Abstract

We study two-dimensional sub-wavelength atom localization based on the microwave coupling field controlling and spontaneously generated coherence (SGC) effect. For a five-level M-type atom, introducing a microwave coupling field between two upper levels and considering the quantum interference between two transitions from two upper levels to lower levels, the analytical expression of conditional position probability (CPP) distribution is obtained using the iterative method. The influence of the detuning of a spontaneously emitted photon, Rabi frequency of the microwave field, and the SGC effect on the CPP are discussed. The two-dimensional sub-half-wavelength atom localization with high-precision and high spatial resolution is achieved by adjusting the detuning and the Rabi frequency, where the atom can be localized in a region smaller thanλ/10×λ/10. The spatial resolution is improved significantly compared with the case without the microwave field.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. W. D. Phillips, “Nobel lecture: Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
  2. K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
    [PubMed]
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    [PubMed]
  4. F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).
  5. Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).
  6. C. Ding, J. Li, R. Yu, X. Hao, and Y. Wu, “High-precision atom localization via controllable spontaneous emission in a cycle-configuration atomic system,” Opt. Express 20(7), 7870–7885 (2012).
    [PubMed]
  7. R. G. Wan and T. Y. Zhang, “Two-dimensional sub-half-wavelength atom localization via controlled spontaneous emission,” Opt. Express 19(25), 25823–25832 (2011).
    [PubMed]
  8. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).
  9. M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).
  10. E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
  11. C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).
  12. R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).
  13. Rahmatullah andS. Qamar, “Two-dimensional atom localization via probe-absorption spectrum,” Phys. Rev. A 88, 013846 (2013).
  14. S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).
  15. S. Y. Zhu and M. O. Scully, “Spectral Line Elimination and Spontaneous Emission Cancellation via Quantum Interference,” Phys. Rev. Lett. 76(3), 388–391 (1996).
    [PubMed]
  16. E. Paspalakis and P. L. Knight, “Phase Control of Spontaneous Emission,” Phys. Rev. Lett. 81, 293–296 (1998).
  17. J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
  18. F. Ghafoor, “Subwavelength atom localization via quantum coherence in a three-level atomic system,” Phys. Rev. A 84, 063849 (2011).
  19. X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).
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  23. X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).
  24. A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).
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    [PubMed]
  26. C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of 85Rb atoms,” Opt. Lett. 33(7), 687–689 (2008).
    [PubMed]
  27. Z. Ficek and S. Swain, “Simulating quantum interference in a three-level system with perpendicular transition dipole moments,” Phys. Rev. A 69, 023401 (2004).
  28. A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).
  29. R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

2016 (1)

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

2013 (2)

R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).

Rahmatullah andS. Qamar, “Two-dimensional atom localization via probe-absorption spectrum,” Phys. Rev. A 88, 013846 (2013).

2012 (2)

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

C. Ding, J. Li, R. Yu, X. Hao, and Y. Wu, “High-precision atom localization via controllable spontaneous emission in a cycle-configuration atomic system,” Opt. Express 20(7), 7870–7885 (2012).
[PubMed]

2011 (5)

R. G. Wan and T. Y. Zhang, “Two-dimensional sub-half-wavelength atom localization via controlled spontaneous emission,” Opt. Express 19(25), 25823–25832 (2011).
[PubMed]

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

F. Ghafoor, “Subwavelength atom localization via quantum coherence in a three-level atomic system,” Phys. Rev. A 84, 063849 (2011).

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

2009 (2)

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).

2008 (2)

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of 85Rb atoms,” Opt. Lett. 33(7), 687–689 (2008).
[PubMed]

2005 (2)

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

2004 (1)

Z. Ficek and S. Swain, “Simulating quantum interference in a three-level system with perpendicular transition dipole moments,” Phys. Rev. A 69, 023401 (2004).

2002 (1)

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).

2001 (1)

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).

2000 (2)

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84(24), 5500–5503 (2000).
[PubMed]

1999 (1)

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).

1998 (3)

W. D. Phillips, “Nobel lecture: Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

E. Paspalakis and P. L. Knight, “Phase Control of Spontaneous Emission,” Phys. Rev. Lett. 81, 293–296 (1998).

1996 (1)

S. Y. Zhu and M. O. Scully, “Spectral Line Elimination and Spontaneous Emission Cancellation via Quantum Interference,” Phys. Rev. Lett. 76(3), 388–391 (1996).
[PubMed]

1995 (1)

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74(20), 4091–4094 (1995).
[PubMed]

1977 (1)

R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

Agarwal, G. S.

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84(24), 5500–5503 (2000).
[PubMed]

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).

Berggren, K. K.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Cao, Z.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Cheng, S. C.

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

Chu, A. P.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Cirac, J. I.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74(20), 4091–4094 (1995).
[PubMed]

Dekker, N. H.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Ding, C.

C. Ding, J. Li, R. Yu, X. Hao, and Y. Wu, “High-precision atom localization via controllable spontaneous emission in a cycle-configuration atomic system,” Opt. Express 20(7), 7870–7885 (2012).
[PubMed]

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

Ding, Y.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

Ezekiel, S.

R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

Ficek, Z.

Z. Ficek and S. Swain, “Simulating quantum interference in a three-level system with perpendicular transition dipole moments,” Phys. Rev. A 69, 023401 (2004).

Gao, J. Y.

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of 85Rb atoms,” Opt. Lett. 33(7), 687–689 (2008).
[PubMed]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

Ghafoor, F.

F. Ghafoor, “Subwavelength atom localization via quantum coherence in a three-level atomic system,” Phys. Rev. A 84, 063849 (2011).

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).

Grove, R. E.

R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

Hao, X.

Hsieh, W. F.

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

Jiang, X. Q.

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

Johnson, K. S.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Kang, Z. H.

Kapale, K. T.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

Knight, P. L.

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).

E. Paspalakis and P. L. Knight, “Phase Control of Spontaneous Emission,” Phys. Rev. Lett. 81, 293–296 (1998).

Kou, J.

R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).

Li, A. J.

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

C. L. Wang, A. J. Li, X. Y. Zhou, Z. H. Kang, J. Yun, and J. Y. Gao, “Investigation of spontaneously generated coherence in dressed states of 85Rb atoms,” Opt. Lett. 33(7), 687–689 (2008).
[PubMed]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

Li, J.

C. Ding, J. Li, R. Yu, X. Hao, and Y. Wu, “High-precision atom localization via controllable spontaneous emission in a cycle-configuration atomic system,” Opt. Express 20(7), 7870–7885 (2012).
[PubMed]

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

Lu, Z. W.

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

Mehmood, A.

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).

Paspalakis, E.

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).

E. Paspalakis and P. L. Knight, “Phase Control of Spontaneous Emission,” Phys. Rev. Lett. 81, 293–296 (1998).

Patnaik, A. K.

A. K. Patnaik and G. S. Agarwal, “Cavity-induced coherence effects in spontaneous emissions from preselection of polarization,” Phys. Rev. A 59, 3015–3020 (1999).

Phillips, W. D.

W. D. Phillips, “Nobel lecture: Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).

Prentiss, M.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Qamar, S.

Rahmatullah andS. Qamar, “Two-dimensional atom localization via probe-absorption spectrum,” Phys. Rev. A 88, 013846 (2013).

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).

Sahrai, M.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

Scully, M. O.

S. Y. Zhu and M. O. Scully, “Spectral Line Elimination and Spontaneous Emission Cancellation via Quantum Interference,” Phys. Rev. Lett. 76(3), 388–391 (1996).
[PubMed]

Song, X. L.

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

Sun, X. D.

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

Swain, S.

Z. Ficek and S. Swain, “Simulating quantum interference in a three-level system with perpendicular transition dipole moments,” Phys. Rev. A 69, 023401 (2004).

Tajalli, H.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

Thywissen, J. H.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Wan, R. G.

R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).

R. G. Wan and T. Y. Zhang, “Two-dimensional sub-half-wavelength atom localization via controlled spontaneous emission,” Opt. Express 19(25), 25823–25832 (2011).
[PubMed]

Wang, C. L.

Wang, L.

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

Wang, Z.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Wei, X. G.

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

Wu, F. Y.

R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

Wu, J. H.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

Wu, J. N.

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

Wu, X.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Wu, Y.

Xiong, H.

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

Xu, F.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Yang, T. J.

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

Yang, X.

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

Younkin, R.

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
[PubMed]

Yu, B.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Yu, R.

Yun, J.

Zhan, Z.

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

Zhang, B.

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

Zhang, D.

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

Zhang, T. Y.

R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).

R. G. Wan and T. Y. Zhang, “Two-dimensional sub-half-wavelength atom localization via controlled spontaneous emission,” Opt. Express 19(25), 25823–25832 (2011).
[PubMed]

Zhao, Y. C.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

Zhen, S.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Zhou, X. Y.

Zhu, J.

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Zhu, S. Y.

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).

S. Y. Zhu and M. O. Scully, “Spectral Line Elimination and Spontaneous Emission Cancellation via Quantum Interference,” Phys. Rev. Lett. 76(3), 388–391 (1996).
[PubMed]

Zoller, P.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74(20), 4091–4094 (1995).
[PubMed]

Zubairy, M. S.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).

Ann. Phys. (2)

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Coupled field induced conversion between destructive and constructive quantum interference,” Ann. Phys. 375, 233–238 (2016).

Z. Wang, B. Yu, J. Zhu, Z. Cao, S. Zhen, X. Wu, and F. Xu, “Atom localization via controlled spontaneous emission in a five-level atomic system,” Ann. Phys. 327, 1132–1145 (2012).

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (17)

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).

Z. Ficek and S. Swain, “Simulating quantum interference in a three-level system with perpendicular transition dipole moments,” Phys. Rev. A 69, 023401 (2004).

A. J. Li, X. L. Song, X. G. Wei, L. Wang, and J. Y. Gao, “Effects of spontaneously generated coherence in a microwave-driven four-level atomic system,” Phys. Rev. A 77(5), 053806 (2008).

R. E. Grove, F. Y. Wu, and S. Ezekiel, “Measurement of the spectrum of resonance fluorescence from a two-level atom in an intense monochromatic field,” Phys. Rev. A 15, 227–233 (1977).

C. Ding, J. Li, Z. Zhan, and X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83, 063834 (2011).

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).

F. Ghafoor, “Subwavelength atom localization via quantum coherence in a three-level atomic system,” Phys. Rev. A 84, 063849 (2011).

S. C. Cheng, J. N. Wu, T. J. Yang, and W. F. Hsieh, “Effect of atomic position on the spontaneous emission of a three-level atom in a coherent photonic-band-gap reservoir,” Phys. Rev. A 79, 013801 (2009).

X. Q. Jiang, B. Zhang, Z. W. Lu, and X. D. Sun, “Control of spontaneous emission from a microwave-field-coupled three-level Λ-type atom in photonic crystals,” Phys. Rev. A 83, 053823 (2011).

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S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).

C. Ding, J. Li, X. Yang, D. Zhang, and H. Xiong, “Proposal for efficient two-dimensional atom localization using probe absorption in a microwave-driven four-level atomic system,” Phys. Rev. A 84, 043840 (2011).

R. G. Wan, T. Y. Zhang, and J. Kou, “Two-dimensional sub-half-wavelength atom localization via phase control of absorption and gain,” Phys. Rev. A 87, 043816 (2013).

Rahmatullah andS. Qamar, “Two-dimensional atom localization via probe-absorption spectrum,” Phys. Rev. A 88, 013846 (2013).

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).

Phys. Rev. Lett. (4)

S. Y. Zhu and M. O. Scully, “Spectral Line Elimination and Spontaneous Emission Cancellation via Quantum Interference,” Phys. Rev. Lett. 76(3), 388–391 (1996).
[PubMed]

E. Paspalakis and P. L. Knight, “Phase Control of Spontaneous Emission,” Phys. Rev. Lett. 81, 293–296 (1998).

G. S. Agarwal, “Anisotropic vacuum-induced interference in decay channels,” Phys. Rev. Lett. 84(24), 5500–5503 (2000).
[PubMed]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74(20), 4091–4094 (1995).
[PubMed]

Rev. Mod. Phys. (1)

W. D. Phillips, “Nobel lecture: Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).

Science (1)

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280(5369), 1583–1586 (1998).
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Figures (4)

Fig. 1
Fig. 1

Schematic diagrams (a) An atom moving alongzaxis and passing through the two orthogonal standing-wave fields in xyplane, (b) Coherently driven M-type five-level atomic system.

Fig. 2
Fig. 2

The conditional position probability distribution versus the position (x,y)for different values of the detuning of spontaneously emitted photon when p=0and a 1 (0)= a 2 (0)= 2 /2. (a) δ k =3.2Γ, (b) δ k =3.53Γ, (c) three-dimensional plot associated with (a), (d) three-dimensional plot associated with (b), other parameters are ω 34 =2Γ, Γ 1 = Γ 2 =Γ, Ω 10 =2Γ, Ω 2 =4Γ, Ω c =Γ.

Fig. 3
Fig. 3

The conditional position probability distribution versus the position (x,y)for different values of the detuning of spontaneously emitted photon when p=1and a 1 (0)= a 2 (0)= 2 /2. (a) δ k =2.0Γ, (b) δ k =1.5Γ, (c) δ k =1.9Γ, (d) δ k =3.96Γ, other parameters are ω 34 =2Γ, Γ 1 = Γ 2 =Γ, Ω 10 =Γ, Ω 2 =4Γ, Ω c =Γ.

Fig. 4
Fig. 4

The influence of microwave coupling field on the conditional position probability distribution versus the position (x,y) p=1and a 1 (0)= a 2 (0)= 2 /2. (a) Ω c =Γ, δ k =3.96Γ, (b) Ω c =0.5Γ, δ k =1.99Γ, (c) three-dimension plot associated with (a), (d) three-dimension plot associated with (b), other parameters are ω 34 =2Γ, Γ 1 = Γ 2 =Γ, Ω 10 =Γ, Ω 2 =4Γ.

Equations (27)

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H int = Ω 1 (x,y)|13|+ Ω 2 |24|+ Ω c |34| + k g 3k exp(i( ω k ω 30 )t)|30| b k + k g 4k exp(i( ω k ω 40 )t)|40| b k +H.c.
| ψ(t)= dxdyf(x,y) | x,y [ a 1 (t)| 1,0+ a 2 (t)| 2,0+ a 3 (t)| 3,0+ a 4 (t)| 4,0+ k a k (t)| 0, 1 k ]
P( x,y )P( x,y;t| 0, 1 k )= N 2 | f(x,y) | 2 | a k (t) | 2
P ( x , y ) = N 2 | f ( x , y ) | 2 | a k ( t ) | 2 .
a ˙ 1 (t)=i Ω 1 (x,y) a 3 (t)
a ˙ 2 (t)=i Ω 2 a 4 (t)
a ˙ 3 (t)=i Ω 1 (x,y) a 1 (t)i Ω c a 4 (t) Γ 1 2 a 3 (t)p Γ 1 Γ 2 2 a 4 (t) e i ω 34 t
a ˙ 4 (t)=i Ω 2 a 2 (t)i Ω c a 3 (t) Γ 2 2 a 4 (t)p Γ 1 Γ 2 2 a 3 (t) e i ω 34 t
a ˙ k (t)=i g 3k e i( ω k ω 30 )t a 3 (t)i g 4k e i( ω k ω 40 )t a 4 (t)
s a 1 (s) a 1 (0)=i Ω 1 (x,y) a 3 (s)
s a 2 (s) a 2 (0)=i Ω 2 a 4 (s)
s a 3 (s) a 3 (0)=i Ω 1 (x,y) a 1 (s)i Ω c a 4 (s) Γ 1 2 a 3 (s)p Γ 1 Γ 2 2 a 4 (si ω 34 )
s a 4 (s) a 4 (0)=i Ω 2 a 2 (s)i Ω c a 3 (s) Γ 2 2 a 4 (s)p Γ 1 Γ 2 2 a 3 (s+i ω 34 )
(s+i δ k ) c k (s)=i g 3k a 3 (s+i ω 34 /2)i g 4k a 4 (si ω 34 /2)
a 3 (s)= B(s) A(s) + C(s) A(s) a 3 (s+i ω 34 )+ D(s) A(s) a 3 (si ω 34 )
a 4 (s)= F(s) E(s) + G(s) E(s) a 4 (s+i ω 34 )+ H(s) E(s) a 4 (si ω 34 )
A ( s ) = s ( s + Γ 1 2 ) + Ω 1 2 ( x , y ) + s 2 Ω c 2 s ( s + Γ 2 / 2 ) + Ω 2 2 p 2 Γ 1 Γ 2 s ( s i ω 34 ) / 4 ( s i ω 34 ) ( s i ω 34 + Γ 2 / 2 ) + Ω 2 2
B ( s ) = s a 3 ( 0 ) i Ω 1 ( x , y ) a 1 ( 0 ) i Ω c s 2 a 4 ( 0 ) i Ω 2 s a 2 ( 0 ) s ( s + Γ 2 / 2 ) + Ω 2 2 + p Γ 1 Γ 2 2 s [ i Ω 2 a 2 ( 0 ) ( s i ω 34 ) a 4 ( 0 ) ] ( s i ω 34 ) ( s i ω 34 + Γ 2 / 2 ) + Ω 2 2
C ( s ) = i p s 2 Ω c Γ 1 Γ 2 / 2 s ( s + Γ 2 / 2 ) + Ω 2 2
D ( s ) = p Γ 1 Γ 2 2 i Ω c s ( s i ω 34 ) ( s i ω 34 ) ( s i ω 34 + Γ 2 / 2 ) + Ω 2 2
E ( s ) = s ( s + Γ 2 2 ) + Ω 2 2 + s 2 Ω c 2 s ( s + Γ 1 / 2 ) + Ω 1 2 ( x , y ) p 2 Γ 1 Γ 2 s ( s + i ω 34 ) / 4 ( s + i ω 34 ) ( s + i ω 34 + Γ 1 / 2 ) + Ω 1 2 ( x , y )
F ( s ) = i Ω 2 a 2 ( 0 ) + s a 4 ( 0 ) i Ω c s 2 a 3 ( 0 ) i Ω 1 ( x , y ) s a 1 ( 0 ) s ( s + Γ 1 / 2 ) + Ω 1 2 ( x , y ) + p Γ 1 Γ 2 2 s [ i Ω 1 ( x , y ) a 1 ( 0 ) ( s + i ω 34 ) a 3 ( 0 ) ] ( s + i ω 34 ) ( s + i ω 34 + Γ 1 / 2 ) + Ω 1 2 ( x , y )
G ( s ) = i p Γ 1 Γ 2 Ω c s ( s + i ω 34 ) / 2 ( s + i ω 34 ) ( s + i ω 34 + Γ 1 / 2 ) + Ω 1 2 ( x , y )
H ( s ) = i p s 2 Ω c Γ 1 Γ 2 / 2 s ( s + Γ 1 / 2 ) + Ω 1 2 ( x , y )
a 31 (s)= a 30 + C(s) A(s) a 30 (s+i ω 34 )+ D(s) A(s) a 30 (si ω 34 )
a 41 (s)= a 40 + G(s) E(s) a 40 (s+i ω 34 )+ H(s) E(s) a 40 (si ω 34 )
c k (t)= lim si δ k (s+i δ k ) c k (s) =i g 3k a 31 (i δ k +i ω 34 /2)i g 4k a 41 (i δ k i ω 34 /2)