Abstract

We propose a scheme for two-dimensional (2D) atom localization based on the controlled spontaneous emission, in which the atom interacts with two orthogonal standing-wave fields. Due to the spatially dependent atom-field interaction, the position probability distribution of the atom can be directly determined by measuring the resulting spontaneously emission spectrum. The phase sensitive property of the atomic system leads to quenching of the spontaneous emission in some regions of the standing-waves, which significantly reduces the uncertainty in the position measurement of the atom. We find that the frequency measurement of the emitted light localizes the atom in half-wavelength domain. Especially the probability of finding the atom at a particular position can reach 100% when a photon with certain frequency is detected. By increasing the Rabi frequencies of the driving fields, such 2D sub-half-wavelength atom localization can acquire high spatial resolution.

© 2011 OSA

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  1. W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70(3), 721–741 (1998).
    [CrossRef]
  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).
    [CrossRef] [PubMed]
  3. K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
    [CrossRef]
  4. J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
    [CrossRef]
  5. R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74(3), 351–354 (1995).
    [CrossRef] [PubMed]
  6. S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
    [CrossRef]
  7. S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
    [CrossRef]
  8. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
    [CrossRef]
  9. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
    [CrossRef]
  10. F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
    [CrossRef]
  11. J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366(3), 276–281 (2007).
    [CrossRef]
  12. 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(1), 013820 (2005).
    [CrossRef]
  13. K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73(2), 023813 (2006).
    [CrossRef]
  14. E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63(6), 065802 (2001).
    [CrossRef]
  15. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39(17), 3437–3446 (2006).
    [CrossRef]
  16. C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
    [CrossRef]
  17. D. C. Cheng, Y. P. Niu, R. X. Li, and S. Q. Gong, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23(10), 2180–2184 (2006).
    [CrossRef]
  18. J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76(1), 013830 (2007).
    [CrossRef]
  19. S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
    [CrossRef]
  20. V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81(3), 033809 (2010).
    [CrossRef]
  21. L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
    [CrossRef]
  22. R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284(4), 985–990 (2011).
    [CrossRef]
  23. R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via controlled spontaneous emission from a driven tripod system,” J. Opt. Soc. Am. B 28(1), 10–17 (2011).
    [CrossRef]
  24. C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
    [CrossRef]
  25. R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via interacting double-dark resonances,” J. Opt. Soc. Am. B 28(4), 622–628 (2011).
    [CrossRef]
  26. C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
    [CrossRef]
  27. L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
    [CrossRef]
  28. F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
    [CrossRef]

2011

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284(4), 985–990 (2011).
[CrossRef]

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via controlled spontaneous emission from a driven tripod system,” J. Opt. Soc. Am. B 28(1), 10–17 (2011).
[CrossRef]

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via interacting double-dark resonances,” J. Opt. Soc. Am. B 28(4), 622–628 (2011).
[CrossRef]

2010

V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81(3), 033809 (2010).
[CrossRef]

2009

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
[CrossRef]

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
[CrossRef]

2008

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
[CrossRef]

2007

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366(3), 276–281 (2007).
[CrossRef]

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76(1), 013830 (2007).
[CrossRef]

2006

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39(17), 3437–3446 (2006).
[CrossRef]

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73(2), 023813 (2006).
[CrossRef]

D. C. Cheng, Y. P. Niu, R. X. Li, and S. Q. Gong, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23(10), 2180–2184 (2006).
[CrossRef]

2005

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(1), 013820 (2005).
[CrossRef]

2003

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
[CrossRef]

2002

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
[CrossRef]

2001

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63(6), 065802 (2001).
[CrossRef]

2000

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
[CrossRef]

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
[CrossRef]

1998

W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70(3), 721–741 (1998).
[CrossRef]

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).
[CrossRef] [PubMed]

1997

S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
[CrossRef]

1995

R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74(3), 351–354 (1995).
[CrossRef] [PubMed]

1994

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39(17), 3437–3446 (2006).
[CrossRef]

Ahufinger, V.

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
[CrossRef]

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).
[CrossRef] [PubMed]

Birkl, G.

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
[CrossRef]

Cheng, D. C.

D. C. Cheng, Y. P. Niu, R. X. Li, and S. Q. Gong, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23(10), 2180–2184 (2006).
[CrossRef]

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

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).
[CrossRef] [PubMed]

Collett, M.

R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74(3), 351–354 (1995).
[CrossRef] [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).
[CrossRef] [PubMed]

Dieckmann, K.

S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
[CrossRef]

Ding, C. L.

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

Fan, X. J.

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

Gao, J. Y.

Ghafoor, F.

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
[CrossRef]

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
[CrossRef]

Gong, S. Q.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
[CrossRef]

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

D. C. Cheng, Y. P. Niu, R. X. Li, and S. Q. Gong, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23(10), 2180–2184 (2006).
[CrossRef]

Hu, X. M.

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366(3), 276–281 (2007).
[CrossRef]

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76(1), 013830 (2007).
[CrossRef]

Ivanov, V.

V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81(3), 033809 (2010).
[CrossRef]

Jiang, L.

Jiang, Y.

Jin, L. L.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
[CrossRef]

Jin, S. Q.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

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).
[CrossRef] [PubMed]

Kapale, K. T.

K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73(2), 023813 (2006).
[CrossRef]

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39(17), 3437–3446 (2006).
[CrossRef]

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(1), 013820 (2005).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
[CrossRef]

Knight, P. L.

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63(6), 065802 (2001).
[CrossRef]

Kou, J.

Kunze, S.

S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
[CrossRef]

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
[CrossRef]

Li, J. H.

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

Li, R. X.

Liu, C. P.

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

Liu, J. B.

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

Mehmood, A.

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
[CrossRef]

Mompart, J.

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
[CrossRef]

Niu, Y. P.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
[CrossRef]

D. C. Cheng, Y. P. Niu, R. X. Li, and S. Q. Gong, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23(10), 2180–2184 (2006).
[CrossRef]

Paspalakis, E.

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63(6), 065802 (2001).
[CrossRef]

Phillips, W. D.

W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70(3), 721–741 (1998).
[CrossRef]

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).
[CrossRef] [PubMed]

Qamar, S.

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
[CrossRef]

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
[CrossRef]

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
[CrossRef]

Quadt, R.

R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74(3), 351–354 (1995).
[CrossRef] [PubMed]

Rempe, G.

S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
[CrossRef]

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
[CrossRef]

Rozhdestvensky, Y.

V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81(3), 033809 (2010).
[CrossRef]

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(1), 013820 (2005).
[CrossRef]

Sun, H.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
[CrossRef]

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(1), 013820 (2005).
[CrossRef]

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).
[CrossRef] [PubMed]

Walls, D. F.

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S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
[CrossRef]

Xu, J.

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76(1), 013830 (2007).
[CrossRef]

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366(3), 276–281 (2007).
[CrossRef]

Xu, Z. Z.

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

Yang, X. X.

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

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).
[CrossRef] [PubMed]

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C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

Zhu, S. Y.

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
[CrossRef]

Zubairy, M. S.

K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73(2), 023813 (2006).
[CrossRef]

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(1), 013820 (2005).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
[CrossRef]

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
[CrossRef]

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
[CrossRef]

Europhys. Lett.

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27(2), 115–121 (1994).
[CrossRef]

J. Mod. Opt.

L. L. Jin, H. Sun, Y. P. Niu, S. Q. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56(6), 805–810 (2009).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

C. L. Ding, J. H. Li, X. X. Yang, Z. M. Zhang, and J. B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44(14), 145501 (2011).
[CrossRef]

L. L. Jin, H. Sun, Y. P. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41(8), 085508 (2008).
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G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39(17), 3437–3446 (2006).
[CrossRef]

Opt. Commun.

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler–Townes microscopy,” Opt. Commun. 176(4-6), 409–416 (2000).
[CrossRef]

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284(4), 985–990 (2011).
[CrossRef]

Phys. Lett. A

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366(3), 276–281 (2007).
[CrossRef]

Phys. Rev. A

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(1), 013820 (2005).
[CrossRef]

K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73(2), 023813 (2006).
[CrossRef]

E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63(6), 065802 (2001).
[CrossRef]

C. P. Liu, S. Q. Gong, D. C. Cheng, X. J. Fan, and Z. Z. Xu, “Atom localization via interference of dark resonances,” Phys. Rev. A 73(2), 025801 (2006).
[CrossRef]

J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76(1), 013830 (2007).
[CrossRef]

S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79(3), 033848 (2009).
[CrossRef]

V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81(3), 033809 (2010).
[CrossRef]

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61(6), 063806 (2000).
[CrossRef]

F. Ghafoor, S. Qamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65(4), 043819 (2002).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67(2), 023805 (2003).
[CrossRef]

J. Mompart, V. Ahufinger, and G. Birkl, “Coherent pattern of matter waves with subwavelength localization,” Phys. Rev. A 79(5), 053638 (2009).
[CrossRef]

C. L. Ding, J. H. Li, Z. M. Zhang, and X. X. Yang, “Two-dimensional atom localization via spontaneous emission in a coherently driven five-level M-type atomic system,” Phys. Rev. A 83(6), 063834 (2011).
[CrossRef]

F. Ghafoor, S. Y. Zhu, and M. S. Zubairy, “Amplitude and phase control of spontaneous emission,” Phys. Rev. A 62(1), 013811 (2000).
[CrossRef]

Phys. Rev. Lett.

R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74(3), 351–354 (1995).
[CrossRef] [PubMed]

S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78(11), 2038–2041 (1997).
[CrossRef]

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W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70(3), 721–741 (1998).
[CrossRef]

Science

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).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagrams: (a) An atom moves along the z axis and interacting with two orthogonal standing-wave fields in the xy plane. (b) Four-level atomic system. Levels |0 , |1 and |2 are driven by three fields Ω 1 , Ω 2 and Ω c , and then form a closed loop. Δ k = ω k ( ω 1j + ω 2j ) /2 is the detuning of the spontaneously emitted photon with frequency ω k from the average atomic transition frequency ( ω 10 + ω 20 ) /2 .

Fig. 2
Fig. 2

The spontaneous emission S( Δ k ;x,y) (in arbitrary unit) which directly describes the conditional position probability distribution as a function of (kx,ky) in dependence on the detuning of the spontaneously emitted photon when ϕ=π/2 . (a) Δ k =10 ; (b) Δ k =4.2 ; (c) Δ k =3.5 ; (d) Δ k =3 . Other parameters are Γ 1 =1 , Γ 2 =1 , Ω 10 =2 , Ω 2 =4 , Ω c =4 , δ=10 , Δ 1 =δ and Δ 2 =δ .

Fig. 3
Fig. 3

The spontaneous emission S( Δ k ;x,y) (in arbitrary unit) which directly describes the conditional position probability distribution as a function of (kx,ky) in dependence on the detuning of the spontaneously emitted photon when ϕ=0 . (a) Δ k =10 ; (b) Δ k =9 ; (c) Δ k =7 ; (d) Δ k =6 . Other parameters are the same as Fig. 2.

Fig. 4
Fig. 4

The spontaneous emission S( Δ k ) as a function of Ω 1 . In (a) ϕ=π/2 and (b) ϕ=0 . (c) and (d) are the density plots of (a) and (b). Other parameters are the same as Fig. 2.

Fig. 5
Fig. 5

The spontaneous emission S( Δ k ;x,y) (in arbitrary unit) which directly describes the conditional position probability distribution as a function of (kx,ky) in dependence on the detuning of the spontaneously emitted photon. Parameters are Δ k =4 , Ω 10 =3 , Ω 2 =6 , Ω c =6 , and ϕ=0 (a); ϕ=π (b). Other parameters are the same as Fig. 2.

Equations (13)

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

H int = Ω 1 (x,y) e i( Δ 1 +δ)t |01|+ Ω 2 e i( Δ 2 δ)t |02|+ Ω c e iϕ e i( Δ 2 Δ 1 2δ)t |12| + k [ g k1 e i( Δ k +δ)t b k |j1|+ g k2 e i( Δ k δ)t b k |j2|] +H.c.,
| ψ(t) = dxdyf(x,y)| x,y {[ a 0 (t)|0+ a 1 (t) e i( Δ 1 +δ)t |1+ a 2 (t) e i( Δ 2 δ)t |1]| {0} + k a jk (t)|j| 1 k },
| ψ j, 1 k =N j, 1 k | ψ(t) =N dxdyf(x,y) a jk (t)|x|y ,
W(x,y;t|j, 1 k )= | N | 2 | x|y| ψ j, 1 k | 2 = | N | 2 | f(x,y) | 2 | a jk (t) | 2 .
a ˙ 0 (t)=i Ω 1 (x,y) a 1 (t)i Ω 2 a 2 (t),
a ˙ 1 (t)=[i( Δ 1 +δ) Γ 1 2 ] a 1 (t)i Ω 1 (x,y) a 0 (t)i Ω c e iϕ a 2 (t),
a ˙ 2 (t)=[i( Δ 2 δ) Γ 2 2 ] a 2 (t)i Ω 2 a 0 (t)i Ω c e iϕ a 1 (t),
a ˙ jk (t)=i g k1 e i( Δ k Δ 1 )t a 1 (t)i g k2 e i( Δ k Δ 2 )t a 2 (t),
a jk (t)=i g k1 a ˜ 1 [s=i( Δ k Δ 1 )]i g k2 a ˜ 2 [s=i( Δ k Δ 2 )],
S( Δ k ;x,y) Γ 1 | a ˜ 1 [s=i( Δ k +δ)] | 2 + Γ 2 | a 2 [s=i( Δ k δ)] | 2 ,
a ˜ 1 [s=i( Δ k +δ)]= Ω 1 (x,y)( Δ k +δ+i Γ 2 2 )+ Ω 2 Ω c e iϕ A + ( Δ k ) ,
a ˜ 2 [s=i( Δ k δ)]= Ω 2 ( Δ k δ+i Γ 1 2 )+ Ω 1 (x,y) Ω c e iϕ A ( Δ k ) ,
A ± ( Δ k )=( Δ k ±δ)( Δ k ±δ+i Γ 1 2 )( Δ k ±δ+i Γ 2 2 ) Ω 1 2 (x,y)( Δ k ±δ+i Γ 2 2 ) Ω 2 2 ( Δ k ±δ+i Γ 1 2 ) Ω c 2 ( Δ k ±δ)2 Ω 1 (x,y) Ω 2 Ω c cosϕ.

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