Abstract

Intense laser ionization expands Einsteins photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of an intense ultraviolet beam bearing OAM, envisaging new scenarios for quantum optics.

© 2010 Optical Society of America

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  1. L. Allen, M. V. 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 (1992).
    [CrossRef] [PubMed]
  2. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  3. M. Bhattacharya and P. Meystre, "Using a Laguerre-Gaussian Beam to Trap and Cool the Rotational Motion of a Mirror," Phys. Rev. Lett. 99, 153603 (2007).
    [CrossRef] [PubMed]
  4. S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
    [CrossRef]
  5. M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
    [CrossRef] [PubMed]
  6. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
    [CrossRef] [PubMed]
  7. R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
    [CrossRef]
  8. G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
    [CrossRef]
  9. M. van Veenendaal and I. McNulty, "Prediction of Strong Dichroism Induced by X Rays Carrying Orbital Momentum," Phys. Rev. Lett. 98, 157401 (2007).
    [CrossRef] [PubMed]
  10. I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, "Creation of optical vortices in femtosecond pulses," Opt. Express 13, 7599 (2005).
    [CrossRef] [PubMed]
  11. I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
    [CrossRef]
  12. A. Einstein, "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light," Ann. Phys. 17, 132 (1905).
    [CrossRef]
  13. P. B. Corkum and F. Krausz, "Attosecond science," Nature Phys. 3, 381 (2007).
    [CrossRef]
  14. C. I. Blaga et al., "Strong-field photoionization revisited," Nature Phys. 5, 335 (2009).
    [CrossRef]
  15. G. A. Mourou, "Optics in the relativistic regime," Rev. Mod. Phys. 78, 309 (2006).
    [CrossRef]
  16. J. R. Vázquez de Aldana and L. Roso, "Magnetic field effects in strong field ionization of single-electron atoms: Three-dimensional numerical simulations," Laser Part. Beams 20185-193 (2002).
  17. S. M. Barnett, "Optical Angular-Momentum Flux," J. Opt. B: Quantum Semiclass. Opt. 4S7 (2002).
    [CrossRef]
  18. S. J. Van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum Opt. 6, 445 (1994).
    [CrossRef]
  19. R. Jáuregui, "Rotational effects of twisted light on atoms beyond the paraxial approximation," Phys. Rev. A 70, 033415 (2004).
    [CrossRef]
  20. A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
    [CrossRef] [PubMed]
  21. G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
    [CrossRef] [PubMed]
  22. Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
    [CrossRef] [PubMed]
  23. T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  24. S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
    [CrossRef] [PubMed]
  25. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
    [CrossRef]
  26. K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
    [CrossRef] [PubMed]
  27. T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
    [CrossRef] [PubMed]
  28. E. Peik and Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in Th-229," Europhys. Lett. 61, 181 (2003).
    [CrossRef]

2009

C. I. Blaga et al., "Strong-field photoionization revisited," Nature Phys. 5, 335 (2009).
[CrossRef]

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

2008

G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
[CrossRef] [PubMed]

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

2007

M. Bhattacharya and P. Meystre, "Using a Laguerre-Gaussian Beam to Trap and Cool the Rotational Motion of a Mirror," Phys. Rev. Lett. 99, 153603 (2007).
[CrossRef] [PubMed]

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

M. van Veenendaal and I. McNulty, "Prediction of Strong Dichroism Induced by X Rays Carrying Orbital Momentum," Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef] [PubMed]

P. B. Corkum and F. Krausz, "Attosecond science," Nature Phys. 3, 381 (2007).
[CrossRef]

2006

G. A. Mourou, "Optics in the relativistic regime," Rev. Mod. Phys. 78, 309 (2006).
[CrossRef]

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
[CrossRef] [PubMed]

T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
[CrossRef] [PubMed]

2005

2004

R. Jáuregui, "Rotational effects of twisted light on atoms beyond the paraxial approximation," Phys. Rev. A 70, 033415 (2004).
[CrossRef]

2003

E. Peik and Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in Th-229," Europhys. Lett. 61, 181 (2003).
[CrossRef]

K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
[CrossRef] [PubMed]

2002

J. R. Vázquez de Aldana and L. Roso, "Magnetic field effects in strong field ionization of single-electron atoms: Three-dimensional numerical simulations," Laser Part. Beams 20185-193 (2002).

S. M. Barnett, "Optical Angular-Momentum Flux," J. Opt. B: Quantum Semiclass. Opt. 4S7 (2002).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

2001

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

2000

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

1997

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
[CrossRef]

1994

S. J. Van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum Opt. 6, 445 (1994).
[CrossRef]

1992

L. Allen, M. V. 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 (1992).
[CrossRef] [PubMed]

1905

A. Einstein, "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light," Ann. Phys. 17, 132 (1905).
[CrossRef]

Alexandrescu, A.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
[CrossRef]

L. Allen, M. V. 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 (1992).
[CrossRef] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Arias, I.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Atencia, J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Barnett, S. M.

S. M. Barnett, "Optical Angular-Momentum Flux," J. Opt. B: Quantum Semiclass. Opt. 4S7 (2002).
[CrossRef]

Barwick, Brett

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

Batelaan, Herman

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

Beijersbergen, M. V.

L. Allen, M. V. 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 (1992).
[CrossRef] [PubMed]

Bhattacharya, M.

M. Bhattacharya and P. Meystre, "Using a Laguerre-Gaussian Beam to Trap and Cool the Rotational Motion of a Mirror," Phys. Rev. Lett. 99, 153603 (2007).
[CrossRef] [PubMed]

Blaga, C. I.

C. I. Blaga et al., "Strong-field photoionization revisited," Nature Phys. 5, 335 (2009).
[CrossRef]

Brabec, T.

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Bramon, A.

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

Bürvenich, T. J.

T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
[CrossRef] [PubMed]

Calvo, G. F.

G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
[CrossRef] [PubMed]

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Cojoc, D.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Collados, V.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Corkum, P. B.

P. B. Corkum and F. Krausz, "Attosecond science," Nature Phys. 3, 381 (2007).
[CrossRef]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Di Fabrizio, E.

A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
[CrossRef] [PubMed]

Einstein, A.

A. Einstein, "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light," Ann. Phys. 17, 132 (1905).
[CrossRef]

Evers, J.

T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
[CrossRef] [PubMed]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Hilbert, Shawn A.

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

Inoue, R.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Jáuregui, R.

R. Jáuregui, "Rotational effects of twisted light on atoms beyond the paraxial approximation," Phys. Rev. A 70, 033415 (2004).
[CrossRef]

Kanai, N.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Keitel, C. H.

T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
[CrossRef] [PubMed]

Koashi, M.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Kozuma, M.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Krausz, F.

P. B. Corkum and F. Krausz, "Attosecond science," Nature Phys. 3, 381 (2007).
[CrossRef]

T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Ledingham, K.W. D.

K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
[CrossRef] [PubMed]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

Mariyenko, I. G.

McKenna, P.

K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
[CrossRef] [PubMed]

McNulty, I.

M. van Veenendaal and I. McNulty, "Prediction of Strong Dichroism Induced by X Rays Carrying Orbital Momentum," Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef] [PubMed]

Méndez, C.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Meystre, P.

M. Bhattacharya and P. Meystre, "Using a Laguerre-Gaussian Beam to Trap and Cool the Rotational Motion of a Mirror," Phys. Rev. Lett. 99, 153603 (2007).
[CrossRef] [PubMed]

Miyamoto, Y.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Mourou, G. A.

G. A. Mourou, "Optics in the relativistic regime," Rev. Mod. Phys. 78, 309 (2006).
[CrossRef]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, "Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes," Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Patchkovskii, S.

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
[CrossRef] [PubMed]

Peik, E.

E. Peik and Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in Th-229," Europhys. Lett. 61, 181 (2003).
[CrossRef]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Picón, A.

G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
[CrossRef] [PubMed]

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

Plaja, L.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Quintanilla, M.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Roso, L.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

J. R. Vázquez de Aldana and L. Roso, "Magnetic field effects in strong field ionization of single-electron atoms: Three-dimensional numerical simulations," Laser Part. Beams 20185-193 (2002).

Ruiz, C.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

San Román, J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Singhal, R. P.

K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
[CrossRef] [PubMed]

Sola, I. J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. V. 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 (1992).
[CrossRef] [PubMed]

Strohaber, J.

Tamm, Chr.

E. Peik and Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in Th-229," Europhys. Lett. 61, 181 (2003).
[CrossRef]

Uiterwaal, C. J. G. J.

Uiterwaala, Cornelis

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

Van Enk, S. J.

S. J. Van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum Opt. 6, 445 (1994).
[CrossRef]

van Veenendaal, M.

M. van Veenendaal and I. McNulty, "Prediction of Strong Dichroism Induced by X Rays Carrying Orbital Momentum," Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef] [PubMed]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

Vázquez de Aldana, J. R.

J. R. Vázquez de Aldana and L. Roso, "Magnetic field effects in strong field ionization of single-electron atoms: Three-dimensional numerical simulations," Laser Part. Beams 20185-193 (2002).

Villamarín, A.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Villeneuve, D. M.

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
[CrossRef] [PubMed]

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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

L. Allen, M. V. 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 (1992).
[CrossRef] [PubMed]

Yonehara, T.

R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

Zambrini, R.

G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

Zewail, Ahmed H.

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

Zhao, Z.

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
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Ann. Phys.

A. Einstein, "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light," Ann. Phys. 17, 132 (1905).
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Appl. Phys. B

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla and L. Roso, "High power vortex generation with volume phase holograms and non-linear experiments in gases," Appl. Phys. B 91, 115-118 (2008).
[CrossRef]

Europhys. Lett.

E. Peik and Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in Th-229," Europhys. Lett. 61, 181 (2003).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

S. M. Barnett, "Optical Angular-Momentum Flux," J. Opt. B: Quantum Semiclass. Opt. 4S7 (2002).
[CrossRef]

Laser Part. Beams

J. R. Vázquez de Aldana and L. Roso, "Magnetic field effects in strong field ionization of single-electron atoms: Three-dimensional numerical simulations," Laser Part. Beams 20185-193 (2002).

Laser Photon. Rev.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Nature

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313 (2001).
[CrossRef] [PubMed]

Nature Phys.

P. B. Corkum and F. Krausz, "Attosecond science," Nature Phys. 3, 381 (2007).
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C. I. Blaga et al., "Strong-field photoionization revisited," Nature Phys. 5, 335 (2009).
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Opt. Express

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R. Inoue, N. Kanai, T. Yonehara, Y. Miyamoto, M. Koashi, and M. Kozuma, "Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon," Phys. Rev. A 74, 053809 (2006).
[CrossRef]

G. F. Calvo, A. Picón, and A. Bramon, "Measuring two-photon orbital angular momentum entanglement," Phys. Rev. A 75, 012319 (2007).
[CrossRef]

L. Allen, M. V. 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 (1992).
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A. Alexandrescu, D. Cojoc, and E. Di Fabrizio, "Mechanism of Angular Momentum Exchange between Molecules and Laguerre-Gaussian Beams," Phys. Rev. Lett. 96, 243001 (2006).
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G. F. Calvo, A. Picón, and R. Zambrini, "Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field," Phys. Rev. Lett. 100, 173902 (2008).
[CrossRef] [PubMed]

S. Patchkovskii, Z. Zhao, T. Brabec, and D. M. Villeneuve, "High Harmonic Generation and Molecular Orbital Tomography in Multielectron Systems: Beyond the Single Active Electron Approximation," Phys. Rev. Lett. 97, 123003 (2006).
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T. J. Bürvenich, J. Evers, and C. H. Keitel, "Nuclear Quantum Optics with X-Ray Laser Pulses," Phys. Rev. Lett. 96, 142501 (2006).
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A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
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M. Bhattacharya and P. Meystre, "Using a Laguerre-Gaussian Beam to Trap and Cool the Rotational Motion of a Mirror," Phys. Rev. Lett. 99, 153603 (2007).
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M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, "Quantized Rotation of Atoms from Photons with Orbital Angular Momentum," Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

M. van Veenendaal and I. McNulty, "Prediction of Strong Dichroism Induced by X Rays Carrying Orbital Momentum," Phys. Rev. Lett. 98, 157401 (2007).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci.

Shawn A. Hilbert, Cornelis Uiterwaala, Brett Barwick, Herman Batelaan and Ahmed H. Zewail, "Temporal lenses for attosecond and femtosecond electron pulses," Proc. Natl. Acad. Sci. 106, 10558 (2009).
[CrossRef] [PubMed]

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S. J. Van Enk, "Selection rules and centre-of-mass motion of ultracold atoms," Quantum Opt. 6, 445 (1994).
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G. A. Mourou, "Optics in the relativistic regime," Rev. Mod. Phys. 78, 309 (2006).
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Science

K.W. D. Ledingham, P. McKenna, and R. P. Singhal, "Applications for Nuclear Phenomena Generated by Ultra-Intense Lasers," Science 300, 1107 (2003).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Light-Matter Interaction Scheme. The addressed problem consists of: A temporal pulse with a well-defined polarization and a transverse profile that takes into account the OAM. The initial state of the electron corresponds to the fundamental state of the hydrogen atom.

Fig. 2.
Fig. 2.

Carrier Envelope Phase for a Laguerre-Gaussian Beam. In the main figure, the polarization of the pulse beam is represented for a transverse plane at z = 0, just when the pulse is maximum. The atom is centered at the origin (coincident with the beam vortex), where the electric field is zero. The arrow size is proportional to the electric field amplitude strength, which increases linearly in the radial direction up to amplitudes of about 5 au in the boundary distance, 20 au (1nm), and it is harmonically modulated by the azimuthal position. The blue line is the nodal line of the electric field, and rotates with the carrier wave frequency ω, setting the electric field distribution during the pulse interaction. The temporal dependence of the pulse beam is also shown at four different positions of the transverse plane. Notice that the carrier envelope phase (CEP) differs from the azimuthal dependence, not the radial.

Fig. 3.
Fig. 3.

Initial Ionization of the Electron Quantum State. (a) In the upper row, projection of the excited state onto the plane xy (∫ dz|δψ(x,y,z)|2) at four different times when the pulse beam is linearly polarized. The electron is beginning to be ionized in the first cycle of the pulse beam (with a period of τ=152 as). In the middle row, the superposition of spherical harmonics with widths given by the numerical simulation is represented; they show perfect agreement with the selection rules (6,7). (b) Same as upper row in (a) but for a left-circularly polarized pulse beam.

Fig. 4.
Fig. 4.

Final Quantum Electron State and their Spherical Harmonic Spectrum. Projection of the excited state (∫ dz|δψ(x,y,z)|2) onto the plane xy after the interaction with the pulse beam for: (a) a Gaussian mode, (b) a Laguerre-Gaussian mode linearly polarized and (c) a Laguerre-Gaussian mode circularly polarized. (d) Spectrum of spherical harmonics for the three different cases (a), (b) and (c).

Fig. 5.
Fig. 5.

Temporal Evolution of the Electron Angular Momentum. Solid red curve represents the OAM of the electron in the z-direction during interaction, parameters as in Fig. 3(a). Notice that the electron begins with null OAM and after the pulse beam it gains up to 1.53 au (1.53h̄). Dash gray curve represents the population of the ground state. As time increases, it is ionized up to 0.52 of the initial population.

Equations (28)

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

A r t = A o w 0 sin 2 ( ω e c ( z + a o ) ω e t ) [ e i ω c ( z ct ) L G , p ρ ϕ z ; ω c + c . c . ]
× [ θ ( z c t + π c / ω e + a o ) θ ( z c t + a o ) ] ,
L G , p ρ ϕ z ; k 0 = 2 p ! π ( + p ) ! 1 w ( z ) L p ( 2 ρ 2 w 2 ( z ) ) ×
( 2 ρ w ( z ) ) exp ( ρ 2 w 2 ( z ) ) exp [ i ϕ + i k 0 ρ 2 2 R ( z ) + i Φ G ( z ) ] ,
L p ( ξ ) = m = 0 p ( 1 ) m ( + p ) ! ( p m ) ! ( + m ) ! m ! ξ m .
i h ̄ t ψ r t = 퓗̂ r p t ψ r t = [ 1 2 m ( p ̂ q A ̂ ( r , t ) ) 2 + q V ̂ ( r ) ] ψ r t ,
ψ f ψ i = i q h ̄ ( E i E f ) ψ f r A ̂ r t ψ i .
Δ L + 1 , Δ M = ± 1 , with ΔL + + 1 even ,
Δ L 2 , Δ M = 2 , with Δ L even .
Ψ f 퓗̂ Ψ i A o 0 dr r 3 ( 2 r w 0 ) u L f , M f * ( r ) u L i , M i ( r ) ×
{ d Ω Y L f * M f [ α ( sin θ ) + 1 cos ϕ e i ( ω t ϕ χ ) + c . c . ] Y L i M i +
d Ω Y L f * M f [ β ( sin θ ) + 1 sin ϕ e i ( ω t ϕ χ ) + c . c . ] Y L i M i } .
( sin θ ) + 1 cos ϕ e i ( ω t ϕ χ ) = e i ( ω t χ ) 2 { ( sin θ ) + 1 e i ( + 1 ) ϕ + ( sin θ ) + 1 e i ( 1 ) ϕ } ,
( sin θ ) + 1 sin ϕ e i ( ω t ϕ χ ) = e i ( ω t χ ) 2 i { ( sin θ ) + 1 e i ( + 1 ) ϕ ( sin θ ) + 1 e i ( 1 ) ϕ } .
( sin θ ) + 1 e i ( + 1 ) ϕ = ( 1 ) 2 ( + 1 ) ( + 1 ) ! 4 π ( 2ℓ + 3 ) ! Y + 1 + 1 ,
( sin θ ) + 1 e i ( 1 ) ϕ = ( 1 ) 2 ( 1 ) ( 1 ) ! 4 π ( 2ℓ 1 ) ! 4 5 3 Y 1 1 ( Y 0 0 1 5 Y 2 0 ) ,
Y l 1 m 1 Y l 2 m 2 = l = l 1 l 2 l 1 + l 2 m = l m = l ( 2 l 1 + 1 ) ( 2 l 2 + 1 ) 4 π ( 2 l + 1 ) l 1 , l 2 ; 0,0 l , 0 l 1 , l 2 ; m 1 , m 2 l , m Y l m ,
a = ( 2ℓ 1 ) 5 4 π ( 2ℓ + 3 ) 1,2 ; 0,0 + 1,0 1,2 ; 1,0 + 1 , 1 ,
c = ( 2ℓ 1 ) 5 4 π ( 2ℓ 1 ) 1,2 ; 0,0 1,0 1,2 ; 1,0 1 , 1 .
( sin θ ) + 1 e i ( + 1 ) ϕ = 2 ( 1 ) ( 1 ) ! 4 π ( 2 1 ) ! 4 5 3 Y 1 + 1 ( Y 0 0 1 5 Y 2 0 ) ,
( sin θ ) + 1 e i ( 1 ) ϕ = 2 ( + 1 ) ( + 1 ) ! 4 π ( 2 + 3 ) ! Y + 1 1 ,
a ́ = ( 2 1 ) 5 4 π ( 2 + 3 ) 1,2 ; 0,0 + 1,0 1,2 ; + 1,0 + 1 , + 1 ,
c ́ = ( 2 1 ) 5 4 π ( 2 1 ) 1,2 ; 0,0 1,0 1,2 ; + 1,0 1 , + 1 ,
Ψ f 퓗̂ 퓘퓘 Ψ i = q 2 2 m Ψ f A 2 r t Ψ i ,
Ψ f 퓗̂ 퓘퓘 Ψ i ( 2 w 0 2 ) Ψ f [ A o ρ l e i ( ω t ϕ χ ) + c . c . ] 2 Ψ i .
[ A o ρ l e i ( ω t ϕ χ ) + c . c . ] 2 = A o 2 r 2 l [ ( α 2 + β 2 ) ( sin θ ) 2 e i 2 ( ω t ϕ χ ) + c . c . ]
+ ( A o ρ l ) 2 ,
( sin θ ) 2 e i 2 ϕ = 2 2ℓ ( 2ℓ ) ! 4 π ( 4ℓ + 1 ) ! Y 2ℓ 2ℓ .

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