Abstract

Strong-field laser-atom interactions provide extreme conditions that may be useful for investigating the de Broglie-Bohm quantum interpretation. Bohmian trajectories representing bound electrons in individual atoms exhibit both even and odd harmonic motion when subjected to a strong external laser field. The phases of the even harmonics depend on the random initial positions of the trajectories within the wave function, making the even harmonics incoherent. In contrast, the phases of odd harmonics remain for the most part coherent regardless of initial position. Under the conjecture that a Bohmian point particle plays the role of emitter, this suggests an experiment to determine whether both even and odd harmonics are produced at the atomic level. Estimates suggest that incoherent emission of even harmonics may be detectable out the side of an intense laser focus interacting with a large number of atoms.

© 2014 Optical Society of America

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References

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  1. X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
    [Crossref]
  2. X. Oriols, Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology (Pan Stanford Publishing, 2012).
  3. J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
    [Crossref]
  4. Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
    [Crossref]
  5. A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
    [Crossref]
  6. J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
    [Crossref]
  7. J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
    [Crossref]
  8. J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
    [Crossref]
  9. Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
    [Crossref]
  10. J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.
  11. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998), pp. 407–411.
  12. S. Backus, J. Peatross, E. Zeek, A. Rundquist, G. Taft, M. M. Murnane, and H. C. Kapteyn, “16 Femtosecond, 1μJ Ultraviolet Pulses Generated by Third-Harmonic Conversion in Air,” Opt. Lett. 21, 665–667 (1996).
    [Crossref] [PubMed]
  13. J. Peatross, S. Backus, J. Zhou, M. M. Murnane, and H. C. Kapteyn, “Spectral-Spatial Measurements of Fundamental and Third-Harmonic Light of Intense 25-fs Laser Pulses Focused in a Gas Cell,” J. Opt. Soc. Am. B 15, 186–192 (1996).
    [Crossref]
  14. D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson, Upper Saddle River NJ, 2005) pp. 5, 15.
  15. D. Bohm and B. J. Hiley, The undivided Universe, (1993) pp. 28–30.

2013 (3)

J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
[Crossref]

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
[Crossref]

2011 (1)

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

2010 (1)

X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
[Crossref]

2008 (1)

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

1996 (2)

1992 (2)

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Augstein, B. B.

J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
[Crossref]

Backus, S.

Balcou, P.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Bandarage, Gunadya

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Black, D.

J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.

Bohm, D.

D. Bohm and B. J. Hiley, The undivided Universe, (1993) pp. 28–30.

Cai, Qing-Yu

X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
[Crossref]

Candel, S.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Cooper, J.

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Corson, J. P.

J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
[Crossref]

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

Cunningham, E.

J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.

Figueira de Morisson Faria, C.

J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
[Crossref]

Griffiths, D. J.

D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson, Upper Saddle River NJ, 2005) pp. 5, 15.

Guo, Fu-Ming

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

Hatsagortsyan, K. Z.

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

Hiley, B. J.

D. Bohm and B. J. Hiley, The undivided Universe, (1993) pp. 28–30.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998), pp. 407–411.

Johansen, J.

J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.

Kapteyn, H. C.

Keitel, C. H.

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

Kulander, K. C.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

L’Huillier, A.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Lai, X. Y.

X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
[Crossref]

Li, Su-Yu

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

Liu, Xue-Shen

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

Maquet, Alfred

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Menis, Thierry

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Müller, C.

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

Murnane, M. M.

Oriols, X.

X. Oriols, Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology (Pan Stanford Publishing, 2012).

Peatross, J.

J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
[Crossref]

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

S. Backus, J. Peatross, E. Zeek, A. Rundquist, G. Taft, M. M. Murnane, and H. C. Kapteyn, “16 Femtosecond, 1μJ Ultraviolet Pulses Generated by Third-Harmonic Conversion in Air,” Opt. Lett. 21, 665–667 (1996).
[Crossref] [PubMed]

J. Peatross, S. Backus, J. Zhou, M. M. Murnane, and H. C. Kapteyn, “Spectral-Spatial Measurements of Fundamental and Third-Harmonic Light of Intense 25-fs Laser Pulses Focused in a Gas Cell,” J. Opt. Soc. Am. B 15, 186–192 (1996).
[Crossref]

J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.

Rundquist, A.

Schafer, K. J.

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

Song, Yang

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

Taft, G.

Taieb, Richard

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Tarbox, G.

J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
[Crossref]

Veniard, Valerie

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Wu, J.

J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
[Crossref]

Yang, Yu-Jun

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

Zeek, E.

Zhan, M. S.

X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
[Crossref]

Zhou, J.

Am. J. of Phys. (1)

J. Peatross, J. P. Corson, and G. Tarbox, “Classical Connection between Near-Field Interactions and Far-Field Radiation and the Relevance to Quantum Photoemission,” Am. J. of Phys. 81, 351–358 (2013).
[Crossref]

Chin. Phys. B (1)

X. Y. Lai, Qing-Yu Cai, and M. S. Zhan, “Bohmian mechanics to high-order harmonic generation,” Chin. Phys. B 19020302 (2010).
[Crossref]

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

Opt. Lett. (1)

Phys. Rev. A (5)

J. Wu, B. B. Augstein, and C. Figueira de Morisson Faria, “Local dynamics in high-order-harmonic generation using Bohmian trajectories,” Phys. Rev. A 88, 023415 (2013).
[Crossref]

Yang Song, Su-Yu Li, Xue-Shen Liu, Fu-Ming Guo, and Yu-Jun Yang, “Investigation of atomic radiative recombination processes by the Bohmian-mechanics method,” Phys. Rev. A 88, 053419 (2013).
[Crossref]

A. L’Huillier, P. Balcou, S. Candel, K. J. Schafer, and K. C. Kulander, “Calculations of high-order harmonic-generation processes in xenon at 1064 nm,” Phys. Rev. A 46, 2778–2790 (1992).
[Crossref]

J. P. Corson, J. Peatross, C. Müller, and K. Z. Hatsagortsyan, “Scattering of Intense Laser Radiation by a Single-Electron Wave Packet,” Phys. Rev. A 84, 053831 (2011).
[Crossref]

Gunadya Bandarage, Alfred Maquet, Thierry Menis, Richard Taieb, Valerie Veniard, and J. Cooper, “Harmonic generation by laser-driven classical hydrogen atoms,” Phys. Rev. A 41, 380–390 (1992).
[Crossref]

Phys. Rev. Lett. (1)

J. Peatross, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Photo-Emission of a Single-Electron Wave-Packet in a Strong Laser Field,” Phys. Rev. Lett. 100, 153601 (2008).
[Crossref]

Other (5)

D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson, Upper Saddle River NJ, 2005) pp. 5, 15.

D. Bohm and B. J. Hiley, The undivided Universe, (1993) pp. 28–30.

J. Johansen, E. Cunningham, D. Black, and J. Peatross, “Bohmian Perspective on High Harmonic Generation,” presented at Super Intense Laser-Atom Physics (SILAP), Zion National Park, Utah, 21–23 Sept.2009.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998), pp. 407–411.

X. Oriols, Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology (Pan Stanford Publishing, 2012).

Supplementary Material (1)

» Media 1: MOV (2957 KB)     

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Figures (1)

Fig. 1
Fig. 1

(a) Media 1 of possible Bohmian trajectories with equally spaced initial positions ranging from x=−5 to x=5 atomic units during atomic exposure to a Gaussian laser pulse. The wave function and potential well are also shown. (b) Close up view of a representative Bohmian trajectory with initial position x = 1. (c) Position of the Bohmian trajectory in (b) plotted as a function of time together with the conventional position expectation 〈x〉 = ∫Ψ*xΨdx. (d) Power spectrum of curves in (c), Bohmian trajectory (solid) and 〈x〉 (dotted), showing harmonic components.

Equations (7)

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

i Ψ t = 2 2 m 2 Ψ + V Ψ
d r d t = m Im { Ψ Ψ }
V ( x , t ) = e 2 4 π ε 0 x 2 + a 2 e x E 0 ( t ) cos ω t
S t = c ε 0 | n = 1 N E n ( r , t ) | 2 t = c p 0 2 sin 2 θ 2 ( 4 π 2 ) ε o k 4 r 2 [ N + n = 1 N m n N cos [ k ( r n r m ) r ^ ( φ n φ m ) ] ]
J + ρ t = 0 where J | Ψ | 2 S m and ρ | Ψ | 2
S t + ( S ) 2 2 m + V + Q = 0 where Q ħ 2 2 m 2 | Ψ | Ψ
d r d t = S ( r , t ) m

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