Abstract

We show that atoms interacting with evanescent light fields, generated at the interface of a dielectric with vacuum, experience artificial gauge potentials. Both the magnitude and the spatial distribution of these potentials depend crucially on the physical parameters that characterize the evanescent fields most notably the refractive index of the dielectric material and the angle of incidence of the laser beam totally internally reflected at the interface. Gauge fields are derived for various evanescent light fields and for both two-level and three-level systems. The use of such artificial gauge potentials for the manipulation of atoms trapped at the interfaces is pointed out and discussed.

© 2014 Optical Society of America

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References

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  1. C. Cohen-Tannoudji and D. Guéry-Odelin, Advances in Atomic Physics: An Overview (World Scientific, 2011).
  2. R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
    [CrossRef]
  3. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).
  4. R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
    [CrossRef]
  5. I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
    [CrossRef]
  6. I. Bloch, “Exploring quantum matter with ultracold atoms in optical lattices,” J. Phys. B 38, S629–S643 (2005).
    [CrossRef]
  7. I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
    [CrossRef]
  8. S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford, 2006).
  9. J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
    [CrossRef]
  10. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Royal Soc. A 392, 45–57 (1984).
    [CrossRef]
  11. R. Dum and M. Olshanii, “Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
    [CrossRef]
  12. P. M. Visser and G. Nienhuis, “Geometric potentials for subrecoil dynamics,” Phys. Rev. A 57, 4581–4591 (1998).
    [CrossRef]
  13. C. Cohen-Tannoudji, Atoms in Electromagnetic Fields (World Scientific, 1994).
  14. C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
    [CrossRef]
  15. V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
    [CrossRef]
  16. L. Allen, M. J. Padgett, and M. Babiker, The Orbital Angular Momentum of Light, E. Wolf, ed., Vol. 39 of Progress in Optics (Elsevier Science, 1999).
  17. R. M. A. Azzam, “Circular and near-circular polarization states of evanescent monochromatic light fields in total internal reflection,” Appl. Opt. 50, 6272–6276 (2011).
    [CrossRef]
  18. G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
    [CrossRef]
  19. G. Juzeliūnas and P. Öhberg, “Creation of an effective magnetic field in ultracold atomic gases using electromagnetically induced transparency,” Opt. Spectrosc. 99, 357–361 (2005).
    [CrossRef]
  20. G. Juzeliūnas and P. Öhberg, Optical Manipulation of Ultracold Atoms, in Structured Light and Its Applications, D. L. Andrews, ed. (Academic, 2008).
  21. T. Graß, “Ultracold atoms in artificial gauge fields,” Ph.D. thesis (Institut de Ciències Fotòniques and Universitat Politècnica de Catalunya, 2012).
  22. D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56 (2003).
    [CrossRef]
  23. E. J. Mueller, “Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids,” Phys. Rev. A 70, 041603 (2004).
    [CrossRef]
  24. A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
    [CrossRef]
  25. V. E. Lembessis and M. Babiker, “Enhanced quadrupole effects for atoms in optical vortices,” Phys. Rev. Lett. 110, 083002 (2013).
    [CrossRef]

2013 (1)

V. E. Lembessis and M. Babiker, “Enhanced quadrupole effects for atoms in optical vortices,” Phys. Rev. Lett. 110, 083002 (2013).
[CrossRef]

2012 (2)

R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
[CrossRef]

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[CrossRef]

2011 (2)

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

R. M. A. Azzam, “Circular and near-circular polarization states of evanescent monochromatic light fields in total internal reflection,” Appl. Opt. 50, 6272–6276 (2011).
[CrossRef]

2009 (1)

V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
[CrossRef]

2006 (1)

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

2005 (4)

G. Juzeliūnas and P. Öhberg, “Creation of an effective magnetic field in ultracold atomic gases using electromagnetically induced transparency,” Opt. Spectrosc. 99, 357–361 (2005).
[CrossRef]

A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
[CrossRef]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[CrossRef]

I. Bloch, “Exploring quantum matter with ultracold atoms in optical lattices,” J. Phys. B 38, S629–S643 (2005).
[CrossRef]

2004 (1)

E. J. Mueller, “Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids,” Phys. Rev. A 70, 041603 (2004).
[CrossRef]

2003 (1)

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56 (2003).
[CrossRef]

2001 (1)

C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
[CrossRef]

1998 (1)

P. M. Visser and G. Nienhuis, “Geometric potentials for subrecoil dynamics,” Phys. Rev. A 57, 4581–4591 (1998).
[CrossRef]

1996 (1)

R. Dum and M. Olshanii, “Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Royal Soc. A 392, 45–57 (1984).
[CrossRef]

1982 (1)

R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
[CrossRef]

Ahufinger, V.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, The Orbital Angular Momentum of Light, E. Wolf, ed., Vol. 39 of Progress in Optics (Elsevier Science, 1999).

Andrews, D. L.

V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
[CrossRef]

Azzam, R. M. A.

Babiker, M.

V. E. Lembessis and M. Babiker, “Enhanced quadrupole effects for atoms in optical vortices,” Phys. Rev. Lett. 110, 083002 (2013).
[CrossRef]

V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
[CrossRef]

C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, The Orbital Angular Momentum of Light, E. Wolf, ed., Vol. 39 of Progress in Optics (Elsevier Science, 1999).

Bennett, C. R.

C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
[CrossRef]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Royal Soc. A 392, 45–57 (1984).
[CrossRef]

Blatt, R.

R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
[CrossRef]

Bloch, I.

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[CrossRef]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[CrossRef]

I. Bloch, “Exploring quantum matter with ultracold atoms in optical lattices,” J. Phys. B 38, S629–S643 (2005).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji and D. Guéry-Odelin, Advances in Atomic Physics: An Overview (World Scientific, 2011).

C. Cohen-Tannoudji, Atoms in Electromagnetic Fields (World Scientific, 1994).

Dalibard, J.

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[CrossRef]

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Damski, B.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Demler, E.

A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
[CrossRef]

Dum, R.

R. Dum and M. Olshanii, “Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef]

Feynman, R.

R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
[CrossRef]

Fleischhauer, M.

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

Gerbier, F.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Graß, T.

T. Graß, “Ultracold atoms in artificial gauge fields,” Ph.D. thesis (Institut de Ciències Fotòniques and Universitat Politècnica de Catalunya, 2012).

Guéry-Odelin, D.

C. Cohen-Tannoudji and D. Guéry-Odelin, Advances in Atomic Physics: An Overview (World Scientific, 2011).

Haroche, S.

S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford, 2006).

Jaksch, D.

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56 (2003).
[CrossRef]

Juzeliunas, G.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

G. Juzeliūnas and P. Öhberg, “Creation of an effective magnetic field in ultracold atomic gases using electromagnetically induced transparency,” Opt. Spectrosc. 99, 357–361 (2005).
[CrossRef]

G. Juzeliūnas and P. Öhberg, Optical Manipulation of Ultracold Atoms, in Structured Light and Its Applications, D. L. Andrews, ed. (Academic, 2008).

Kirk, J. B.

C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
[CrossRef]

Lembessis, V. E.

V. E. Lembessis and M. Babiker, “Enhanced quadrupole effects for atoms in optical vortices,” Phys. Rev. Lett. 110, 083002 (2013).
[CrossRef]

V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
[CrossRef]

Lewenstein, M.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Lukin, M. D.

A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
[CrossRef]

Mueller, E. J.

E. J. Mueller, “Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids,” Phys. Rev. A 70, 041603 (2004).
[CrossRef]

Nascimbène, S.

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[CrossRef]

Nienhuis, G.

P. M. Visser and G. Nienhuis, “Geometric potentials for subrecoil dynamics,” Phys. Rev. A 57, 4581–4591 (1998).
[CrossRef]

Öhberg, P.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

G. Juzeliūnas and P. Öhberg, “Creation of an effective magnetic field in ultracold atomic gases using electromagnetically induced transparency,” Opt. Spectrosc. 99, 357–361 (2005).
[CrossRef]

G. Juzeliūnas and P. Öhberg, Optical Manipulation of Ultracold Atoms, in Structured Light and Its Applications, D. L. Andrews, ed. (Academic, 2008).

Olshanii, M.

R. Dum and M. Olshanii, “Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, The Orbital Angular Momentum of Light, E. Wolf, ed., Vol. 39 of Progress in Optics (Elsevier Science, 1999).

Raimond, J.-M.

S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford, 2006).

Roos, C. F.

R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
[CrossRef]

Ruseckas, J.

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

Sanpera, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Sen, A.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Sen, U.

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

Sørensen, A. S.

A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
[CrossRef]

Visser, P. M.

P. M. Visser and G. Nienhuis, “Geometric potentials for subrecoil dynamics,” Phys. Rev. A 57, 4581–4591 (1998).
[CrossRef]

Zoller, P.

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56 (2003).
[CrossRef]

Appl. Opt. (1)

Int. J. Theor. Phys. (1)

R. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21, 467–488 (1982).
[CrossRef]

J. Phys. B (1)

I. Bloch, “Exploring quantum matter with ultracold atoms in optical lattices,” J. Phys. B 38, S629–S643 (2005).
[CrossRef]

Nat. Phys. (3)

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[CrossRef]

R. Blatt and C. F. Roos, “Quantum simulations with trapped ions,” Nat. Phys. 8, 277–284 (2012).
[CrossRef]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[CrossRef]

New J. Phys. (1)

D. Jaksch and P. Zoller, “Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms,” New J. Phys. 5, 56 (2003).
[CrossRef]

Opt. Spectrosc. (1)

G. Juzeliūnas and P. Öhberg, “Creation of an effective magnetic field in ultracold atomic gases using electromagnetically induced transparency,” Opt. Spectrosc. 99, 357–361 (2005).
[CrossRef]

Phys. Rev. A (5)

E. J. Mueller, “Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids,” Phys. Rev. A 70, 041603 (2004).
[CrossRef]

G. Juzeliūnas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, “Light-induced effective magnetic fields for ultracold atoms in planar geometries,” Phys. Rev. A 73, 025602 (2006).
[CrossRef]

C. R. Bennett, J. B. Kirk, and M. Babiker, “Theory of evanescent mode atomic mirrors with a metallic layer,” Phys. Rev. A 63, 033405 (2001) and references therein.
[CrossRef]

V. E. Lembessis, M. Babiker, and D. L. Andrews, “Surface optical vortices,” Phys. Rev. A 79, 011806(R) (2009).
[CrossRef]

P. M. Visser and G. Nienhuis, “Geometric potentials for subrecoil dynamics,” Phys. Rev. A 57, 4581–4591 (1998).
[CrossRef]

Phys. Rev. Lett. (3)

R. Dum and M. Olshanii, “Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef]

A. S. Sørensen, E. Demler, and M. D. Lukin, “Fractional quantum Hall states of atoms in optical lattices,” Phys. Rev. Lett. 94, 086803 (2005).
[CrossRef]

V. E. Lembessis and M. Babiker, “Enhanced quadrupole effects for atoms in optical vortices,” Phys. Rev. Lett. 110, 083002 (2013).
[CrossRef]

Proc. Royal Soc. A (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. Royal Soc. A 392, 45–57 (1984).
[CrossRef]

Rev. Mod. Phys. (1)

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, “Artificial gauge potentials for neutral atoms,” Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Other (7)

C. Cohen-Tannoudji and D. Guéry-Odelin, Advances in Atomic Physics: An Overview (World Scientific, 2011).

S. Haroche and J.-M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons (Oxford, 2006).

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, and U. Sen, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” arXiv:0606771v2 (2007).

C. Cohen-Tannoudji, Atoms in Electromagnetic Fields (World Scientific, 1994).

L. Allen, M. J. Padgett, and M. Babiker, The Orbital Angular Momentum of Light, E. Wolf, ed., Vol. 39 of Progress in Optics (Elsevier Science, 1999).

G. Juzeliūnas and P. Öhberg, Optical Manipulation of Ultracold Atoms, in Structured Light and Its Applications, D. L. Andrews, ed. (Academic, 2008).

T. Graß, “Ultracold atoms in artificial gauge fields,” Ph.D. thesis (Institut de Ciències Fotòniques and Universitat Politècnica de Catalunya, 2012).

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Figures (8)

Fig. 1.
Fig. 1.

Creation of an evanescent light field by total internal reflection of a light beam at an angle θ (larger than the critical angle). The incident beam is arranged such that at θ=0 the beam waist coincides with the surface at z=0. The evanescent field is exponentially decaying in the direction normal to the surface.

Fig. 2.
Fig. 2.

Components of the artificial magnetic field along the y and z directions (left and right, respectively) in the case of a beam waist equal to 1 μm. The x and y axes are scaled in w0 units. The magnetic field is given in B0=(k0/qw0) units. We see that the y component is one order of magnitude greater than the z component. In both figures the color scale extends from magenta (minimum) to red (maximum).

Fig. 3.
Fig. 3.

Components of the artificial magnetic field along the y and the z directions (left and right, respectively) in the case of a refractive index n=3.5 and beam waist 1 μm. The x and y axes are scaled in w0 units. The magnetic field is given in B0=(k0/qw0) units. We see that the y-component is two orders of magnitude greater than the z-component. The color scale goes from magenta (minimum) to red (maximum).

Fig. 4.
Fig. 4.

Components of the artificial magnetic field along the y and z directions (left and right, respectively) for a beam with mode indices p=0, l=1 in the case of a beam waist equal to 10 μm and a refractive index n=1.5. The x and y axes are scaled in w0 units. The magnetic field is given in B0=(k0/qw0) units. We see that the y component is two orders of magnitude greater than the z component. The color scale goes from magenta (minimum) to red (maximum).

Fig. 5.
Fig. 5.

Components of the artificial magnetic field along the y and z directions (left and right, respectively) for a beam with mode indices p=0, l=5 in the case of a beam waist equal to 10 μm and a refractive index n=1.5. The x and y axes are scaled in w0 units. The magnetic field is given in B0=(k0/qw0) units. We see that the y component is two orders of magnitude greater than the z component. The color scale goes from magenta (minimum) to red (maximum).

Fig. 6.
Fig. 6.

Components of the artificial magnetic field along the y and z directions (left and right, respectively) for a beam with mode indices p=0, l=5 in the case of refractive index n=3.5 and a beam waist equal to 10 μm. The x and y axes are scaled in w0 units. The magnetic field is given in B0=(k0/qw0) units. We see that the y component is two orders of magnitude greater than the z component. The color scale goes from magenta (minimum) to red (maximum).

Fig. 7.
Fig. 7.

Schematic representation of generation of two displaced counterpropagating evanescent fields.

Fig. 8.
Fig. 8.

Artificial magnetic field along the z direction for two displaced Gaussian evanescent waves in the case of beam waists equal to 8 μm. The x and y axes are scaled in units. The two beams are displaced in the y direction by a distance a=0.8w0. The magnetic field is given in Tesla. The color scale goes from magenta (minimum) to red (maximum).

Equations (29)

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

E(x,y,z,t)=yF(x,y,z)eiΘ(R)eiωt,
Eevan(x,y,z,t)=E(xxcosθ;y;zxsinθ,t)ezk0n2sin2θ1eik0nxsinθ.
|χ1(R)=(cos(θ(R)/2)eiϕ(R)sin(θ(R)/2)),|χ2(R)=(eiϕ(R)sin(θ(R)/2)cos(θ(R)/2)),
cos(θ(R))=δ/δ2+Ω2(R).
qB(R)=δΩ(R)(δ2+Ω2(R))3/2∇⃗Ω(R)×∇⃗φ(R).
F(x,y,z)=1(1+z2/zR2)exp((x2+y2)w2(z)),
w2(z)=2(zR2+z2)/kzR.
Θ(R)=kz.
Eevan(x,y,z,t)=yE00(1+x2sin2θ/zR2)exp((x2cos2θ+y2)w02(1+x2sin2θ/zR2)1/2)ezk0n2sin2θ1eik0nxsinθ.
Ω(R)=Ω00G(R),
G(R)=1(1+x2sin2θ/zR2)×exp((x2cos2θ+y2)w02(1+x2sin2θ/zR2)1/2)×exp(zk0n2sin2θ1),
ϕ(R)=xk0nsinθ.
B(R)=(k0nsinθ)qw0δΩ2(R)(δ2+Ω2(R))3/2{2yw0(1+x2sin2θ/zR2)1/2z^w0k0n2sin2θ1y^}.
F(x,y,z)=1(1+z2/zR2)[2(x2+y2)w2(z)]|l|/2Lp|l|(2(x2+y2)w2(z))exp((x2+y2)w2(z)),
Θ(R)=kz+lϕ+k(x2+y2)z2(z2+zR2)+(2p+|l|+1)arctan(z/zR).
G(R)=1(1+x2sin2θ/zR2)×[2(x2cos2θ+y2)w02(1+x2sin2θ/zR2)]|l|/2Lp|l|[2(x2cos2θ+y2)w02(1+x2sin2θ/zR2)]exp((x2cos2θ+y2)w02(1+x2sin2θ/zR2)1/2)×exp(zk0n2sin2θ1),
ϕ(R)=xk0nsinθ+larctan(y/xcosθ).
B(R)=Bxx^+Byy^+Bzz^,
Bx=δΩ2(R)q(δ2+Ω2(R))3/2k0n2sin2θ1(xcosθx2cos2θ+y2),
By=δΩ2(R)q(δ2+Ω2(R))3/2k0n2sin2θ1(k0nsinθ+ycosθx2cos2θ+y2),
Bz=δΩ2(R)q(δ2+Ω2(R))3/2{(xcosθx2cos2θ+y2)[xsin2θzR2(1+x2cos2θ/zR2)+2xw02(1+x2sin2θ/zR2)(cos2θ+sin2θ(x2cos2θ+y2)zR2)+2x(x2cos2θ+y2)(cos2θsin2θ(x2cos2θ+y2)zR2)(p(p+|l|)Lp1|l|(u)Lp|l|(u)|)|l|2(x2cos2θ+y2)(2xcos2θ2xsin2θ(x2cosθ+y2)(1+x2sin2θ/zR2)zR2)]+(k0nsinθ+ycosθx2cos2θ+y2)[ly(x2cos2θ+y2)2yw02(1+x2sin2θ/zR2)+(2yx2cos2θ+y2)(p(p+|l|)Lp1|l|(u)Lp|l|(u)|)]},
u=2(x2cos2θ+y2)w02(1+x2sin2θ/zR2).
ER=(k)22M+(l)22Mr2.
Ω1(R)=Ω00(1+x2sin2θ/zR2)×exp((x2cos2θ+(ya)2)w02(1+x2sin2θ/zR2)1/2)×exp(zk0n2sin2θ1),
Ω2(R)=Ω00(1+x2sin2θ/zR2)×exp((x2cos2θ+y2)w02(1+x2sin2θ/zR2)1/2)×exp(zk0n2sin2θ1).
qB=∇⃗S×∇⃗|ζ|2(1+|ζ|2)2,
ζ=Ω1Ω2,S=2xk0nsinθ.
B=8k0nasinθqw02(1+x2sin2θ/zR2)1/21cosh2uz,
u=a22ayw02(1+x2sin2θ/zR2)1/2.

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