-

*l*-1,

*l*,

*j*-1;

*m*, -

*m*, 0) is Clebsch-Gordan coefficient.

11. A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A **35**(9), 3753–3757 (1987). [CrossRef] [PubMed]

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A **45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

23. A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A **42**(11), 6629–6640 (1990). [CrossRef] [PubMed]

*m*= 0 substates. In the present work we consider three basis states, and include all possible

*m*states. The transition probability is found by summing over the final level populations and averaging over the initial state populations. And then, by considering the probability density function of relative velocity between two colliding atoms in three-dimensional space under thermal equilibrium condition, the laser-induced collision cross section at given temperature can be obtained by

*M*is the reduced mass of the two colliding atoms,

*T*is the thermodynamic temperature and

*k*is the Boltzmann constant.

## 3. Application to Sr-Ca system

*ω*

_{21}= −151.152 cm

^{−1}.

^{−1}) and the impact parameter

*b*is equal to 0.9nm and 1.15nm respectively, through an immediate integration on formula (7), the collisional transition probability |

*a*

_{3}(

*t*)|

^{2}versus time

*t*in this Sr-Ca system is calculated as Fig. 4 shown. The results show that |

*a*

_{3}(

*t*)|

^{2}oscillates over time, the smaller the b is, the stronger the |

*a*

_{3}(

*t*)|

^{2}oscillates. When|

*t*|≥20ps, |

*a*

_{3}(

*t*)|

^{2}approach to a definite value, which indicate that the laser induced collision process occurs for~40ps.

^{2}and the relative speed between the two colliding atoms is 600m/s, the collisional transition probability |

*a*

_{3}( + ∞)|

^{2}versus the impact parameter b can be obtained through numerical integrations with different laser detuning Δ and the profiles obtained are shown in Fig. 5 . It appears that |

*a*

_{3}( + ∞)|

^{2}oscillates over b. To the quasimolecule system formed in the collisional process, there is an effective curve crossing at some

*R*, i.e., at some

_{x}*R*the argument of the exponent in equation of motion for the probability amplitudes equals zero at

_{x}*t*such that

*R*(

*t*) =

*R*

_{x}. As the Landau-Zener theory of the curve crossing section, the transition probability is only large for b≤

*R*. At a given impact parameter

_{x}*a*

_{3}(

*t*) accumulates during each of the two times that the crossing distance is neared. And the oscillation of |

*a*

_{3}( + ∞)|

^{2}results from the adding and subtracting of the phased contributions at each of the two crossing [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. **13**(12), 972–978 (1977). [CrossRef]

*ω*>

*ω*

_{0}there is a such

*R*where ω can equal E

_{3}(

*R*)-E

_{2}(

*R*), while in the wing of

*ω*<

*ω*

_{0}there is no such value of

*R*which leads to the sharply reduce of the transition probability in anti-static wing. Furthermore, it is shown in Fig. 6 that as far as this Sr-Ca system is concerned, the peak of the cross section profiles is not found when the transfer laser is strictly resonant (i.e. Δ = 0cm

^{−1}), but it is found when the transfer laser detunes a little from Δ = 0cm

^{−1}in the quasi-static wing (in this paper, peak of the profiles is found when Δ = 1.5cm

^{−1}).

*ω*approaches to

*ω*

_{31}which is <

*ω*

_{32}, resulting in the bathochromic shift [13

13. S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A **45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

^{−9}I(W/cm

^{2})cm

^{−1}.

23. A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A **42**(11), 6629–6640 (1990). [CrossRef] [PubMed]

**45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

^{−13}cm

^{2}at a laser intensity of 8.29 × 10

^{9}W/cm

^{2}is obtained which indicate that the laser induced dipole-quadrupole and dipole-dipole collision have comparable magnitude. So the dipole-quadrupole process also can be the effective way to transfer energy selectively from a storage state of arbitrary parity to a target state of arbitrary parity.

*σ*(Δ) versus laser detuning Δ through numerical integrations are shown in Fig. 11 . It can be seen that the variation in the LICET profile to laser detuning has a certain tunable range. Full width at half peak of the profile and cross section at fixed laser detuning become smaller as the relative speed increases. Moreover, the quasi-static wings approximately have the same trend at different relative speed, while the anti-static wings become steeper as the speed increases. A understanding of this is that based on the [9

9. S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. **13**(12), 972–978 (1977). [CrossRef]

**45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

^{8}W/cm

^{2}. It can be seen that velocity-distribution considered collision cross section larger than fixed-velocity cross section in the spectrum center and the quasi-static wing, while in anti-static wing the fixed-velocity spectrum is steeper, indicating that it is necessary to consider this distribution in the calculations.

## 4. Conclusion

*m*states. The transition probability is found by summing over the final level populations and averaging over the initial state populations. In view of the probability density function of relative velocity between two colliding atoms in three-dimensional space under thermal equilibrium condition, the laser-induced collision cross section at given temperature is obtained, and spectral profiles of LICET are calculated through immediate integrations. It appears that the dipole-quadrupole and dipole-dipole LICET spectrum profiles [9

**13**(12), 972–978 (1977). [CrossRef]

**45**(7), 4792–4798 (1992). [CrossRef] [PubMed]

**13**(12), 972–978 (1977). [CrossRef]

## References and links

1. | R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A |

2. | A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B |

3. | C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A |

4. | F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A |

5. | B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. |

6. | D. Z. Zhang, B. Nikolaus, and P. E. Toschek, Appl. Phys. B |

7. | M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A |

8. | S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A |

9. | S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. |

10. | A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A |

11. | A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A |

12. | A. Agresti, P. R. Berman, A. Bambini, and A. Stefanel, “Analysis of the far-wing behavior in the spectrum of the light-induced collisional-energy-transfer process,” Phys. Rev. A |

13. | S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A |

14. | A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A |

15. | C. Deying, W. Qi, and M. Zuguang, “Four-level model of laser-induced collisional energy transfer,” Acta Opt. Sin. |

16. | C. Deying, W. Qi, and M. Zuguang, “Numerical calculation of laser-induced collisional energy transfer in Eu-Sr,” Sci. China Ser. A |

17. | Z. Hongying, C. Deying, L. Zhenzhong, F. Rongwei, and X. Yuanqin, “Numerical calculation of laser-induced collisional energy transfer in Ba-Sr system,” Acta Phys. Sin. |

18. | W. R. Green, M. D. Wright, J. Lukasik, J. F. Young, and S. E. Harris, “Observation of a laser-induced dipole-quadrupole collision,” Opt. Lett. |

19. | J. C. White, “Observation of dipole - quadrupole radiative collisional fluorescence,” Opt. Lett. |

20. | J. O. Hirschfelder and W. J. Meath, “The nature of intermolecular forces,” Adv. Chem. Phys. |

21. | M. E. Rose, “The Electrostatic Interaction of Two Arbitrary Charge Distributions,” J. Math. Phys. |

22. | Z. H. C. Deying, L. Zhenzhong, X. Yuanqin, and F. Rongwei, “Impacts of Relative velocity distribution between two colliding atoms on laser-induced collisional energy transfer,” Chin. J. Lasers |

23. | A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A |

**OCIS Codes**

(020.3690) Atomic and molecular physics : Line shapes and shifts

(190.0190) Nonlinear optics : Nonlinear optics

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: June 25, 2010

Revised Manuscript: September 8, 2010

Manuscript Accepted: September 8, 2010

Published: September 21, 2010

**Citation**

Zhenzhong Lu, Deying Chen, Yuanqin Xia, Rongwei Fan, and Hongying Zhang, "Calculations of laser induced dipole-quadrupole collisional energy transfer in Sr-Ca," Opt. Express **18**, 21062-21073 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21062

Sort: Year | Journal | Reset

### References

- R. W. Falcone, R. W. Green, J. White, J. Young, and S. Harris, “Observation of laser-induced inelastic collisions,” Phys. Rev. A 15(3), 1333–1335 (1977). [CrossRef]
- A. Debarre, “High-resolution study of light-induced collisional energy transfer in Na-Ca mixture,” J. Phys. B 16(3), 431–436 (1983). [CrossRef]
- C. Brechnignac, Ph. Cahuzac, and P. E. Toschek, “High-resolution studies on laser-induced collisional-energy-transfer profiles,” Phys. Rev. A 21(6), 1969–1974 (1980). [CrossRef]
- F. Dorsch, S. Geltman, and P. E. Toschek, “Laser-induced collisional-energy transfer in thermal collisions of lithium and strontium,” Phys. Rev. A 37(7), 2441–2447 (1988). [CrossRef] [PubMed]
- B. Cheron and H. Lemery, “Observation of laser induced collisional energy transfer in a rubidium-potassium mixture,” Opt. Commun. 42(2), 109–112 (1982). [CrossRef]
- D. Z. Zhang, B. Nikolaus, and P. E. Toschek, Appl. Phys. B 28, 195 (1981).
- M. Matera, M. Mazzoni, R. Buffa, S. Cavalieri, and E. Arimondo, “Far-wing study of laser-induced collisional energy transfer,” Phys. Rev. A 36(3), 1471–1473 (1987). [CrossRef] [PubMed]
- S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]
- S. E. Harris and J. White, “Numerical analysis of laser induced inelastic collisions,” IEEE J. Quantum Electron. 13(12), 972–978 (1977). [CrossRef]
- A. Gallagher and T. Holstein, “Collision-induced absorption in atomic electronic transitions,” Phys. Rev. A 16(6), 2413–2431 (1977). [CrossRef]
- A. Bambini and P. R. Berman, “Quasistatic wing behavior of collisional-radiative line profiles,” Phys. Rev. A 35(9), 3753–3757 (1987). [CrossRef] [PubMed]
- A. Agresti, P. R. Berman, A. Bambini, and A. Stefanel, “Analysis of the far-wing behavior in the spectrum of the light-induced collisional-energy-transfer process,” Phys. Rev. A 38(5), 2259–2273 (1988). [CrossRef] [PubMed]
- S. Geltman, “Calculations on laser-induced collisional energy transfer,” Phys. Rev. A 45(7), 4792–4798 (1992). [CrossRef] [PubMed]
- A. Bambini and S. Geltman, “Theory of strong-field light-induced collisional energy transfer in Eu and Sr,” Phys. Rev. A 50(6), 5081–5091 (1994). [CrossRef] [PubMed]
- C. Deying, W. Qi, and M. Zuguang, “Four-level model of laser-induced collisional energy transfer,” Acta Opt. Sin. 16, 1653–1655 (1996).
- C. Deying, W. Qi, and M. Zuguang, “Numerical calculation of laser-induced collisional energy transfer in Eu-Sr,” Sci. China Ser. A 27, 449 (1997).
- Z. Hongying, C. Deying, L. Zhenzhong, F. Rongwei, and X. Yuanqin, “Numerical calculation of laser-induced collisional energy transfer in Ba-Sr system,” Acta Phys. Sin. 57, 7600–7605 (2008).
- W. R. Green, M. D. Wright, J. Lukasik, J. F. Young, and S. E. Harris, “Observation of a laser-induced dipole-quadrupole collision,” Opt. Lett. 4(9), 265–267 (1979). [CrossRef] [PubMed]
- J. C. White, “Observation of dipole - quadrupole radiative collisional fluorescence,” Opt. Lett. 5(6), 239–241 (1980). [CrossRef] [PubMed]
- J. O. Hirschfelder and W. J. Meath, “The nature of intermolecular forces,” Adv. Chem. Phys. 12, 1 (1967).
- M. E. Rose, “The Electrostatic Interaction of Two Arbitrary Charge Distributions,” J. Math. Phys. 37, 215–222 (1958).
- Z. H. C. Deying, L. Zhenzhong, X. Yuanqin, and F. Rongwei, “Impacts of Relative velocity distribution between two colliding atoms on laser-induced collisional energy transfer,” Chin. J. Lasers 35, 0077–0080 (2008).
- A. Bambini, M. Matera, A. Agresti, and M. Bianconi, “Strong-field effects on light-induced collisional energy transfer,” Phys. Rev. A 42(11), 6629–6640 (1990). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1 |
Fig. 2 |
Fig. 3 |

Fig. 4 |
Fig. 5 |
Fig. 6 |

Fig. 8 |
Fig. 7 |
Fig. 9 |

Fig. 10 |
Fig. 11 |
Fig. 12 |

Fig. 13 |
||

« Previous Article | Next Article »

OSA is a member of CrossRef.