Abstract

A scheme for two-dimensional (2D) subwavelength atom localization is proposed, in which the atom is in a four-level tripod configuration and driven by two orthogonal standing-wave lasers. Because of the spatial dependence of atom–field interaction, the spontaneously emitted photon carries information about the position of the atom in standing-wave fields. We exploit this fact to 2D atom localization conditioned on the measurement of spontaneously emitted photon at a particular frequency, and obtain a high precision and resolution in the position probability distribution. Moreover, an improvement by a factor of 2 in the detecting probability of an atom can be achieved by initially preparing the atom in the coherent population trapping state. Qualitatively, the high- precision, high-resolution atom localization can be attributed to the quantum interference effect between competitive multiple spontaneous decay channels.

© 2011 Optical Society of America

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  1. W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721-741 (1998).
    [CrossRef]
  2. G. P. Collins, “Experimenters produce new Bose-Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49, 18-21 (1996).
    [CrossRef]
  3. K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
    [CrossRef] [PubMed]
  4. K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805 (2003).
    [CrossRef]
  5. P. Storey and M. Collett, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405-418 (1993).
    [CrossRef] [PubMed]
  6. A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
    [CrossRef]
  7. F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
    [CrossRef]
  8. S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27, 115-121(1994).
    [CrossRef]
  9. R. Quadt, M. Collett, and D. F. Walls, “Measurement of atomic motion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74, 351-354 (1995).
    [CrossRef] [PubMed]
  10. S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78, 2038-2041 (1997).
    [CrossRef]
  11. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using Autler-Townes microscopy,” Opt. Commun. 176, 409-416 (2000).
    [CrossRef]
  12. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).
    [CrossRef]
  13. 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).
    [CrossRef]
  14. W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 013830 (2007).
    [CrossRef]
  15. 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).
    [CrossRef]
  16. K. T. Kapale and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum II,” Phys. Rev. A 73, 023813 (2006).
    [CrossRef]
  17. E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
    [CrossRef]
  18. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437-3446(2006).
    [CrossRef]
  19. 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, 2180-2184 (2006).
    [CrossRef]
  20. J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via phase control of a pair of bichromatic fields,” Phys. Rev. A 76, 013830 (2007).
    [CrossRef]
  21. 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, 085508 (2008).
    [CrossRef]
  22. S. Qamar, A. Mehmood, and S. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).
    [CrossRef]
  23. J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(2007).
    [CrossRef]
  24. V. Ivanov and Y. Rozhdestvensky, “Two-dimensional atom localization in a four-level tripod system in laser fields,” Phys. Rev. A 81, 033809 (2010).
    [CrossRef]
  25. D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
    [CrossRef] [PubMed]
  26. S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
    [CrossRef] [PubMed]
  27. 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).
    [CrossRef]
  28. J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
    [CrossRef]
  29. 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, 053806 (2008).
    [CrossRef]
  30. N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
    [CrossRef]

2010 (1)

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

2009 (1)

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

2008 (2)

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, 085508 (2008).
[CrossRef]

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, 053806 (2008).
[CrossRef]

2007 (3)

J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(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, 013830 (2007).
[CrossRef]

W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 013830 (2007).
[CrossRef]

2006 (4)

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

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437-3446(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, 2180-2184 (2006).
[CrossRef]

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[CrossRef]

2005 (2)

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

2003 (1)

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

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).
[CrossRef]

2001 (1)

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

2000 (2)

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

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

1999 (1)

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
[CrossRef]

1998 (2)

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

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [PubMed]

1997 (2)

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

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

1996 (2)

A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
[CrossRef]

G. P. Collins, “Experimenters produce new Bose-Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49, 18-21 (1996).
[CrossRef]

1995 (2)

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

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
[CrossRef] [PubMed]

1994 (1)

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

1993 (1)

P. Storey and M. Collett, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

1991 (1)

D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
[CrossRef] [PubMed]

Agarwal, G. S.

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

Berggren, K. K.

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [PubMed]

Carmichael, H. J.

A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
[CrossRef]

Chen, A. X.

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[CrossRef]

Cheng, D. C.

Chu, A. P.

K. S. Johnson, J. H. Thywissen, W. 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, 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, 351-354 (1995).
[CrossRef] [PubMed]

P. Storey and M. Collett, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

Collins, G. P.

G. P. Collins, “Experimenters produce new Bose-Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49, 18-21 (1996).
[CrossRef]

Dekker, W. H.

K. S. Johnson, J. H. Thywissen, W. 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, 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, 2038-2041 (1997).
[CrossRef]

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).
[CrossRef]

Evers, J.

J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(2007).
[CrossRef]

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, 053806 (2008).
[CrossRef]

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).
[CrossRef]

Gauthier, D. J.

D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
[CrossRef] [PubMed]

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, 043819 (2002).
[CrossRef]

Gong, S. Q.

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, 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, 2180-2184 (2006).
[CrossRef]

Herkommer, A. M.

A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
[CrossRef]

Hu, X. M.

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

W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 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, 033809 (2010).
[CrossRef]

Jin, L. L.

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, 085508 (2008).
[CrossRef]

Johnson, K. S.

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [PubMed]

Kapale, K. T.

G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437-3446(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, 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, 013820(2005).
[CrossRef]

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

Kienm, F. L.

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

Knight, P. L.

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

Kunze, S.

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

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

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, 053806 (2008).
[CrossRef]

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).
[CrossRef]

Li, J. H.

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[CrossRef]

Li, R. X.

Liu, J. B.

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[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, 033848 (2009).
[CrossRef]

Mossberg, T. W.

D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
[CrossRef] [PubMed]

Narducci, L. M.

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
[CrossRef] [PubMed]

Niu, Y. P.

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, 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, 2180-2184 (2006).
[CrossRef]

Paspalakis, E.

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

Phillips, W. D.

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

Prentiss, M.

K. S. Johnson, J. H. Thywissen, W. 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, 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, 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, 033848 (2009).
[CrossRef]

J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(2007).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 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, 043819 (2002).
[CrossRef]

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

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

Qi, C. C.

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[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, 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, 2038-2041 (1997).
[CrossRef]

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27, 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, 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, 013820(2005).
[CrossRef]

Schleich, W. P.

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
[CrossRef]

Scully, M. O.

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
[CrossRef] [PubMed]

Shen, W. B.

W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 013830 (2007).
[CrossRef]

Shore, B. W.

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
[CrossRef]

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, 053806 (2008).
[CrossRef]

Storey, P.

P. Storey and M. Collett, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

Sun, H.

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, 085508 (2008).
[CrossRef]

Suominen, K. A.

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
[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, 013820(2005).
[CrossRef]

Thywissen, J. H.

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [PubMed]

Vitanov, N. V.

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
[CrossRef]

Walls, D. F.

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

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, 053806 (2008).
[CrossRef]

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, 053806 (2008).
[CrossRef]

Wilkens, M.

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

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).
[CrossRef]

Xu, J.

W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 013830 (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, 013830 (2007).
[CrossRef]

Younkin, R.

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [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).
[CrossRef]

Zhu, S. Y.

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

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

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
[CrossRef] [PubMed]

Zhu, Y.

D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
[CrossRef] [PubMed]

Zubairy, M. S.

J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(2007).
[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, 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, 013820(2005).
[CrossRef]

K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 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, 043819 (2002).
[CrossRef]

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

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

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

Europhys. Lett. (1)

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

J. Opt. Soc. Am. B (1)

J. Phys. B (3)

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

N. V. Vitanov, K. A. Suominen, and B. W. Shore, “Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage,” J. Phys. B 32, 4535 (1999).
[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, 085508 (2008).
[CrossRef]

Opt. Commun. (1)

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

Phys. Rev. A (17)

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 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, 043819 (2002).
[CrossRef]

W. B. Shen, X. M. Hu, and J. Xu, “Sub-half-wavelength atom localization via coherence-controlled resonance fluorescence,” Phys. Rev. A 76, 013830 (2007).
[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, 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, 023813 (2006).
[CrossRef]

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

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

J. Evers, S. Qamar, and M. S. Zubairy, “Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements,” Phys. Rev. A 75, 053809(2007).
[CrossRef]

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

F. L. Kienm, G. Rempe, W. P. Schleich, and M. S. Zubairy, “Atom localization via Ramsey interferometry: a coherent cavity field provides a better resolution,” Phys. Rev. A 56, 2972-2977 (1997).
[CrossRef]

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

P. Storey and M. Collett, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

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

S. Y. Zhu, L. M. Narducci, and M. O. Scully, “Quantum-mechanical interference effects in the spontaneous-emission spectrum of a driven atom,” Phys. Rev. A 52, 4791-4802 (1995).
[CrossRef] [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).
[CrossRef]

J. H. Li, J. B. Liu, A. X. Chen, and C. C. Qi, “Spontaneous emission spectra and simulating multiple spontaneous generation coherence in a five-level atomic medium,” Phys. Rev. A 74, 033816 (2006).
[CrossRef]

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, 053806 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

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

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

D. J. Gauthier, Y. Zhu, and T. W. Mossberg, “Observation of linewidth narrowing due to coherent stabilization of quantum fluctuations,” Phys. Rev. Lett. 66, 2460-2463 (1991).
[CrossRef] [PubMed]

Phys. Today (1)

G. P. Collins, “Experimenters produce new Bose-Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49, 18-21 (1996).
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A. M. Herkommer, H. J. Carmichael, and W. P. Schleich, “Localization of an atom by homodyne measurement,” Quantum Semiclass. Opt. 8, 189-203 (1996).
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W. D. Phillips, “Nobel lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721-741 (1998).
[CrossRef]

Science (1)

K. S. Johnson, J. H. Thywissen, W. 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, 1583-1586 (1998).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagrams: (a) Atom moving along the z axis and interacting with two orthogonal standing-wave fields aligned along the x and y directions, respectively. (b) Energy structure of the atom, in which the two standing-wave fields couple the | 0 | 1 and | 0 | 2 transitions, and the transition | 0 | j is coupled to vacuum modes in the free space.

Fig. 2
Fig. 2

Positions of peak maxima of F ( x , y ) , i.e., the solutions of Eq. (10), as a function of ( k 1 x , k 2 y ) in dependence on the detuning of spontaneously emitted photon. (a) δ k = 6 ; (b) δ k = 10 ; (c) δ k = 12 . Other parameters are as follows: Γ 0 = 2 , Ω 1 = 10 , Ω 2 = 10 , Δ 1 = 0 , and Δ 2 = 0 . The atom is initially in Ψ ( 0 ) = | 0 .

Fig. 3
Fig. 3

Filter function F ( x , y ) , which directly reflects the conditional position probability distribution, as a function of ( k 1 x , k 2 y ) in dependence on the detuning of spontaneously emitted photon. (a) δ k = 6 ; (b) δ k = 10 ; (c) δ k = 10 ; (d) δ k = 10 2 . The spatial distributions of the position probability represent such 3D periodic structures with (a) craterlike pattern, (b) latticelike pattern, (c) craterlike pattern, and (d) spikelike pattern. Other parameters are the same as Fig. 2.

Fig. 4
Fig. 4

Filter function F ( x , y ) as a function of ( k 1 x , k 2 y ) . In (a), δ k = 0 , Δ 1 = 5 , and Δ 2 = 5 , the atom is localized at intersections of the nodes, where sin ( k 1 x ) = 0 and sin ( k 2 y ) = 0 . In (b), δ k = 35.6 , Δ 1 = 30 , and Δ 2 = 30 , the atom is localized at intersections at the antinodes, where sin ( k 1 x ) = 1 and sin ( k 2 y ) = 1 . Other parameters are the same as Fig. 2.

Fig. 5
Fig. 5

Filter function F ( x , y ) as a function of ( k 1 x , k 2 y ) . All the parameters are the same as Fig. 2, except the atom is initially in Ψ ( 0 ) = ( | 1 | 2 ) / 2 .

Fig. 6
Fig. 6

Density plot of filter function F ( x , y ) shown in Fig. 5.

Fig. 7
Fig. 7

Filter function F ( x , y ) as a function of ( k 1 x , k 2 y ) . All the parameters are the same as Fig. 2, except the atom is initially in Ψ ( 0 ) = ( | 1 + | 2 ) / 2 .

Equations (13)

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H I = Ω 1 sin ( k 1 x ) e i Δ 1 t | 0 1 | + Ω 2 sin ( k 2 y ) e i Δ 2 t | 0 2 | + k g k e i δ k t | 0 j | b k + h.c.
| Ψ ( t ) = d x d y f ( x , y ) | x | y [ C 0 , 0 k ( x , y ; t ) | 0 , 0 k + C 1 , 0 k ( x , y ; t ) | 1 , 0 k + C 2 , 0 k ( x , y ; t ) | 2 , 0 k + k C j , 1 k ( x , y ; t ) | j , 1 k ] ,
| ψ j , 1 k = N j , 1 k | Ψ ( t ) = N d x d y f ( x , y ) C j , 1 k ( x , y ; t ) | x | y ,
W ( x , y ; t | j , 1 k ) = | N | 2 | x | y | ψ j , 1 k | 2 = | N | 2 | C j , 1 k ( x , y ; t ) | 2 | f ( x , y ) | 2 ,
i C ˙ 0 , 0 k ( t ) = Ω 1 sin ( k 1 x ) e i Δ 1 t C 1 , 0 k ( t ) + Ω 2 sin ( k 2 y ) e i Δ 2 t C 2 , 0 k ( t ) i Γ 0 2 C 0 , 0 k ( t ) ,
i C ˙ 1 , 0 k ( t ) = Ω 1 sin ( k 1 x ) e i Δ 1 t C 0 , 0 k ( t ) ,
i C ˙ 2 , 0 k ( t ) = Ω 2 sin ( k 2 y ) e i Δ 2 t C 0 , 0 k ( t ) ,
i C ˙ j , 1 k ( t ) = g k * e i δ k t C 0 , 0 k ( t ) ,
C j , 1 k ( x , y ; t ) = i g k * C ˜ 0 , 0 k ( s = i δ k ) = g k * · C 0 , 0 k ( 0 ) + Ω 1 sin ( k 1 x ) δ k Δ 1 C 1 , 0 k ( 0 ) + Ω 2 sin ( k 2 x ) δ k Δ 2 C 2 , 0 k ( 0 ) δ k + i Γ 0 2 Ω 1 2 sin 2 ( k 1 x ) δ k Δ 1 Ω 2 2 sin 2 ( k 2 y ) δ k Δ 2 ,
W ( x , y ; t | j , 1 k ) = | N | 2 | C j , 1 k ( x , y ; t ) | 2 | f ( x , y ) | 2 = | N | 2 | f ( x , y ) | 2 | g k | 2 · [ C 0 , 0 k ( 0 ) + Ω 1 sin ( k 1 x ) δ k Δ 1 C 1 , 0 k ( 0 ) + Ω 2 sin ( k 2 x ) δ k Δ 2 C 2 , 0 k ( 0 ) ] 2 [ δ k Ω 1 2 sin 2 ( k 1 x ) δ k Δ 1 Ω 2 2 sin 2 ( k 2 y ) δ k Δ 2 ] 2 + Γ 0 2 4 .
F ( x , y ) = [ C 0 , 0 k ( 0 ) + Ω 1 sin ( k 1 x ) δ k Δ 1 C 1 , 0 k ( 0 ) + Ω 2 sin ( k 2 x ) δ k Δ 2 C 2 , 0 k ( 0 ) ] 2 [ δ k Ω 1 2 sin 2 ( k 1 x ) δ k Δ 1 Ω 2 2 sin 2 ( k 2 y ) δ k Δ 2 ] 2 + Γ 0 2 4 .
δ k Ω 1 2 sin 2 ( k 1 x ) δ k Δ 1 Ω 2 2 sin 2 ( k 2 y ) δ k Δ 2 = 0 .
sin 2 ( k 1 x ) + sin 2 ( k 2 y ) = δ k 2 Ω 1 2 .

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