Abstract

We theoretically investigate the effect that twisted light has on the orbital and spin dynamics of electrons in quantum rings possessing sizable Rashba spin-orbit interaction. The system Hamiltonian for such a strongly inhomogeneous light field exhibits terms which induce both spin-conserving and spin-flip processes. We analyze the dynamics in terms of the perturbation introduced by a weak light field on the Rasha electronic states, and describe the effects that the orbital angular momentum as well as the inhomogeneous character of the beam have on the orbital and the spin dynamics.

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References

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  1. D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, 2008).
    [PubMed]
  2. G. F. Quinteiro and J. Berakdar, “Electric currents induced by twisted light in quantum rings,” Opt. Express 17, 20465 (2009).
    [CrossRef] [PubMed]
  3. G. F. Quinteiro and P. I. Tamborenea, “Electronic transitions in disk-shaped quantum dots induced by twisted light,” Phys. Rev. B 79, 155450 (2009).
    [CrossRef]
  4. G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
    [CrossRef]
  5. A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
    [CrossRef] [PubMed]
  6. M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
    [CrossRef] [PubMed]
  7. Z.-G. Zhu and J. Berakdar, “Photoinduced nonequilibrium spin and charge polarization in quantum rings,” Phys. Rev. B 77, 235438 (2008).
    [CrossRef]
  8. C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
    [CrossRef]
  9. J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
    [CrossRef]
  10. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific Publishing Co., 2004).
  11. W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
    [CrossRef] [PubMed]
  12. K. Rzazewski and R. W. Boyd, “Equivalence of interaction Hamiltonians in the eElectric dipole approximation,” J. Mod. Opt. 51, 1137–1147 (2004).

2010 (1)

G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
[CrossRef]

2009 (2)

G. F. Quinteiro and P. I. Tamborenea, “Electronic transitions in disk-shaped quantum dots induced by twisted light,” Phys. Rev. B 79, 155450 (2009).
[CrossRef]

G. F. Quinteiro and J. Berakdar, “Electric currents induced by twisted light in quantum rings,” Opt. Express 17, 20465 (2009).
[CrossRef] [PubMed]

2008 (1)

Z.-G. Zhu and J. Berakdar, “Photoinduced nonequilibrium spin and charge polarization in quantum rings,” Phys. Rev. B 77, 235438 (2008).
[CrossRef]

2005 (1)

C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
[CrossRef]

2004 (1)

K. Rzazewski and R. W. Boyd, “Equivalence of interaction Hamiltonians in the eElectric dipole approximation,” J. Mod. Opt. 51, 1137–1147 (2004).

2003 (1)

J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
[CrossRef]

2002 (1)

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

2001 (1)

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

1987 (1)

W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
[CrossRef] [PubMed]

Andrews, D. L.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, 2008).
[PubMed]

Babiker, M.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Bennett, C. R.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Berakdar, J.

G. F. Quinteiro and J. Berakdar, “Electric currents induced by twisted light in quantum rings,” Opt. Express 17, 20465 (2009).
[CrossRef] [PubMed]

Z.-G. Zhu and J. Berakdar, “Photoinduced nonequilibrium spin and charge polarization in quantum rings,” Phys. Rev. B 77, 235438 (2008).
[CrossRef]

Bichler, M.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Boyd, R. W.

K. Rzazewski and R. W. Boyd, “Equivalence of interaction Hamiltonians in the eElectric dipole approximation,” J. Mod. Opt. 51, 1137–1147 (2004).

Dávila Romero, L. C.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Ensslin, K.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Fuhrer, A.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Governale, M.

J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
[CrossRef]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific Publishing Co., 2004).

Heinzel, T.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Ihn, T.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Koch, S. W.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific Publishing Co., 2004).

Lamb, W. E.

W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
[CrossRef] [PubMed]

Lucero, A. O.

G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
[CrossRef]

Luscher, S.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Quinteiro, G. F.

G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
[CrossRef]

G. F. Quinteiro and P. I. Tamborenea, “Electronic transitions in disk-shaped quantum dots induced by twisted light,” Phys. Rev. B 79, 155450 (2009).
[CrossRef]

G. F. Quinteiro and J. Berakdar, “Electric currents induced by twisted light in quantum rings,” Opt. Express 17, 20465 (2009).
[CrossRef] [PubMed]

Romano, C. L.

C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
[CrossRef]

Rzazewski, K.

K. Rzazewski and R. W. Boyd, “Equivalence of interaction Hamiltonians in the eElectric dipole approximation,” J. Mod. Opt. 51, 1137–1147 (2004).

Schlicher, R. R.

W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
[CrossRef] [PubMed]

Scully, M. O.

W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
[CrossRef] [PubMed]

Splettstoesser, J.

J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
[CrossRef]

Tamborenea, P. I.

G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
[CrossRef]

G. F. Quinteiro and P. I. Tamborenea, “Electronic transitions in disk-shaped quantum dots induced by twisted light,” Phys. Rev. B 79, 155450 (2009).
[CrossRef]

C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
[CrossRef]

Ulloa, S. E.

C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
[CrossRef]

Wegscheider, W.

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Zhu, Z.-G.

Z.-G. Zhu and J. Berakdar, “Photoinduced nonequilibrium spin and charge polarization in quantum rings,” Phys. Rev. B 77, 235438 (2008).
[CrossRef]

Zülicke, U.

J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
[CrossRef]

J. Mod. Opt. (1)

K. Rzazewski and R. W. Boyd, “Equivalence of interaction Hamiltonians in the eElectric dipole approximation,” J. Mod. Opt. 51, 1137–1147 (2004).

J. Phys.: Condens. Matter (1)

G. F. Quinteiro, A. O. Lucero, and P. I. Tamborenea, “Electronic transitions in quantum dots and rings induced by inhomogeneous off-centered light beams,” J. Phys.: Condens. Matter 22, 505802 (2010).
[CrossRef]

Nature (1)

A. Fuhrer, S. Luscher, T. Ihn, T. Heinzel, K. Ensslin, W. Wegscheider, and M. Bichler, “Energy spectra and broken symmetry in quantum rings,” Nature 413, 822–825 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (1)

W. E. Lamb, R. R. Schlicher, and M. O. Scully, “Matter-field interaction in atomic physics and quantum optics,” Phys. Rev. A 36, 2763–2772 (1987).
[CrossRef] [PubMed]

Phys. Rev. B (4)

G. F. Quinteiro and P. I. Tamborenea, “Electronic transitions in disk-shaped quantum dots induced by twisted light,” Phys. Rev. B 79, 155450 (2009).
[CrossRef]

Z.-G. Zhu and J. Berakdar, “Photoinduced nonequilibrium spin and charge polarization in quantum rings,” Phys. Rev. B 77, 235438 (2008).
[CrossRef]

C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, “Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures,” Phys. Rev. B 71, 035336 (2005).
[CrossRef]

J. Splettstoesser, M. Governale, and U. Zülicke, “Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling,” Phys. Rev. B 68, 165341 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Other (2)

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific Publishing Co., 2004).

D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic Press, 2008).
[PubMed]

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Figures (1)

Fig. 1
Fig. 1

Pictorial representation of the electronic bands and a transition induced by TL having OAM l = 1 and σ = 1. According to time-dependent perturbation theory: an electron initially in the state {n0, ↑} evolves into a superposition of neighboring states having the same and the opposite spin states. Transitions, indicated by enclosed numbers (blue), correspond to the coefficients: (1) a n 0 2 , 1 ( 1 ) ( t ), (2) a n 0 + 2 , 1 ( 1 ) ( t ), (3) a n 0 + 2 , 1 ( 1 ) ( t ), (4) a n 0 2 , 1 ( 1 ) ( t ), of Eqs. (19).

Tables (1)

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Table 1 Notation

Equations (23)

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A ( r , t ) = ɛ σ F l ( q r r ) e i ( q z z ω t ) e i l ϕ + c . c . = A ( + ) ( r , t ) + A ( ) ( r , t ) ,
H = H SOI + H 1 ,
H SOI = p ^ 2 2 m e * + V ( r ) + α R h ¯ [ σ ^ × p ^ ] z
H 1 = q m e A ( r , t ) p ^ q α R h ¯ [ σ ^ × A ( r , t ) ] z
ψ n s ( φ ) = 1 2 π e i ( n + 1 / 2 ) φ ν s ( γ , φ ) ,
ν 1 ( γ , φ ) = ( cos ( γ / 2 ) e i φ / 2 sin ( γ / 2 ) e i φ / 2 )
ν 1 ( γ , φ ) = ( sin ( γ / 2 ) e i φ / 2 cos ( γ / 2 ) e i φ / 2 ) ,
ɛ n s = h ¯ ω 0 2 [ ( n x s ) 2 Q R 2 4 ] ,
H 11 = H 11 ( + ) + H 11 ( ) = q m e [ A ( + ) ( r , t ) + A ( ) ( r , t ) ] p ^ .
n s | H 11 ( + ) | n s = σ 1 2 h ¯ q m e e i q z z 0 F l ( q r a ) e i ω t × V d 3 r Φ n s * ( r ) e i ( l + σ ) φ [ 1 r φ Φ n s ( r ) ] .
φ ψ n s ( φ ) = i ( n + 1 / 2 ) ψ n s ( φ ) i s 2 2 π e i ( n + 1 / 2 ) φ ν s ( γ , φ ) .
n s | H 11 ( + ) | n s = ξ σ e i ω t δ l + σ , n n [ δ s , s ( n + 1 / 2 s cos γ ) + δ s , s sin γ ] ,
H 12 = q α R h ¯ [ σ ^ × A ( r , t ) ] z
n s | H 12 ( + ) | n s = q α R 2 π 2 h ¯ e i q z z 0 F l ( q r a ) e i ω t × V d φ e i ( n n l ) φ ν s ( γ , φ ) ( σ i σ ^ x σ ^ y ) ν s ( γ , φ ) .
i σ e i σ φ ( sin γ cos γ + σ cos γ σ sin γ ) = i σ e i σ φ M σ .
n s | H 12 ( + ) | n s = η σ e i ω t δ n n , l + σ M σ s s ,
H 1 , n n = e i ω t δ n n , l + σ × [ ξ σ ( n + 1 2 cos γ sin γ sin γ n + 1 2 + cos γ ) + η σ ( sin γ cos γ + σ cos γ σ sin γ ) ] + H . c . ,
Ψ ( r , t ) = a n s ( t ) e i ɛ n s t / h ¯ ψ n s ( φ )
a n s ( 1 ) ( t ) = 1 h ¯ n s | H 1 ( + ) ( 0 ) | n 0 s 0 1 e i ( ω f i ω ) t ω f i ω + 1 h ¯ n s | H 1 ( ) ( 0 ) | n 0 s 0 1 e i ( ω f i + ω ) t ω f i + ω
H 1 , n n = e i ω t δ n n , l + σ × [ ξ σ ( n 1 2 γ γ n + 3 2 ) + η σ ( 0 1 + σ 1 σ 0 ) ] + H . c .
a n 0 2 , 1 ( 1 ) ( T ) = 1 e i ( ω f i + ω ) T h ¯ ( ω f i + ω ) ( ξ 1 * γ + 2 η 1 * ) a n 0 + 2 , 1 ( 1 ) ( T ) = 1 e i ( ω f i ω ) T h ¯ ( ω f i ω ) ξ 1 γ a n 0 + 2 , 1 ( 1 ) ( T ) = 1 e i ( ω f i ω ) T h ¯ ( ω f i ω ) ξ 1 ( n 0 1 / 2 ) a n 0 2 , 1 ( 1 ) ( T ) = 1 e i ( ω f i + ω ) T h ¯ ( ω f i + ω ) ξ 1 * ( n 0 5 / 2 ) ,
m | H 11 ( + ) | m = ξ σ e i ω t δ l + σ , m m m .
J q h ¯ m { m 0 + 2 | ξ | 2 D 2 m 0 3 } ,

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