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]
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    [CrossRef]
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    [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).
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    [CrossRef]
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    [CrossRef]

2012 (2)

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 (9)

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 (3)

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 (2)

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 (1)

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 (2)

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 (6)

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 (2)

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 (1)

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 (2)

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 (1)

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

2000 (2)

S. Qamar, S. Y. Zhu, and M. S. Zubairy, “Precision localization of single atom using 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 (2)

K. S. Johnson, J. H. Thywissen, N. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable atom beams with optical standing waves: nanolithography at the Heisenberg limit,” Science 280, 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 (3)

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 (2)

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

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

1994 (2)

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 (3)

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 (2)

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 (1)

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

1972 (1)

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

1968 (1)

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

1927 (1)

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]

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

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]

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

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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).
[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).
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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).
[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]

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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]

Jin, S.

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]

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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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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).
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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).
[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]

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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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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).
[CrossRef]

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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).
[CrossRef]

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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]

S. Kunze, G. Rempe, and M. Wilkens, “Atomic-position measurement via internal-state encoding,” Europhys. Lett. 27, 115–121 (1994).
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M. Lax, “Multitime correspondence between quantum and classical stochastic processes,” Phys. Rev. 172, 350–361 (1968).
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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).
[CrossRef]

Li, J. H.

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]

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]

Liu, J. -B.

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]

Liu, M.

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).
[CrossRef]

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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).
[CrossRef]

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

Niu, Y.

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.

Paspalakis, E.

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

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

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

Prentiss, M.

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

Qamar, S.

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).
[CrossRef]

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).
[CrossRef]

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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).
[CrossRef]

Quang, T.

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]

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]

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

Rozhdestvensky, Y.

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

Sahrai, M.

M. Sahrai, 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]

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

Scully, M. O.

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]

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

Sergent, M.

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

Shin, S. G.

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

Simmons, Z. J.

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]

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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).
[CrossRef]

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

Sun, H.

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]

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. 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]

Wang, 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]

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, 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]

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]

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]

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, 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]

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, “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 AutlerTownes microscopy,” Opt. Commun. 176, 409–416 (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]

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]

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]

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Figures (7)

Fig. 1.
Fig. 1.

(A) Schematic presentation of field-coupled energy levels of a two-level atom. The atom is interacting with three coherent fields EP(ωp) and Ej(ωs) (j=1, 2) of frequencies ωp and ωs respectively. γ is the decay rate of the excited energy level. (B) Schematic setup to represent atom-field interaction in the standing-wave regime constructed by the superposition of two standing-wave fields with angular separation θ. The atom is denoted by the blackened circular spot. k1 and k2 denote the wave vectors of the fields E1 and E2, respectively. Along the x direction, for the fields E1 and E2 taken in cross-configuration, the counterpropagating x-components of two degenerate wave vectors constitute the standing-waves that superpose to each other. For vanishing angular separation between the wave vectors, the fields E1 and E2 would be in parallel configuration.

Fig. 2.
Fig. 2.

Subwavelength localization of the atom for the resonant fields E1 and E2 chosen in parallel configuration: For Δs=δ=0, R=10γ, and η1=η2=1, plot of F(x) versus kx is represented by the solid line in (A) ϕ=0, (B) ϕ=0.128π, (C) ϕ=0.89π, (D) ϕ=1.91π. The curves represented by the dotted line stand for normalized sin-squared function Ω2(x)/4R2 in the standing-wave regime.

Fig. 3.
Fig. 3.

Subwavelength localization of the atom for the resonant fields E1 and E2 chosen in cross-configuration: Plot of F(x) versus kx is represented by the solid line in (A) ϕ=0, (B) ϕ=0.255π, (C) ϕ=0.32π, (D) ϕ=0.51π with η1=η2=0.8. Other parameters are the same as set in Fig. 2. The curves represented by the dotted line stand for normalized sin-squared function Ω2(x)/4R2 in the standing-wave regime.

Fig. 4.
Fig. 4.

Shifting of the single-peak localization in half-wavelength range due to cross-configuration of the resonant fields E1 and E2: Plot of F(x) versus kx in the curves a (η1=η2=0.9), b (η1=η2=0.8) and c (η1=η2=0.7) with R=80γ and ϕ=0.12π. Other parameters are the same as set in Fig. 2.

Fig. 5.
Fig. 5.

Subwavelength localization of the atom interacting nonresonantly with the fields at smaller detuning mismatch: Plot of F(x) versus kx is represented by the solid line in (A) Δs=±γ, δ=0, ϕ=0 and η1=η2=1, (B) Δs=0, δ=±γ, ϕ=0 and η1=η2=1, (C) Δs=0, δ=±γ, ϕ=0.191π and η1=η2=0.7, (D) Δs=±γ, δ=±γ, ϕ=0.191π and η1=η2=0.7, (E) Δs=γ, δ=±γ, ϕ=0.191π and η1=η2=0.7 with R=10γ. The curves partially represented by the dotted line stand for normalized sin-squared function Ω2(x)/4R2 in the standing-wave regime.

Fig. 6.
Fig. 6.

Subwavelength localization of the atom interacting non-resonantly with the fields at larger detuning mismatch: Plot of F(x) versus kx is represented by the solid line in (A) Δs=0, δ=±10γ, ϕ=0 and η1=η2=1, (B) Δs=10γ, δ=±10γ, ϕ=0 and η1=η2=1, and (C) Δs=10γ, δ=±10γ, ϕ=0.191π and η1=η2=0.7 with R=10γ. The curve partially represented by the dotted line stand for normalized sin-squared function Ω2(x)/4R2 in the standing-wave regime.

Fig. 7.
Fig. 7.

Variation of width (FWHM) per unit wavelength with the Rabi-frequency: Plot of the curve with ϕ=0 and η1=η2=0.8. Other parameters are the same as set in Fig. 2.

Equations (20)

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A¯j(x)=ϵ¯jsin(kjxx),
H=j=1,2ωj|jj|[Ω(x,t)|12|+Ω*(x,t)|21|],
ρt=i[H,ρ]+(ρt)irreversible,
(ρt)irreversible=γ2[2|12|ρ|21||22|ρρ|22|].
ρ12=ρ˜12eiωst,
ρ˙11=γρ22+iΩ(x)(ρ˜21ρ˜12)
ρ˙22=γρ22+iΩ(x)(ρ˜12ρ˜21)
ρ˜˙12=(γ/2+iΔs)ρ˜12+iΩ(x)(ρ22ρ11)
ρ˜˙21=(γ/2iΔs)ρ˜21iΩ(x)(ρ22ρ11),
χ(ωp)=i2N|μ12|20[σ12(τ),σ21]seiωpτ,
σzt=γ(1+σz)+i2Ω(x)(σ˜21σ˜12)
σ˜21t=(γ2+iΔs)σ˜21+iσzΩ(x)
σ˜12t=(γ2iΔs)σ˜12iσzΩ(x),
χ(ωp,x)=N|μ12|2γ2+4Δs2γ2+4Δs2+8Ω2(x)×2Ω2(x)δi(γiδ)(γ/2+i(Δsδ))(γ/2+iΔs)(γ/2+iΔs)[(γiδ)(γ/2+i(Δsδ))(γ/2i(Δs+δ))+4Ω2(x)(γ/2iδ)],
A=A0F(x),
F(x)=C1+C2Ω2(x)+C3Ω4(x)D1+D2Ω2(x)+D3Ω4(x)+D4Ω6(x),
F(x)=γ4(γ2+8Ω2(x))2.
R1sin(η1kx)+R2sin(η2kx+ϕ)=0.
Δx=2π(η1+η2)sin1(21γ42Rcosϕ2)λ.
Δx=2142π(γηR)λ.

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