Abstract

In this paper, an open-loop control is applied to stabilize a two-level quantum particle by an external optical field. To achieve this goal, the speed gradient method is implemented. The efficiency of this method is shown by numerical experiments.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. S. Letokhov, Laser Control of Atoms and Molecules (Oxford University, 2007).
  2. M. Nihtila, P. Kokkonen, and J. Levine, “Parametrizations of a two-level quantum control system,” in Proceedings of AFRICON, doi: 10.1109/AFRCON.2007.4401567 (IEEE, 2007).
  3. W. Zhang and J. Zhuang, “Dynamical control of two-level system decay and long time freezing,” Phys. Rev. A 79, 012310(2009).
    [CrossRef]
  4. X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).
  5. V. A. Astapenko, “Coherent control of two-level system under bichromatic excitation,” Proc. SPIE 6729, 67291E (2007).
    [CrossRef]
  6. N. Imoto, “Controlling two-level atoms with a quantized π- and π/2-pulse,” Prog. Cryst. Growth Charact. Mater. 33, 295–301 (1996).
    [CrossRef]
  7. M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
    [CrossRef]
  8. A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
    [CrossRef]
  9. C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055–1058 (1996).
    [CrossRef]
  10. S. Borisenok and S. Ullah, “Linear feedforward control of two-level quantum system by modulated external field,” Opt. Commun. 284, 3562–3567 (2011).
    [CrossRef]
  11. A. L. Fradkov and A. Y. Pogromsky, Introduction to Control of Oscillations and Chaos (World Scientific, 1999).
  12. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

2011 (1)

S. Borisenok and S. Ullah, “Linear feedforward control of two-level quantum system by modulated external field,” Opt. Commun. 284, 3562–3567 (2011).
[CrossRef]

2009 (1)

W. Zhang and J. Zhuang, “Dynamical control of two-level system decay and long time freezing,” Phys. Rev. A 79, 012310(2009).
[CrossRef]

2007 (1)

V. A. Astapenko, “Coherent control of two-level system under bichromatic excitation,” Proc. SPIE 6729, 67291E (2007).
[CrossRef]

2004 (1)

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

2001 (1)

A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
[CrossRef]

1996 (2)

C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055–1058 (1996).
[CrossRef]

N. Imoto, “Controlling two-level atoms with a quantized π- and π/2-pulse,” Prog. Cryst. Growth Charact. Mater. 33, 295–301 (1996).
[CrossRef]

Astapenko, V. A.

V. A. Astapenko, “Coherent control of two-level system under bichromatic excitation,” Proc. SPIE 6729, 67291E (2007).
[CrossRef]

Babbitt, W. R.

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

Barber, Z. W.

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

Borisenok, S.

S. Borisenok and S. Ullah, “Linear feedforward control of two-level quantum system by modulated external field,” Opt. Commun. 284, 3562–3567 (2011).
[CrossRef]

Di. Piazza, A.

A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
[CrossRef]

Eberly, J. H.

C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055–1058 (1996).
[CrossRef]

Fiordilino, E.

A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
[CrossRef]

Fischer, J. A.

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

Fradkov, A. L.

A. L. Fradkov and A. Y. Pogromsky, Introduction to Control of Oscillations and Chaos (World Scientific, 1999).

Gong, S.

X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).

Imoto, N.

N. Imoto, “Controlling two-level atoms with a quantized π- and π/2-pulse,” Prog. Cryst. Growth Charact. Mater. 33, 295–301 (1996).
[CrossRef]

Kokkonen, P.

M. Nihtila, P. Kokkonen, and J. Levine, “Parametrizations of a two-level quantum control system,” in Proceedings of AFRICON, doi: 10.1109/AFRCON.2007.4401567 (IEEE, 2007).

Law, C. K.

C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055–1058 (1996).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov, Laser Control of Atoms and Molecules (Oxford University, 2007).

Levine, J.

M. Nihtila, P. Kokkonen, and J. Levine, “Parametrizations of a two-level quantum control system,” in Proceedings of AFRICON, doi: 10.1109/AFRCON.2007.4401567 (IEEE, 2007).

Liu, C.

X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).

Mittleman, M. H.

A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
[CrossRef]

Nihtila, M.

M. Nihtila, P. Kokkonen, and J. Levine, “Parametrizations of a two-level quantum control system,” in Proceedings of AFRICON, doi: 10.1109/AFRCON.2007.4401567 (IEEE, 2007).

Pogromsky, A. Y.

A. L. Fradkov and A. Y. Pogromsky, Introduction to Control of Oscillations and Chaos (World Scientific, 1999).

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Song, X.

X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).

Tian, M.

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

Ullah, S.

S. Borisenok and S. Ullah, “Linear feedforward control of two-level quantum system by modulated external field,” Opt. Commun. 284, 3562–3567 (2011).
[CrossRef]

Xu, Z.

X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).

Zhang, W.

W. Zhang and J. Zhuang, “Dynamical control of two-level system decay and long time freezing,” Phys. Rev. A 79, 012310(2009).
[CrossRef]

Zhuang, J.

W. Zhang and J. Zhuang, “Dynamical control of two-level system decay and long time freezing,” Phys. Rev. A 79, 012310(2009).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

J. Lumin. (1)

M. Tian, Z. W. Barber, J. A. Fischer, and W. R. Babbitt, “The geometric phase in two-level atomic systems,” J. Lumin. 107, 155–159 (2004).
[CrossRef]

J. Phys. B (1)

A. Di. Piazza, E. Fiordilino, and M. H. Mittleman, “Pulse shape control of the spectrum emitted by two-level atom,” J. Phys. B 34, 3655–3667 (2001).
[CrossRef]

Opt. Commun. (1)

S. Borisenok and S. Ullah, “Linear feedforward control of two-level quantum system by modulated external field,” Opt. Commun. 284, 3562–3567 (2011).
[CrossRef]

Phys. Rev. A (1)

W. Zhang and J. Zhuang, “Dynamical control of two-level system decay and long time freezing,” Phys. Rev. A 79, 012310(2009).
[CrossRef]

Phys. Rev. Lett. (1)

C. K. Law and J. H. Eberly, “Arbitrary control of a quantum electromagnetic field,” Phys. Rev. Lett. 76, 1055–1058 (1996).
[CrossRef]

Proc. SPIE (1)

V. A. Astapenko, “Coherent control of two-level system under bichromatic excitation,” Proc. SPIE 6729, 67291E (2007).
[CrossRef]

Prog. Cryst. Growth Charact. Mater. (1)

N. Imoto, “Controlling two-level atoms with a quantized π- and π/2-pulse,” Prog. Cryst. Growth Charact. Mater. 33, 295–301 (1996).
[CrossRef]

Other (5)

X. Song, C. Liu, S. Gong, and Z. Xu, “Phase control of spectra in a two-level system driven by ultrashort two-color pulse fields,” in Proceeding of the 5th Pacific Rim Conference on Lasers and Electro-Optics, doi: 10.1109/CLEOPR.2003.1274689 (IEEE, 2003).

V. S. Letokhov, Laser Control of Atoms and Molecules (Oxford University, 2007).

M. Nihtila, P. Kokkonen, and J. Levine, “Parametrizations of a two-level quantum control system,” in Proceedings of AFRICON, doi: 10.1109/AFRCON.2007.4401567 (IEEE, 2007).

A. L. Fradkov and A. Y. Pogromsky, Introduction to Control of Oscillations and Chaos (World Scientific, 1999).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Interaction of a single two-level atom with an external optical field.

Fig. 2.
Fig. 2.

(a) Density matrix element x(τ) for the control procedure Eqs. (9) and (10). (b) The control signal u(τ) for Eq. (10).

Fig. 3.
Fig. 3.

(a) Density matrix element x(τ) for the control procedure Eqs. (9) and (10). (b) The control signal u(τ) for Eq. (10).

Fig. 4.
Fig. 4.

(a) Density matrix element x(τ) for the control procedure Eqs. (9) and (10). (b) The control signal u(τ) for Eq. (10).

Equations (11)

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

ρ˙aa=γaρaa+iE(𝒫abρbaeiωt𝒫ab*ρabeiωt);ρ˙bb=γbρbbiE(𝒫abρbaeiωt𝒫ab*ρabeiωt);ρ˙ab=γabρabiE𝒫ab(ρaaρbb)eiωt,
ρ+ρbaei(ωt+ϕ)+ρabei(ωt+ϕ);ρi[ρbaei(ωt+ϕ)ρabei(ωt+ϕ)].
ρ˙aa=γaρaa+|𝒫ab|Eρ;ρ˙bb=γbρbb|𝒫ab|Eρ;ρ˙+=γabρ++ωρ;ρ˙=γabρωρ+2|𝒫ab|E(ρaaρbb).
(ρaa+ρbb)(t)=eγt(ρaa+ρbb)(0).
ρaa(t)ρbb(t)eγtx(t);ρ+(t)eγty(t);ρ(t)eγtz(t).
x˙=u·z;y˙=ϵ·y+z;z˙=ϵ·zyu·x.
limtQ(x(t),t)0.
Q=(x1)2.
u=ΓQ˙u,
u=2Γ(x1)·z.
x˙=2Γ(x1)·z2;y˙=ϵ·y+z;z˙=ϵ·zy+2Γx(x1)·z,

Metrics