Abstract

The Aharonov–Bohm effect is usually associated with a path-dependent phase accumulated by a charged matter wave and determined by an effective vector potential. In a more general geometrical framework, such phase alterations have been the hallmark of a host of related phenomena in many different fields. However, besides phase changes, it was suggested that for finite wave-packets there is also an additional deflection leading to observable changes in the wave’s canonical momentum. In this paper, we create an optical scattering situation that permits observing nonconservative reaction forces, which result from the conservation of canonical momentum. We demonstrate experimentally, for the first time, the presence of such mechanical forces with the magnitude and direction determined by the phase dislocation of the vortex state. Our experimental results offer insights into essentially untested phenomena, where forces act on vortex fields, and allow examining the role of conservation laws and symmetries in complex interacting systems.

© 2014 Optical Society of America

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References

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  1. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
    [Crossref]
  2. R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
    [Crossref]
  3. E. B. Sonin, “The Aharonov–Bohm effect in neutral liquids,” J. Phys. A 43, 354003 (2010).
    [Crossref]
  4. C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).
  5. M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
    [Crossref]
  6. S. V. Iordanskii, “On the mutual friction between the normal and superfluid components in a rotating Bose gas,” Ann. Phys. 29, 335–349 (1964).
    [Crossref]
  7. M. Stone, “Iordanskii force and the gravitational Aharonov-Bohm effect for a moving vortex,” Phys. Rev. B 61, 11780 (2000).
  8. U. Leonhardt, P. Ohberg, “Optical analog of the Iordanskii Force in a Bose-Einstein condensate,” Phys. Rev. A 67, 053616 (2003).
    [Crossref]
  9. D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
    [Crossref]
  10. K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
    [Crossref]
  11. E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).
  12. C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
    [Crossref]
  13. C. Z. Tan, “Aharonov–Bohm effect in optical activity,” J. Phys. A 43, 354007 (2010).
    [Crossref]
  14. S. Longhi, “Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields,” Opt. Lett. 39, 5892–5895 (2014).
    [Crossref]
  15. Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).
  16. S. Olariu, I. I. Popescu, “The Aharonov–Bohm effect,” Rev. Mod. Phys. 57, 339–436 (1985).
    [Crossref]
  17. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics: Mainly Electromagnetism and Matter (Addison-Wesley, 1969), Vol. 2.
  18. M. D. Semon, J. R. Taylor, “The Aharonov-Bohm effect: still a thought-provoking experiment,” Found. Phys. 18, 731–740 (1988).
    [Crossref]
  19. A. L. Shelankov, “Magnetic force exerted by the Aharonov-Bohm line,” Europhys. Lett. 43, 623–628 (1998).
    [Crossref]
  20. M. V. Berry, “Aharonov-Bohm beam deflection: Shelankov’s formula, exact solution, asymptotics and an optical analogue,” J. Phys. A 32, 5627–5641 (1999).
  21. C. Schwartz, A. Dogariu, “Conservation of angular momentum of light in single scattering,” Opt. Express 14, 8425–8433 (2006).
    [Crossref]
  22. A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
    [Crossref]
  23. D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
    [Crossref]
  24. S. Sukhov, A. Dogariu, “Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
    [Crossref]
  25. F. Borghese, P. Denti, R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007).
  26. In dynamic situations involving magnetic field and charged particles, canonical momentum accounting for both particles and field is conserved. Newton’s laws are notorious for their restriction to isolated environments, and absence of high-order interactions.
  27. U. Leonhardt, P. Piwnicki, “Relativistic effects of light in moving media with extremely low group velocity,” Phys. Rev. Lett. 84, 822–825 (2000).
    [Crossref]
  28. This nondissipative, yet non-Hamiltonian, dynamics has interesting features. For example, Noether’s theorem does not apply, so there can be symmetries not associated directly with a conservation law, and conversely, conserved quantities not associated with any symmetry; M. Berry, P. Shukla, “Classical dynamics with curl forces, and motion driven by time-dependent flux,” J. Phys. A 45, 305201 (2012).
    [Crossref]

2014 (3)

M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
[Crossref]

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

S. Longhi, “Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields,” Opt. Lett. 39, 5892–5895 (2014).
[Crossref]

2013 (1)

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

2012 (2)

This nondissipative, yet non-Hamiltonian, dynamics has interesting features. For example, Noether’s theorem does not apply, so there can be symmetries not associated directly with a conservation law, and conversely, conserved quantities not associated with any symmetry; M. Berry, P. Shukla, “Classical dynamics with curl forces, and motion driven by time-dependent flux,” J. Phys. A 45, 305201 (2012).
[Crossref]

K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

2011 (2)

C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
[Crossref]

S. Sukhov, A. Dogariu, “Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[Crossref]

2010 (3)

C. Z. Tan, “Aharonov–Bohm effect in optical activity,” J. Phys. A 43, 354007 (2010).
[Crossref]

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

E. B. Sonin, “The Aharonov–Bohm effect in neutral liquids,” J. Phys. A 43, 354003 (2010).
[Crossref]

2009 (1)

D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
[Crossref]

2006 (1)

2003 (1)

U. Leonhardt, P. Ohberg, “Optical analog of the Iordanskii Force in a Bose-Einstein condensate,” Phys. Rev. A 67, 053616 (2003).
[Crossref]

2001 (1)

D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[Crossref]

2000 (2)

M. Stone, “Iordanskii force and the gravitational Aharonov-Bohm effect for a moving vortex,” Phys. Rev. B 61, 11780 (2000).

U. Leonhardt, P. Piwnicki, “Relativistic effects of light in moving media with extremely low group velocity,” Phys. Rev. Lett. 84, 822–825 (2000).
[Crossref]

1999 (1)

M. V. Berry, “Aharonov-Bohm beam deflection: Shelankov’s formula, exact solution, asymptotics and an optical analogue,” J. Phys. A 32, 5627–5641 (1999).

1998 (1)

A. L. Shelankov, “Magnetic force exerted by the Aharonov-Bohm line,” Europhys. Lett. 43, 623–628 (1998).
[Crossref]

1995 (1)

R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
[Crossref]

1988 (1)

M. D. Semon, J. R. Taylor, “The Aharonov-Bohm effect: still a thought-provoking experiment,” Found. Phys. 18, 731–740 (1988).
[Crossref]

1985 (1)

S. Olariu, I. I. Popescu, “The Aharonov–Bohm effect,” Rev. Mod. Phys. 57, 339–436 (1985).
[Crossref]

1980 (1)

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

1964 (2)

C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).

S. V. Iordanskii, “On the mutual friction between the normal and superfluid components in a rotating Bose gas,” Ann. Phys. 29, 335–349 (1964).
[Crossref]

Béché, A.

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

Berry, M.

This nondissipative, yet non-Hamiltonian, dynamics has interesting features. For example, Noether’s theorem does not apply, so there can be symmetries not associated directly with a conservation law, and conversely, conserved quantities not associated with any symmetry; M. Berry, P. Shukla, “Classical dynamics with curl forces, and motion driven by time-dependent flux,” J. Phys. A 45, 305201 (2012).
[Crossref]

Berry, M. V.

M. V. Berry, “Aharonov-Bohm beam deflection: Shelankov’s formula, exact solution, asymptotics and an optical analogue,” J. Phys. A 32, 5627–5641 (1999).

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Borghese, F.

F. Borghese, P. Denti, R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007).

Cabrera, G. G.

C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
[Crossref]

Carvalho, M. A.

M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
[Crossref]

Chambers, R. G.

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Cook, R. J.

R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
[Crossref]

Coste, C.

C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).

Dartora, C. A.

C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
[Crossref]

Denti, P.

F. Borghese, P. Denti, R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007).

Dogariu, A.

S. Sukhov, A. Dogariu, “Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[Crossref]

D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
[Crossref]

C. Schwartz, A. Dogariu, “Conservation of angular momentum of light in single scattering,” Opt. Express 14, 8425–8433 (2006).
[Crossref]

Eggleton, B. J.

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

Fan, S.

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

Fang, K.

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

Fearn, H.

R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
[Crossref]

Feynman, R. P.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics: Mainly Electromagnetism and Matter (Addison-Wesley, 1969), Vol. 2.

Furtado, C.

M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
[Crossref]

Gorodetski, Y.

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

Haefner, D.

D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
[Crossref]

Hasman, E.

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

Iordanskii, S. V.

S. V. Iordanskii, “On the mutual friction between the normal and superfluid components in a rotating Bose gas,” Ann. Phys. 29, 335–349 (1964).
[Crossref]

Kivshar, Y. S.

D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[Crossref]

Kleiner, V.

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

Large, M. D.

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Leighton, R. B.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics: Mainly Electromagnetism and Matter (Addison-Wesley, 1969), Vol. 2.

Leonhardt, U.

U. Leonhardt, P. Ohberg, “Optical analog of the Iordanskii Force in a Bose-Einstein condensate,” Phys. Rev. A 67, 053616 (2003).
[Crossref]

U. Leonhardt, P. Piwnicki, “Relativistic effects of light in moving media with extremely low group velocity,” Phys. Rev. Lett. 84, 822–825 (2000).
[Crossref]

Li, E.

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

Longhi, S.

Lund, F.

C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).

Milonni, P. W.

R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
[Crossref]

Nechayev, S.

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

Nepomnyashchy, A.

D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[Crossref]

Neshev, D.

D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[Crossref]

Nobrega, K. Z.

C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
[Crossref]

Ohberg, P.

U. Leonhardt, P. Ohberg, “Optical analog of the Iordanskii Force in a Bose-Einstein condensate,” Phys. Rev. A 67, 053616 (2003).
[Crossref]

Olariu, S.

S. Olariu, I. I. Popescu, “The Aharonov–Bohm effect,” Rev. Mod. Phys. 57, 339–436 (1985).
[Crossref]

Piwnicki, P.

U. Leonhardt, P. Piwnicki, “Relativistic effects of light in moving media with extremely low group velocity,” Phys. Rev. Lett. 84, 822–825 (2000).
[Crossref]

Popescu, I. I.

S. Olariu, I. I. Popescu, “The Aharonov–Bohm effect,” Rev. Mod. Phys. 57, 339–436 (1985).
[Crossref]

Saija, R.

F. Borghese, P. Denti, R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007).

Sands, M.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics: Mainly Electromagnetism and Matter (Addison-Wesley, 1969), Vol. 2.

Schwartz, C.

Semon, M. D.

M. D. Semon, J. R. Taylor, “The Aharonov-Bohm effect: still a thought-provoking experiment,” Found. Phys. 18, 731–740 (1988).
[Crossref]

Shelankov, A. L.

A. L. Shelankov, “Magnetic force exerted by the Aharonov-Bohm line,” Europhys. Lett. 43, 623–628 (1998).
[Crossref]

Shukla, P.

This nondissipative, yet non-Hamiltonian, dynamics has interesting features. For example, Noether’s theorem does not apply, so there can be symmetries not associated directly with a conservation law, and conversely, conserved quantities not associated with any symmetry; M. Berry, P. Shukla, “Classical dynamics with curl forces, and motion driven by time-dependent flux,” J. Phys. A 45, 305201 (2012).
[Crossref]

Sonin, E. B.

E. B. Sonin, “The Aharonov–Bohm effect in neutral liquids,” J. Phys. A 43, 354003 (2010).
[Crossref]

Stone, M.

M. Stone, “Iordanskii force and the gravitational Aharonov-Bohm effect for a moving vortex,” Phys. Rev. B 61, 11780 (2000).

Sukhov, S.

S. Sukhov, A. Dogariu, “Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[Crossref]

D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
[Crossref]

Tan, C. Z.

C. Z. Tan, “Aharonov–Bohm effect in optical activity,” J. Phys. A 43, 354007 (2010).
[Crossref]

Taylor, J. R.

M. D. Semon, J. R. Taylor, “The Aharonov-Bohm effect: still a thought-provoking experiment,” Found. Phys. 18, 731–740 (1988).
[Crossref]

Umeki, M.

C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).

Upstill, C.

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Van Boxem, R.

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

Van Tendeloo, G.

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

Verbeeck, J.

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

Vieira, M.

M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
[Crossref]

Walmsley, J. C.

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Yu, Z.

K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

Am. J. Phys. (1)

R. J. Cook, H. Fearn, P. W. Milonni, “Fizeau’s experiment and the Aharonov-Bohm effect,” Am. J. Phys. 63, 705–709 (1995).
[Crossref]

Ann. Phys. (1)

S. V. Iordanskii, “On the mutual friction between the normal and superfluid components in a rotating Bose gas,” Ann. Phys. 29, 335–349 (1964).
[Crossref]

Eur. J. Phys. (1)

M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, “Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue,” Eur. J. Phys. 1, 154–162 (1980).
[Crossref]

Europhys. Lett. (1)

A. L. Shelankov, “Magnetic force exerted by the Aharonov-Bohm line,” Europhys. Lett. 43, 623–628 (1998).
[Crossref]

Found. Phys. (1)

M. D. Semon, J. R. Taylor, “The Aharonov-Bohm effect: still a thought-provoking experiment,” Found. Phys. 18, 731–740 (1988).
[Crossref]

J. Phys. A (4)

This nondissipative, yet non-Hamiltonian, dynamics has interesting features. For example, Noether’s theorem does not apply, so there can be symmetries not associated directly with a conservation law, and conversely, conserved quantities not associated with any symmetry; M. Berry, P. Shukla, “Classical dynamics with curl forces, and motion driven by time-dependent flux,” J. Phys. A 45, 305201 (2012).
[Crossref]

M. V. Berry, “Aharonov-Bohm beam deflection: Shelankov’s formula, exact solution, asymptotics and an optical analogue,” J. Phys. A 32, 5627–5641 (1999).

C. Z. Tan, “Aharonov–Bohm effect in optical activity,” J. Phys. A 43, 354007 (2010).
[Crossref]

E. B. Sonin, “The Aharonov–Bohm effect in neutral liquids,” J. Phys. A 43, 354003 (2010).
[Crossref]

Nat. Commun. (1)

E. Li, B. J. Eggleton, K. Fang, S. Fan, “Photonic Aharonov–Bohm effect in photon–phonon interactions,” Nat. Commun. 5, 3225 (2014).

Nat. Phys. (1)

A. Béché, R. Van Boxem, G. Van Tendeloo, J. Verbeeck, “Magnetic monopole field exposed by electrons,” Nat. Phys. 10, 26–29 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

C. A. Dartora, K. Z. Nobrega, G. G. Cabrera, “Optical analogue of the Aharonov–Bohm effect using anisotropic media,” Phys. Lett. A 375, 2254–2257 (2011).
[Crossref]

Phys. Rev. A (2)

M. Vieira, M. A. Carvalho, C. Furtado, “Aharonov-Bohm effect for light in a moving medium,” Phys. Rev. A 90, 012105 (2014).
[Crossref]

U. Leonhardt, P. Ohberg, “Optical analog of the Iordanskii Force in a Bose-Einstein condensate,” Phys. Rev. A 67, 053616 (2003).
[Crossref]

Phys. Rev. B (2)

M. Stone, “Iordanskii force and the gravitational Aharonov-Bohm effect for a moving vortex,” Phys. Rev. B 61, 11780 (2000).

Y. Gorodetski, S. Nechayev, V. Kleiner, E. Hasman, “Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter,” Phys. Rev. B 82, 125433 (2010).

Phys. Rev. E (1)

C. Coste, F. Lund, M. Umeki, “Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect,” Phys. Rev. E 60, 4908–4916 (1964).

Phys. Rev. Lett. (5)

D. Neshev, A. Nepomnyashchy, Y. S. Kivshar, “Nonlinear Aharonov-Bohm scattering by optical vortices,” Phys. Rev. Lett. 87, 043901 (2001).
[Crossref]

K. Fang, Z. Yu, S. Fan, “Photonic Aharonov-Bohm effect based on dynamic modulation,” Phys. Rev. Lett. 108, 153901 (2012).
[Crossref]

D. Haefner, S. Sukhov, A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett. 102, 123903 (2009).
[Crossref]

S. Sukhov, A. Dogariu, “Negative nonconservative forces: optical ‘tractor beams’ for arbitrary objects,” Phys. Rev. Lett. 107, 203602 (2011).
[Crossref]

U. Leonhardt, P. Piwnicki, “Relativistic effects of light in moving media with extremely low group velocity,” Phys. Rev. Lett. 84, 822–825 (2000).
[Crossref]

Rev. Mod. Phys. (1)

S. Olariu, I. I. Popescu, “The Aharonov–Bohm effect,” Rev. Mod. Phys. 57, 339–436 (1985).
[Crossref]

Other (3)

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics: Mainly Electromagnetism and Matter (Addison-Wesley, 1969), Vol. 2.

F. Borghese, P. Denti, R. Saija, Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics (Springer, 2007).

In dynamic situations involving magnetic field and charged particles, canonical momentum accounting for both particles and field is conserved. Newton’s laws are notorious for their restriction to isolated environments, and absence of high-order interactions.

Supplementary Material (1)

» Supplement 1: PDF (611 KB)     

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Figures (4)

Fig. 1.
Fig. 1. Optical setting: vortex generation by scattering on a spherical particle; (a) spherical particle illuminated by a circularly polarized plane wave with electric field strength E1 and wavevector k1; (b) power flow in the plane z=0 clearly demonstrates the vortex structure; (c) second linearly polarized wave E2 provides the interferometric reference.
Fig. 2.
Fig. 2. Effective interference leading to changes in the wave’s momentum density. Due to the transformation of angular momentum during scattering of circularly polarized light on a spherical object (gray), when seen from the far-field the sphere appears at a shifted virtual location (smaller red sphere). This shift Δ in the apparent location depends on the spin of the incident wave: (a) σ=1; (b) σ=+1. Corresponding maximum of interference pattern (indicated by a small red dot) shifts to the left or to the right with respect to the symmetry point depending on the helicity of the incident wave.
Fig. 3.
Fig. 3. Amplitude of transversal force FAB, as a function of particle size. Forces are calculated directly from Mie scattering phase functions according to Eq. (4). Calculations were performed for a polystyrene sphere, with refractive index 1.6 in water, which is illuminated with radiation of 532 nm wavelength, from a 50 mW beam power focused into a 10 μm radius spot. Magnitude of the transversal force (solid blue curve) is much smaller than the corresponding radiation pressure (red dashed curve), which makes the FAB detection challenging.
Fig. 4.
Fig. 4. Experimental verification of transversal FAB force; (a) experimental setup; (b) schematics of the periodic behavior of FAB forces acting on a particle in the observation plane. Particles trajectories are also influenced by overwhelming Brownian motion; (c) amplitude of reconstructed periodic motion (with noise subtracted) as a function of spatial frequency for combinations of circular and linear polarized waves (top and bottom panels) and for a combination of two linearly polarized waves (center panel).

Equations (5)

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E1sE1[S2θ^+iS1ϕ^]eiϕ.
I(x)|A1(x,Δ)eiσϕ+A2(x)|2,
xI(x)dx0,
Fx=ε0r22Ω|A1(r^,Δ)eiσϕ+A2(r^)|2r^xdΩ,
Fx=ε0r2ΩRe[A1(r^,Δ)eiσϕA2*(r^)]r^xdΩ.

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