Abstract

We propose an atom localization scheme for a tripod-type atom making use of the sharp absorption peak resulting from interacting double-dark resonances. It is demonstrated that the probability of finding the atom at a particular position, as well as the localization precision, can be dramatically enhanced. The probability can be doubled by adjusting the Rabi frequency of the control field to the maximum Rabi frequency of the standing-wave field. Moreover, much better spatial resolution can be achieved for smaller detunings of the control and the standing-wave fields.

© 2006 Optical Society of America

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  1. J. E. Thomas, "Quantum theory of atomic position measurement using optical fields," Phys. Rev. A 42, 5652-5666 (1990).
    [CrossRef] [PubMed]
  2. A. M. Herkommer, V. M. Akulin, and W. P. Schleich, "Quantum demolition measurement of photon statistics by atomic beam deflection," Phys. Rev. Lett. 69, 3298-3301 (1992).
    [CrossRef] [PubMed]
  3. P. Storey, M. Collett, and D. Walls, "Measurement-induced diffraction and interference of atoms," Phys. Rev. Lett. 68, 472-475 (1992).
    [CrossRef] [PubMed]
  4. J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
    [CrossRef] [PubMed]
  5. P. Storey, M. Collett, and D. Walls, "Atomic-position resolution by quadrature-field measurement," Phys. Rev. A 47, 405-418 (1993).
    [CrossRef] [PubMed]
  6. J. E. Thomas and L. J. Wang, "Precision position measurement of moving atoms," Phys. Rep. 262, 311-366 (1995).
    [CrossRef]
  7. 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]
  8. S. Kunze, K. Dieckmann, and G. Rempe, "Diffraction of atoms from a measurement induced grating," Phys. Rev. Lett. 78, 2038-2041 (1997).
    [CrossRef]
  9. F. L. Kien, 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]
  10. H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
    [CrossRef]
  11. S. Qamar, S. Y. Zhu, and M. S. Zubairy, "Atom localization via resonance fluorescence," Phys. Rev. A 61, 063806 (2000).
    [CrossRef]
  12. A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).
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    [CrossRef]
  14. 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]
  15. K. T. Kapale, S. Qamar, and M. S. Zubairy, "Spectroscopic measurement of an atomic wave function," Phys. Rev. A 67, 023805 (2003).
    [CrossRef]
  16. T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
    [CrossRef]
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  23. 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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    [CrossRef]
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    [CrossRef]
  26. S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
    [CrossRef]
  27. N. Mulchan, D. Ducreay, R. Pina, M. Yan, and Y. Zhu, "Nonlinear excitation by quantum interference in a Doppler-broadened rubidium atomic system," J. Opt. Soc. Am. B 17, 820-826 (2000).
    [CrossRef]
  28. G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (2001).
    [CrossRef]
  29. E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
    [CrossRef]
  30. S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
    [CrossRef]
  31. Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
    [CrossRef]
  32. S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
    [CrossRef]
  33. E. Paspalakis and P. L. Knight, "Transparency and parametric generation in a four-level system," J. Mod. Opt. 49, 87-95 (2002).
    [CrossRef]
  34. E. Paspalakis and P. L. Knight, "Transparency, slow light and enhanced nonlinear optics in a four-level scheme," J. Opt. B: Quantum Semiclassical Opt. 4, S372-S375 (2002).
    [CrossRef]
  35. E. Paspalakis and P. L. Knight, "Electromagnetically induced transparency and controlled group velocity in a multilevel system," Phys. Rev. A 66, 015802 (2002).
    [CrossRef]
  36. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
    [CrossRef]
  37. Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, "Giant Kerr nonlinearity induced by interacting dark resonances," Opt. Lett. 30, 3371-3373 (2005).
    [CrossRef]
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    [CrossRef]
  40. H. R. Gray, R. M. Whitley, and C. R. Stroud, Jr., "Coherent trapping of atomic populations," Opt. Lett. 3, 218-220 (1978).
    [CrossRef] [PubMed]
  41. R. Blatt and P. Zoller, "Quantum jumps in atomic systems," Eur. J. Phys. 9, 250-256 (1988).
    [CrossRef]
  42. J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
    [CrossRef]
  43. J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
    [CrossRef]
  44. S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
    [CrossRef]

2006 (1)

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]

2005 (3)

E. Paspalakis, A. F. Terzis, and P. L. Knight, "Quantum interference induced sub-wavelength atomic localization," J. Mod. Opt. 52, 1685-1694 (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]

Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, "Giant Kerr nonlinearity induced by interacting dark resonances," Opt. Lett. 30, 3371-3373 (2005).
[CrossRef]

2004 (4)

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
[CrossRef]

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
[CrossRef]

T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
[CrossRef]

2003 (2)

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

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

2002 (7)

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, "Unexpected Doppler-free resonance in generalized double dark states," Phys. Rev. A 65, 043805 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency and parametric generation in a four-level system," J. Mod. Opt. 49, 87-95 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency, slow light and enhanced nonlinear optics in a four-level scheme," J. Opt. B: Quantum Semiclassical Opt. 4, S372-S375 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Electromagnetically induced transparency and controlled group velocity in a multilevel system," Phys. Rev. A 66, 015802 (2002).
[CrossRef]

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[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]

H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
[CrossRef]

2001 (3)

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

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (2001).
[CrossRef]

2000 (4)

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

N. Mulchan, D. Ducreay, R. Pina, M. Yan, and Y. Zhu, "Nonlinear excitation by quantum interference in a Doppler-broadened rubidium atomic system," J. Opt. Soc. Am. B 17, 820-826 (2000).
[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]

1999 (1)

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (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 (5)

A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).

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. Kien, 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]

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[CrossRef]

1995 (2)

J. E. Thomas and L. J. Wang, "Precision position measurement of moving atoms," Phys. Rep. 262, 311-366 (1995).
[CrossRef]

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]

1993 (2)

J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
[CrossRef] [PubMed]

P. Storey, M. Collett, and D. Walls, "Atomic-position resolution by quadrature-field measurement," Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

1992 (2)

A. M. Herkommer, V. M. Akulin, and W. P. Schleich, "Quantum demolition measurement of photon statistics by atomic beam deflection," Phys. Rev. Lett. 69, 3298-3301 (1992).
[CrossRef] [PubMed]

P. Storey, M. Collett, and D. Walls, "Measurement-induced diffraction and interference of atoms," Phys. Rev. Lett. 68, 472-475 (1992).
[CrossRef] [PubMed]

1990 (1)

J. E. Thomas, "Quantum theory of atomic position measurement using optical fields," Phys. Rev. A 42, 5652-5666 (1990).
[CrossRef] [PubMed]

1988 (1)

R. Blatt and P. Zoller, "Quantum jumps in atomic systems," Eur. J. Phys. 9, 250-256 (1988).
[CrossRef]

1978 (1)

1976 (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. T. Kapale, "Extreme subwavelength atom localization via coherent population trapping," arXiv.org e-Print archive, quantum-ph/05090682005, http://arxiv.org/pdf/quant-ph/0505014.

Akulin, V. M.

A. M. Herkommer, V. M. Akulin, and W. P. Schleich, "Quantum demolition measurement of photon statistics by atomic beam deflection," Phys. Rev. Lett. 69, 3298-3301 (1992).
[CrossRef] [PubMed]

Alzetta, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

An, K.

H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
[CrossRef]

Artoni, M.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Azim, T.

T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
[CrossRef]

Baldauf, H. W.

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[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]

Blatt, R.

R. Blatt and P. Zoller, "Quantum jumps in atomic systems," Eur. J. Phys. 9, 250-256 (1988).
[CrossRef]

Cataliotti, F.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Chang, J. S.

H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
[CrossRef]

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, M. Collett, and D. Walls, "Atomic-position resolution by quadrature-field measurement," Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

P. Storey, M. Collett, and D. Walls, "Measurement-induced diffraction and interference of atoms," Phys. Rev. Lett. 68, 472-475 (1992).
[CrossRef] [PubMed]

Corbalán, R.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

de Echaniz, S. R.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[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]

Ducreay, D.

Durrant, A. V.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

Eichler, T.

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Friedmann, H.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
[CrossRef]

Fry, E. S.

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

Gardner, J. R.

J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
[CrossRef] [PubMed]

Gawlik, W.

G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (2001).
[CrossRef]

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.

Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, "Giant Kerr nonlinearity induced by interacting dark resonances," Opt. Lett. 30, 3371-3373 (2005).
[CrossRef]

S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
[CrossRef]

Goren, C.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
[CrossRef]

Gozzini, A.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Gray, H. R.

Greentree, A. D.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

Helmfrid, S. R.

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

Herkommer, A. M.

A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).

A. M. Herkommer, V. M. Akulin, and W. P. Schleich, "Quantum demolition measurement of photon statistics by atomic beam deflection," Phys. Rev. Lett. 69, 3298-3301 (1992).
[CrossRef] [PubMed]

Höffges, J. T.

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[CrossRef]

Ikram, M.

T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
[CrossRef]

Jin, S.

S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
[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.

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]

G. S. Agarwal and K. T. Kapale, "Extreme subwavelength atom localization via coherent population trapping," arXiv.org e-Print archive, quantum-ph/05090682005, http://arxiv.org/pdf/quant-ph/0505014.

Kash, M. M.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Kien, F. L.

F. L. Kien, 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, A. F. Terzis, and P. L. Knight, "Quantum interference induced sub-wavelength atomic localization," J. Mod. Opt. 52, 1685-1694 (2005).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency and parametric generation in a four-level system," J. Mod. Opt. 49, 87-95 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency, slow light and enhanced nonlinear optics in a four-level scheme," J. Opt. B: Quantum Semiclassical Opt. 4, S372-S375 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Electromagnetically induced transparency and controlled group velocity in a multilevel system," Phys. Rev. A 66, 015802 (2002).
[CrossRef]

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

Kowal, Z.

G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (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]

Lange, W.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[CrossRef]

Lee, J. H.

H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
[CrossRef]

Li, R.

Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, "Giant Kerr nonlinearity induced by interacting dark resonances," Opt. Lett. 30, 3371-3373 (2005).
[CrossRef]

S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
[CrossRef]

Li, Y. F.

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[CrossRef]

Liang, X.

Lukin, M. D.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Marable, M. L.

J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
[CrossRef] [PubMed]

Marangos, J. P.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

Meystre, P.

P. Meystre and M. Sargent III, Elements of Quantum Optics, 3rd ed. (Springer-Verlag, 1999).

Moi, L.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Mulchan, N.

Nha, H.

H. Nha, J. H. Lee, J. S. Chang, and K. An, "Atomic-position localization via dual measurement," Phys. Rev. A 65, 033827 (2002).
[CrossRef]

Niu, Y.

Orriols, G.

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Ottaviani, C.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Paspalakis, E.

E. Paspalakis, A. F. Terzis, and P. L. Knight, "Quantum interference induced sub-wavelength atomic localization," J. Mod. Opt. 52, 1685-1694 (2005).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency and parametric generation in a four-level system," J. Mod. Opt. 49, 87-95 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Electromagnetically induced transparency and controlled group velocity in a multilevel system," Phys. Rev. A 66, 015802 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency, slow light and enhanced nonlinear optics in a four-level scheme," J. Opt. B: Quantum Semiclassical Opt. 4, S372-S375 (2002).
[CrossRef]

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]

Pina, R.

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.

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, "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]

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]

Rebic, S.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

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. Kien, 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]

Rosenbluh, M.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
[CrossRef]

Rostovtsev, Yu. V.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, "Unexpected Doppler-free resonance in generalized double dark states," Phys. Rev. A 65, 043805 (2002).
[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]

Sargent, M.

P. Meystre and M. Sargent III, Elements of Quantum Optics, 3rd ed. (Springer-Verlag, 1999).

Sautenkov, V. A.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Schleich, W. P.

F. L. Kien, 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, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).

A. M. Herkommer, V. M. Akulin, and W. P. Schleich, "Quantum demolition measurement of photon statistics by atomic beam deflection," Phys. Rev. Lett. 69, 3298-3301 (1992).
[CrossRef] [PubMed]

Scully, M. O.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, "Unexpected Doppler-free resonance in generalized double dark states," Phys. Rev. A 65, 043805 (2002).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Segal, D. M.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

Storey, P.

P. Storey, M. Collett, and D. Walls, "Atomic-position resolution by quadrature-field measurement," Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

P. Storey, M. Collett, and D. Walls, "Measurement-induced diffraction and interference of atoms," Phys. Rev. Lett. 68, 472-475 (1992).
[CrossRef] [PubMed]

Stroud, C. R.

Sun, J. F.

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[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]

Terzis, A. F.

E. Paspalakis, A. F. Terzis, and P. L. Knight, "Quantum interference induced sub-wavelength atomic localization," J. Mod. Opt. 52, 1685-1694 (2005).
[CrossRef]

Thomas, J. E.

J. E. Thomas and L. J. Wang, "Precision position measurement of moving atoms," Phys. Rep. 262, 311-366 (1995).
[CrossRef]

J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
[CrossRef] [PubMed]

J. E. Thomas, "Quantum theory of atomic position measurement using optical fields," Phys. Rev. A 42, 5652-5666 (1990).
[CrossRef] [PubMed]

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]

Tombesi, P.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Vaccaro, J. A.

S. R. de Echaniz, A. D. Greentree, A. V. Durrant, D. M. Segal, J. P. Marangos, and J. A. Vaccaro, "Observations of a doubly driven V system probed to a fourth level in a laser-cooled rubidium," Phys. Rev. A 64, 013812 (2001).
[CrossRef]

Vitali, D.

S. Rebic, D. Vitali, C. Ottaviani, P. Tombesi, M. Artoni, F. Cataliotti, and R. Corbalán, "Polarization phase gate with a tripod atomic system," Phys. Rev. A 70, 032317 (2004).
[CrossRef]

Walls, D.

P. Storey, M. Collett, and D. Walls, "Atomic-position resolution by quadrature-field measurement," Phys. Rev. A 47, 405-418 (1993).
[CrossRef] [PubMed]

P. Storey, M. Collett, and D. Walls, "Measurement-induced diffraction and interference of atoms," Phys. Rev. Lett. 68, 472-475 (1992).
[CrossRef] [PubMed]

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]

Walther, H.

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[CrossRef]

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

Walther, T.

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

Wang, L. J.

J. E. Thomas and L. J. Wang, "Precision position measurement of moving atoms," Phys. Rep. 262, 311-366 (1995).
[CrossRef]

Wang, Y. C.

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[CrossRef]

Wasik, G.

G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (2001).
[CrossRef]

Welch, G. R.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, "Suboptical wavelength position measurement of moving atoms using optical fields," Phys. Rev. Lett. 70, 3404-3407 (1993).
[CrossRef] [PubMed]

Whitley, R. M.

Wilson-Gordon, A. D.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, "Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system," Phys. Rev. A 69, 063802 (2004).
[CrossRef]

Xu, Z.

Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, "Giant Kerr nonlinearity induced by interacting dark resonances," Opt. Lett. 30, 3371-3373 (2005).
[CrossRef]

S. Jin, S. Gong, R. Li, and Z. Xu, "Coherent population transfer and superposition of atomic states via stimulated Raman adiabatic passage using an excited-doublet four-level atom," Phys. Rev. A 69, 023408 (2004).
[CrossRef]

Yan, M.

Ye, C. Y.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, "Unexpected Doppler-free resonance in generalized double dark states," Phys. Rev. A 65, 043805 (2002).
[CrossRef]

Yelin, S. F.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[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]

Zachorowkwski, J.

G. Wasik, W. Gawlik, J. Zachorowkwski, and Z. Kowal, "Competition of dark states: optical resonances with anomalous magnetic field dependence," Phys. Rev. A 64, 051802(R) (2001).
[CrossRef]

Zhang, X. Y.

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[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]

Zhu, Y.

Zibrov, A. S.

C. Y. Ye, A. S. Zibrov, Yu. V. Rostovtsev, and M. O. Scully, "Unexpected Doppler-free resonance in generalized double dark states," Phys. Rev. A 65, 043805 (2002).
[CrossRef]

Zoller, P.

R. Blatt and P. Zoller, "Quantum jumps in atomic systems," Eur. J. Phys. 9, 250-256 (1988).
[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, 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]

T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
[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, "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]

A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).

F. L. Kien, 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]

Eur. J. Phys. (1)

R. Blatt and P. Zoller, "Quantum jumps in atomic systems," Eur. J. Phys. 9, 250-256 (1988).
[CrossRef]

J. Mod. Opt. (4)

J. T. Höffges, H. W. Baldauf, W. Lange, and H. Walther, "Heterodyne measurement of the resonance fluorescence of a single ion," J. Mod. Opt. 44, 1999-2010 (1997).
[CrossRef]

A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, "Autler-Townes microscopy on a sigle atom," J. Mod. Opt. 44, 2507-2513 (1997).

E. Paspalakis, A. F. Terzis, and P. L. Knight, "Quantum interference induced sub-wavelength atomic localization," J. Mod. Opt. 52, 1685-1694 (2005).
[CrossRef]

E. Paspalakis and P. L. Knight, "Transparency and parametric generation in a four-level system," J. Mod. Opt. 49, 87-95 (2002).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (2)

E. Paspalakis and P. L. Knight, "Transparency, slow light and enhanced nonlinear optics in a four-level scheme," J. Opt. B: Quantum Semiclassical Opt. 4, S372-S375 (2002).
[CrossRef]

T. Azim, M. Ikram, and M. S. Zubairy, "Sub-wavelength atom localization via Autler-Townes spectroscopy: effect of the quantized field," J. Opt. B: Quantum Semiclassical Opt. 6, 248-255 (2004).
[CrossRef]

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

Nuovo Cimento Soc. Ital. Fis., B (1)

G. Alzetta, A. Gozzini, L. Moi, and G. Orriols, "An experimental method for the observation of RF transitions and laser beat resonances in oriented Na vapor," Nuovo Cimento Soc. Ital. Fis., B 36, 5-20 (1976).
[CrossRef]

Opt. Commun. (4)

J. T. Höffges, H. W. Baldauf, T. Eichler, S. R. Helmfrid, and H. Walther, "Heterodyne measurement of the fluorescent radiation of a single trapped ion," Opt. Commun. 133, 170-174 (1997).
[CrossRef]

E. S. Fry, M. D. Lukin, T. Walther, and G. R. Welch, "Four-level atomic coherence and cw VUV lasers," Opt. Commun. 179, 499-504 (2000).
[CrossRef]

Y. F. Li, J. F. Sun, X. Y. Zhang, and Y. C. Wang, "Laser-induced double-dark resonances and double-transparencies in a four-level system," Opt. Commun. 202, 97-102 (2002).
[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]

Opt. Lett. (2)

Phys. Rep. (1)

J. E. Thomas and L. J. Wang, "Precision position measurement of moving atoms," Phys. Rep. 262, 311-366 (1995).
[CrossRef]

Phys. Rev. A (19)

F. L. Kien, 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]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the system under consideration. The atom interacts with a standing-wave field that couples the 3 1 transition, a probe laser field that couples the 3 0 transition, and a control laser field that couples the 3 2 transition.

Fig. 2
Fig. 2

Filter function F ( x ) (solid curve) as a function of κ x when Ω 2 = 2.00 . The dashed curve is a sine-squared function. The parameters are δ 0 = 0.00 , δ 2 = δ 1 = 1.50 , Ω 1 = 3.00 , and γ = 0.20 . All parameters are measured in arbitrary units.

Fig. 3
Fig. 3

Filter function F ( x ) as a function of κ x when Ω 2 = 3.00 . The parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

Filter function F ( x ) as a function of κ x when Ω 2 = 2.00 . The parameters are the same as in Fig. 2 but with δ 2 = δ 1 = 0.15 .

Fig. 5
Fig. 5

Filter function F ( x ) as a function of κ x when Ω 2 = 3.00 . The parameters are the same as in Fig. 3 but with δ 2 = δ 1 = 0.15 .

Equations (15)

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H = Ω 0 exp ( i δ 0 t ) 3 0 + Ω 1 ( x ) exp ( i δ 1 t ) 3 1 + Ω 2 exp ( i δ 2 t ) 3 2 + H.c. ,
ψ ( t ) = d x f ( x ) x [ a 0 ( x , t ) 0 + a 1 ( x , t ) 1 + a 2 ( x , t ) 2 + a 3 ( x , t ) 3 ] ,
P ( x , t 3 ) = N 2 f ( x ) 2 a 3 ( x , t ) 2 .
i b ̇ 0 ( x , t ) = Ω 0 b 3 ( x , t ) ,
i b ̇ 1 ( x , t ) = ( δ 0 δ 1 ) b 1 ( x , t ) + Ω 1 ( x ) b 3 ( x , t ) ,
i b ̇ 2 ( x , t ) = ( δ 0 δ 2 ) b 2 ( x , t ) + Ω 2 b 3 ( x , t ) ,
i b ̇ 3 ( x , t ) = ( δ 0 i γ 2 ) b 3 ( x , t ) + Ω 0 b 0 ( x , t ) + Ω 1 ( x ) b 1 ( x , t ) + Ω 2 b 2 ( x , t ) ,
b 3 ( 1 ) ( x , t ) = Ω 0 δ 0 + Ω 2 2 δ 2 δ 0 Ω 1 ( x ) 2 δ 0 δ 1 i γ 2 .
P ( x , t 3 ) = N 2 f ( x ) 2 Ω 0 2 [ δ 0 + Ω 2 2 δ 2 δ 0 Ω 1 ( x ) 2 δ 0 δ 1 ] 2 + γ 2 4 .
F ( x ) = Ω 0 2 [ δ 0 + Ω 2 2 δ 2 δ 0 Ω 1 2 sin 2 ( κ x ) δ 0 δ 1 ] 2 + γ 2 4 .
κ x = ± arcsin [ δ 0 + Ω 2 2 ( δ 2 δ 0 ) ] ( δ 0 δ 1 ) Ω 1 + m π ,
w = arcsin [ [ δ 0 + Ω 2 2 ( δ 2 δ 0 ) + γ 2 ] ( δ 0 δ 1 ) Ω 1 ] arcsin [ [ δ 0 + Ω 2 2 ( δ 2 δ 0 ) γ 2 ] ( δ 0 δ 1 ) Ω 1 ] .
F ( x ) = Ω 0 2 [ Ω 2 2 Ω 1 2 sin 2 ( κ x ) δ 2 ] 2 + γ 2 4 ,
κ x = ± arcsin Ω 2 Ω 1 + m π ,
w = arcsin Ω 2 2 + γ δ 2 2 Ω 1 arcsin Ω 2 2 γ δ 2 2 Ω 1 .

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