Abstract

A scheme is proposed to achieve one-dimensional localization of a two-level atom moving through a standing wave regime constructed by two classical standing-wave fields. Precise position information of the atom can be obtained by measuring resonant absorption of a weak coherent field probing the transition strongly driven by the resonant standing-wave fields. Behavior of atomic localization has been shown for symmetric superposition of the standing-wave fields arranged in two distinct configurations: (i) parallel and (ii) cross. In the cross-configuration, we have shown 100% detection probability of the atom within one wavelength range with the evolution of single localization peak in the sub-half-wavelength range due to the variation of spatial phase shift of one of the standing-wave fields. In case of nonresonant coupling of the atom with the standing-wave fields, a single localization peak in the sub-half-wavelength range can be obtained by changing the relative detuning of frequency of the probe field. For achieving high resolution single-peak localization of a two-level atom, the present scheme would be of great interest from the experimental point of view.

© 2012 Optical Society of America

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    [CrossRef]
  37. R. -G. Wan, J. Kou, L. 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).
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  38. R. -G. Wan, J. Kou, L. Jiang, and J. -Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284, 985–990 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  45. J. E. Thomas and L. J. Wang, “Precision position measurement of moving atoms,” Phys. Rep. 262, 311–366 (1995).
    [CrossRef]
  46. K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
    [CrossRef]
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    [CrossRef]
  49. Z. -H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

S. Yang, M. A. -Amri, and M. S. Zubairy, “Single-atom localization via resonance- fluorescence photon statistics,” Phys. Rev. A 85, 023831 (2012).
[CrossRef]

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

2011

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

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

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

R. -G. Wan, J. Kou, L. 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]

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

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

J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
[CrossRef]

N. A. Proite, Z. J. Simmons, and D. D. Yavuz, “Observation of atomic localization using electromagnetically induced transparency,” Phys. Rev. A 83, 041803(R) (2011).
[CrossRef]

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

2010

Z. Wang and J. Jiang, “Sub-half-wavelength atom localization via probe absorption spectrum in a four-level atomic system,” Phys. Lett. A 374, 4853–4858 (2010).
[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]

Z. -H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

2009

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

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

2008

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

2007

M. Sahrai, M. Mahmoudi, and R. Kheradmand, “Atom localization of a two-level pump-probe system via the absorption spectrum,” Laser Phys. 17, 40–44 (2007).
[CrossRef]

J. Xu and X. -M. Hu, “Localization of a two-level atom via the absorption spectrum,” Phys. Lett. A 364, 208–213 (2007).
[CrossRef]

2006

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

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]

J. -T. Chang, J. Evers, M. O. Scully, and M. S. Zubairy, “Measurement of the separation between atoms beyond diffraction limit,” Phys. Rev. A 73, 031803 (2006).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Electromagnetically induced grating in a three-level -type system driven by a strong standing wave pump and weak probe fields,” J. Phys. B 39, 1145–1157 (2006).
[CrossRef]

2005

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

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

2004

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 Semiclass. Opt. 6, 248–255 (2004).
[CrossRef]

2002

H. Nha, J. -H. Lee, J. -S. Chang, and K. An, “Atomic-position localization via dual measurement,” Phys. Rev. A 65, 033827 (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]

2001

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

2000

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using AutlerTownes 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]

1998

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

E. Paspalakis, C. H. Keitel, and P. L. Knight, “Fluorescence control through multiple interference mechanisms,” Phys. Rev. A 58, 4868–4877 (1998).
[CrossRef]

1997

A. M. Herkomer, W. P. Schleich, and M. S. Zubairy, “Autler-Townes microscopy on a single atom,” J. Mod. Opt. 44, 2507–2513 (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]

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]

1995

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

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

1994

C. S. Adams, M. Seigel, and J. Mlynek, “Atom optics,” Phys. Rep. 240, 143–210 (1994).
[CrossRef]

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

1993

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

J. R. Gardner, M. 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]

T. Quang and H. Freedhoff, “Index of refraction of a system of strongly driven two-level atoms,” Phys. Rev. A 48, 3216–3218 (1993).
[CrossRef]

1992

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

M. A. M. Marte and P. Zoller, “Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering,” Appl. Phys. B 54, 477–485 (1992).
[CrossRef]

1988

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

1972

B. R. Mollow, “Stimulated emission and absorption near resonance for driven systems,” Phys. Rev. A 5, 2217–2222 (1972).
[CrossRef]

1968

M. Lax, “Multitime correspondence between quantum and classical stochastic processes,” Phys. Rev. 172, 350–361 (1968).
[CrossRef]

1927

W. Heisenberg, “The actual content of quantum theoretical kinematics and mechanics,” Z. Phys. 43, 172–198 (1927).
[CrossRef]

Adams, C. S.

C. S. Adams, M. Seigel, and J. Mlynek, “Atom optics,” Phys. Rep. 240, 143–210 (1994).
[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]

-Amri, M. A.

S. Yang, M. A. -Amri, and M. S. Zubairy, “Single-atom localization via resonance- fluorescence photon statistics,” Phys. Rev. A 85, 023831 (2012).
[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]

Arimondo, E.

E. Arimondo, in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 35.

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 Semiclass. Opt. 6, 248–255 (2004).
[CrossRef]

Berggren, K. K.

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

Blatt, R.

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

Cao, Z.

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

Chang, J. -T.

J. -T. Chang, J. Evers, M. O. Scully, and M. S. Zubairy, “Measurement of the separation between atoms beyond diffraction limit,” Phys. Rev. A 73, 031803 (2006).
[CrossRef]

Cheng, D.

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

Cheng, D. -C.

Chu, A. P.

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

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

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

Dekker, N. H.

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

Ding, C.

J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
[CrossRef]

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

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

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

Dutta, B. K.

B. K. Dutta and P. K. Mahapatra, “Electromagnetically induced grating in a three-level -type system driven by a strong standing wave pump and weak probe fields,” J. Phys. B 39, 1145–1157 (2006).
[CrossRef]

Evers, J.

J. -T. Chang, J. Evers, M. O. Scully, and M. S. Zubairy, “Measurement of the separation between atoms beyond diffraction limit,” Phys. Rev. A 73, 031803 (2006).
[CrossRef]

Fan, X.

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

Freedhoff, H.

T. Quang and H. Freedhoff, “Index of refraction of a system of strongly driven two-level atoms,” Phys. Rev. A 48, 3216–3218 (1993).
[CrossRef]

Gao, J. -Y.

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

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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).
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L. Jin, H. Sun, Y. Niu, S. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56, 805–810 (2009).
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L. Jin, H. Sun, Y. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41, 085508 (2008).
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J. Xu and X. -M. Hu, “Localization of a two-level atom via the absorption spectrum,” Phys. Lett. A 364, 208–213 (2007).
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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 Semiclass. Opt. 6, 248–255 (2004).
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Z. Wang and J. Jiang, “Sub-half-wavelength atom localization via probe absorption spectrum in a four-level atomic system,” Phys. Lett. A 374, 4853–4858 (2010).
[CrossRef]

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R. -G. Wan, J. Kou, L. 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).
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R. -G. Wan, J. Kou, L. Jiang, and J. -Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284, 985–990 (2011).
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L. Jin, H. Sun, Y. Niu, S. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56, 805–810 (2009).
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L. Jin, H. Sun, Y. Niu, and S. Q. Gong, “Sub-half-wavelength atom localization via two standing-wave fields,” J. Phys. B 41, 085508 (2008).
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L. Jin, H. Sun, Y. Niu, S. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56, 805–810 (2009).
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K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
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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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E. Paspalakis, C. H. Keitel, and P. L. Knight, “Fluorescence control through multiple interference mechanisms,” Phys. Rev. A 58, 4868–4877 (1998).
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M. Sahrai, M. Mahmoudi, and R. Kheradmand, “Atom localization of a two-level pump-probe system via the absorption spectrum,” Laser Phys. 17, 40–44 (2007).
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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).
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Z. -H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
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E. Paspalakis, A. F. Terzis, and P. L. Knight, “Quantum interference induced sub- wavelength atomic localization,” J. Mod. Opt. 52, 1685 (2005).
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E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
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E. Paspalakis, C. H. Keitel, and P. L. Knight, “Fluorescence control through multiple interference mechanisms,” Phys. Rev. A 58, 4868–4877 (1998).
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R. -G. Wan, J. Kou, L. Jiang, and J. -Y. Gao, “Two-dimensional atom localization via quantum interference in a coherently driven inverted-Y system,” Opt. Commun. 284, 985–990 (2011).
[CrossRef]

R. -G. Wan, J. Kou, L. 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).
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S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78, 2038–2041 (1997).
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S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27, 115–121 (1994).
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H. Nha, J. -H. Lee, J. -S. Chang, and K. An, “Atomic-position localization via dual measurement,” Phys. Rev. A 65, 033827 (2002).
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J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
[CrossRef]

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

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

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

Li, R. -X.

Liu, C.

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

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C. Ding, J. H. Li, X. Yang, Z. Zhan, and J. -B. Liu, “Two-dimensional atom localization via a coherence-controlled absorption spectrum in an N-tripod-type five-level atomic system,” J. Phys. B 44, 145501 (2011).
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J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
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M. Sahrai, M. Mahmoudi, and R. Kheradmand, “Atom localization of a two-level pump-probe system via the absorption spectrum,” Laser Phys. 17, 40–44 (2007).
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J. R. Gardner, M. 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).
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M. A. M. Marte and P. Zoller, “Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering,” Appl. Phys. B 54, 477–485 (1992).
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S. Qamar, A. Mehmood, and Sh. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).
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P. Meystre and M. Sergent, Elements of Quantum Optics, 3rd ed. (Springer-Verlag, 1999).

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C. S. Adams, M. Seigel, and J. Mlynek, “Atom optics,” Phys. Rep. 240, 143–210 (1994).
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H. Nha, J. -H. Lee, J. -S. Chang, and K. An, “Atomic-position localization via dual measurement,” Phys. Rev. A 65, 033827 (2002).
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L. Jin, H. Sun, Y. Niu, S. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56, 805–810 (2009).
[CrossRef]

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

Niu, Y. -P.

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E. Paspalakis, A. F. Terzis, and P. L. Knight, “Quantum interference induced sub- wavelength atomic localization,” J. Mod. Opt. 52, 1685 (2005).
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E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
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E. Paspalakis, C. H. Keitel, and P. L. Knight, “Fluorescence control through multiple interference mechanisms,” Phys. Rev. A 58, 4868–4877 (1998).
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K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
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N. A. Proite, Z. J. Simmons, and D. D. Yavuz, “Observation of atomic localization using electromagnetically induced transparency,” Phys. Rev. A 83, 041803(R) (2011).
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S. Qamar, A. Mehmood, and Sh. Qamar, “Subwavelength atom localization via coherent manipulation of the Raman gain process,” Phys. Rev. A 79, 033848 (2009).
[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 AutlerTownes 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).
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Qamar, Sh.

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

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

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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]

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M. Sahrai, M. Mahmoudi, and R. Kheradmand, “Atom localization of a two-level pump-probe system via the absorption spectrum,” Laser Phys. 17, 40–44 (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]

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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. Herkomer, W. P. Schleich, and M. S. Zubairy, “Autler-Townes microscopy on a single atom,” J. Mod. Opt. 44, 2507–2513 (1997).
[CrossRef]

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J. -T. Chang, J. Evers, M. O. Scully, and M. S. Zubairy, “Measurement of the separation between atoms beyond diffraction limit,” Phys. Rev. A 73, 031803 (2006).
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C. S. Adams, M. Seigel, and J. Mlynek, “Atom optics,” Phys. Rep. 240, 143–210 (1994).
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P. Meystre and M. Sergent, Elements of Quantum Optics, 3rd ed. (Springer-Verlag, 1999).

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Z. -H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

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N. A. Proite, Z. J. Simmons, and D. D. Yavuz, “Observation of atomic localization using electromagnetically induced transparency,” Phys. Rev. A 83, 041803(R) (2011).
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P. Storey, M. Collett, and D. F. Walls, “Atom-position resolution by quadrature-field measurement,” Phys. Rev. A 47, 405–418 (1993).
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P. Storey, M. Collett, and D. F. Walls, “Measurement-induced diffraction and interference of atoms,” Phys. Rev. Lett. 68, 472–475 (1992).
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L. Jin, H. Sun, Y. Niu, S. Jin, and S. Q. Gong, “Two-dimension atom nano-lithograph via atom localization,” J. Mod. Opt. 56, 805–810 (2009).
[CrossRef]

L. Jin, H. Sun, Y. 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]

Terzis, A. F.

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

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

J. R. Gardner, M. 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]

Thywissen, J. H.

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

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

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

Wan, R. -G.

Wang, L. J.

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

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

Z. Wang and J. Jiang, “Sub-half-wavelength atom localization via probe absorption spectrum in a four-level atomic system,” Phys. Lett. A 374, 4853–4858 (2010).
[CrossRef]

Welch, G. R.

J. R. Gardner, M. 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]

Wilkens, M.

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

Wu, X.

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

Xiao, Z. -H.

Z. -H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Xiong, H.

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

Xu, F.

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

Xu, J.

J. Xu and X. -M. Hu, “Localization of a two-level atom via the absorption spectrum,” Phys. Lett. A 364, 208–213 (2007).
[CrossRef]

Xu, Z.

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

Yang, S.

S. Yang, M. A. -Amri, and M. S. Zubairy, “Single-atom localization via resonance- fluorescence photon statistics,” Phys. Rev. A 85, 023831 (2012).
[CrossRef]

Yang, X.

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

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

J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
[CrossRef]

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

Yavuz, D. D.

N. A. Proite, Z. J. Simmons, and D. D. Yavuz, “Observation of atomic localization using electromagnetically induced transparency,” Phys. Rev. A 83, 041803(R) (2011).
[CrossRef]

Younkin, R.

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

Yu, B.

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

Yu, R.

J. H. Li, R. Yu, M. Liu, C. Ding, and X. Yang, “Efficient two-dimensional atom localization via phasesensitive absorption spectrum in a radio-frequency-driven four-level atomic system,” Phys. Lett. A 375, 3978–3985 (2011).
[CrossRef]

Zhan, Z.

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

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

Zhang, D.

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

Zhang, T. -Y.

Zhen, S.

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

Zhu, J.

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

Zhu, S. Y.

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using AutlerTownes 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]

Zoller, P.

M. A. M. Marte and P. Zoller, “Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering,” Appl. Phys. B 54, 477–485 (1992).
[CrossRef]

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

Zubairy, M. S.

S. Yang, M. A. -Amri, and M. S. Zubairy, “Single-atom localization via resonance- fluorescence photon statistics,” Phys. Rev. A 85, 023831 (2012).
[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]

J. -T. Chang, J. Evers, M. O. Scully, and M. S. Zubairy, “Measurement of the separation between atoms beyond diffraction limit,” Phys. Rev. A 73, 031803 (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 Semiclass. Opt. 6, 248–255 (2004).
[CrossRef]

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