Abstract

A scheme of two-dimensional (2D) atom localization based on the interference of double-dark resonances is proposed, in which the N-type atom interacts with two orthogonal standing-wave fields. Because of the spatial-dependent atom–field interaction, 2D atom localization can be realized via measuring the upper state population or the probe absorption. We obtain that the maximum probability of finding an atom at a particular position in a wavelength domain (λ1×λ2) is 1/2 when the atom is localized at the intersection of the antinodes of quadrants I and III of the standing-wave plane. This scheme shows more advantages than other schemes of 2D atom localization.

© 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. 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]
  3. K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805(2003).
    [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78, 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, 409–416 (2000).
    [CrossRef]
  9. S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).
    [CrossRef]
  10. J. Xu and X. M. Hu, “Sub-half-wavelength atom localization via bichromatic phase control of spontaneous emission,” Phys. Lett. A 366, 276–281 (2007).
    [CrossRef]
  11. 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]
  12. E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
    [CrossRef]
  13. G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437–3446(2006).
    [CrossRef]
  14. 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, 025801 (2006).
    [CrossRef]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  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, 805–810 (2009).
    [CrossRef]
  22. 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, 10–17(2011).
    [CrossRef]
  23. 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]
  24. Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
    [CrossRef]
  25. 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]
  26. Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonances,” Opt. Lett. 30, 3371–3373 (2005).
    [CrossRef]

2011 (1)

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 (2)

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, 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, 033848 (2009).
[CrossRef]

2008 (1)

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]

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]

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

2006 (3)

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

2005 (2)

Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonances,” Opt. Lett. 30, 3371–3373 (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 (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]

2001 (2)

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

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)

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]

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 (1)

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]

1995 (1)

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]

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]

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, Y. C.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

Cheng, D. C.

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, 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, 2180–2184 (2006).
[CrossRef]

Chiu, H. Y.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[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]

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]

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]

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]

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]

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, 025801 (2006).
[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]

Gao, J. Y.

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, 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, 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, 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, 2180–2184 (2006).
[CrossRef]

Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonances,” Opt. Lett. 30, 3371–3373 (2005).
[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]

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

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, 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, 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, 805–810 (2009).
[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]

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]

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]

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]

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]

Kou, J.

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]

Li, R. X.

Liang, X. Y.

Liao, Y. A.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

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, 025801 (2006).
[CrossRef]

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]

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]

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]

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, 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, 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]

Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonances,” Opt. Lett. 30, 3371–3373 (2005).
[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]

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]

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]

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]

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]

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. 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.

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]

Su, J. J.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[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, 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, 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, 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]

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]

Wan, R. G.

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]

Xu, J.

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[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).
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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, 025801 (2006).
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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]

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Zhu, S. Y.

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

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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).
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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).
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K. T. Kapale, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805(2003).
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S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806 (2000).
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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).
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J. Mod. Opt. (1)

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, 805–810 (2009).
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G. S. Agarwal and K. T. Kapale, “Subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437–3446(2006).
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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. (1)

Phys. Lett. A (1)

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

Phys. Rev. A (13)

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]

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

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, 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, 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, 033848 (2009).
[CrossRef]

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

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

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[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]

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Rev. Mod. Phys. (1)

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

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