Abstract

Coherent interaction of an atom with a position-dependent standing-wave cavity field can impart position information of a moving atom through the cavity leading to subwavelength atom localization. We show that the position of the atom along the standing-wave field is determined when the probe-field absorption is measured. We find out that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. In addition, we demonstrate that the position information of a three-level V-shaped moving atom strongly depends on the relative phase of applied fields. By appropriate choice of the relative phase, it is shown that the scheme can be used for localizing an atom flying through the standing-wave field to the sub-half-wavelength domain.

© 2013 Optical Society of America

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  1. K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
    [CrossRef]
  2. J. R. Gardner, M. L. Marable, G. R. Welch, and J. E. Thomas, “Suboptical wavelength position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 70, 3404–3407 (1993).
    [CrossRef]
  3. W. D. Phillips, “Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
    [CrossRef]
  4. G. P. Collins, “Experimenters produce new Bose–Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49(3), 18–21 (1996).
    [CrossRef]
  5. K. S. Johnson, J. H. Thywissen, W. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
    [CrossRef]
  6. K. T. Kapalle, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805–023810 (2003).
    [CrossRef]
  7. P. Storey, M. Collet, and D. F. Walls, “Measurement-induced diffraction and interference of atoms,” Phys. Rev. Lett. 68, 472–475 (1992).
    [CrossRef]
  8. S. Kunze, K. Dieckmann, and G. Rempe, “Diffraction of atoms from a measurement induced grating,” Phys. Rev. Lett. 78, 2038–2041 (1997).
    [CrossRef]
  9. R. Quadt, M. Collet, and D. F. Walls, “Measurement of atomic notion in a standing light field by homodyne detection,” Phys. Rev. Lett. 74, 351–354 (1995).
    [CrossRef]
  10. 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]
  11. P. Rudy, R. Ejnisman, and N. P. Bigelow, “Fluorescence investigation of parametrically excited motional wave packets in optical lattices,” Phys. Rev. Lett. 78, 4906–4909 (1997).
    [CrossRef]
  12. M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
    [CrossRef]
  13. S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806(2000).
    [CrossRef]
  14. F. Ghafoor, S. Gamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).
    [CrossRef]
  15. E. Paspalakis and P. L. Knight, “Localizing an atom via quantum interference,” Phys. Rev. A 63, 065802 (2001).
    [CrossRef]
  16. G. S. Agarwal and K. T. Kapale, “Extreme subwavelength atom localization via coherent population trapping,” J. Phys. B 39, 3437–3446 (2006).
    [CrossRef]
  17. M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
    [CrossRef]
  18. D.-C. Zhang, Y.-P. Niu, R.-X. Li, and S.-Q. Gang, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23, 2180–2184 (2006).
    [CrossRef]
  19. J. Everes, 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. H. Tajalli and M. Sahrai, “Atom localization via electromagnetically induced transparency,” Laser Phys. 7, 1007–1011 (2004).
  21. M. Sahrai, H. Tajalli, K. Kapale, and M. S. Zubairy, “Subwavelength atom localization via amplitude and phase control of the absorption spectrum,” Phys. Rev. A 72, 013820 (2005).
    [CrossRef]
  22. 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]
  23. M. Sahrai, “Atom localization via absorption spectrum,” Laser Phys. 17, 98–102 (2007).
    [CrossRef]
  24. E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296(1998).
    [CrossRef]
  25. D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Freidman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
    [CrossRef]
  26. M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
    [CrossRef]
  27. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

2010

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
[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]

M. Sahrai, “Atom localization via absorption spectrum,” Laser Phys. 17, 98–102 (2007).
[CrossRef]

J. Everes, 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]

M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
[CrossRef]

2006

D.-C. Zhang, Y.-P. Niu, R.-X. Li, and S.-Q. Gang, “Controllable atom localization via double-dark resonances in a tripod system,” J. Opt. Soc. Am. B 23, 2180–2184 (2006).
[CrossRef]

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

2005

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

2004

H. Tajalli and M. Sahrai, “Atom localization via electromagnetically induced transparency,” Laser Phys. 7, 1007–1011 (2004).

2003

K. T. Kapalle, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805–023810 (2003).
[CrossRef]

2002

F. Ghafoor, S. Gamar, 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]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Freidman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

2000

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, W. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

W. D. Phillips, “Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
[CrossRef]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296(1998).
[CrossRef]

1997

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

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

P. Rudy, R. Ejnisman, and N. P. Bigelow, “Fluorescence investigation of parametrically excited motional wave packets in optical lattices,” Phys. Rev. Lett. 78, 4906–4909 (1997).
[CrossRef]

1996

M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
[CrossRef]

G. P. Collins, “Experimenters produce new Bose–Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49(3), 18–21 (1996).
[CrossRef]

1995

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

1993

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

1992

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

1991

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. T. Kapale, “Extreme 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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Bigelow, N. P.

P. Rudy, R. Ejnisman, and N. P. Bigelow, “Fluorescence investigation of parametrically excited motional wave packets in optical lattices,” Phys. Rev. Lett. 78, 4906–4909 (1997).
[CrossRef]

Bortman-Arbiv, D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Freidman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Collet, M.

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

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

Collins, G. P.

G. P. Collins, “Experimenters produce new Bose–Einstein condensate(s) and possible puzzles for theorists,” Phys. Today 49(3), 18–21 (1996).
[CrossRef]

Dekker, W. H.

K. S. Johnson, J. H. Thywissen, W. H. Dekker, K. K. Berggren, A. P. Chu, R. Younkin, and M. Prentiss, “Localization of metastable 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]

Ejnisman, R.

P. Rudy, R. Ejnisman, and N. P. Bigelow, “Fluorescence investigation of parametrically excited motional wave packets in optical lattices,” Phys. Rev. Lett. 78, 4906–4909 (1997).
[CrossRef]

Everes, J.

J. Everes, 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]

Evers, J.

M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
[CrossRef]

Freidman, H.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Freidman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Gamar, S.

F. Ghafoor, S. Gamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).
[CrossRef]

Gang, S.-Q.

Gardner, J. R.

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

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Ghafoor, F.

F. Ghafoor, S. Gamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).
[CrossRef]

Hemmati, R.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
[CrossRef]

Holland, M.

M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
[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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Kapale, K.

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

Kapale, K. T.

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

Kapalle, K. T.

K. T. Kapalle, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805–023810 (2003).
[CrossRef]

Keitel, C. H.

M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
[CrossRef]

Kheradmand, R.

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]

Kien, F. L.

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

Knight, P. L.

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

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296(1998).
[CrossRef]

Kunze, S.

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

Li, R.-X.

Macovei, M.

M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
[CrossRef]

Mahmoudi, M.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
[CrossRef]

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]

Maleki, A.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
[CrossRef]

Marable, M.

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Marable, M. L.

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

Marksteiner, S.

M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
[CrossRef]

Marte, P.

M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
[CrossRef]

Niu, Y.-P.

Paspalakis, E.

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

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296(1998).
[CrossRef]

Phillips, W. D.

W. D. Phillips, “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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Qamar, S.

J. Everes, 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. Kapalle, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805–023810 (2003).
[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. Collet, and D. F. Walls, “Measurement of atomic notion 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. 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]

Rudy, P.

P. Rudy, R. Ejnisman, and N. P. Bigelow, “Fluorescence investigation of parametrically excited motional wave packets in optical lattices,” Phys. Rev. Lett. 78, 4906–4909 (1997).
[CrossRef]

Sahrai, M.

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
[CrossRef]

M. Sahrai, “Atom localization via absorption spectrum,” Laser Phys. 17, 98–102 (2007).
[CrossRef]

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

H. Tajalli and M. Sahrai, “Atom localization via electromagnetically induced transparency,” Laser Phys. 7, 1007–1011 (2004).

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]

Schnurr, C.

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Stokes, K. D.

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Storey, P.

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

Tajalli, H.

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

H. Tajalli and M. Sahrai, “Atom localization via electromagnetically induced transparency,” Laser Phys. 7, 1007–1011 (2004).

Thomad, J. E.

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Thomas, J. E.

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

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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Walls, D. F.

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

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

Welch, G. R.

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

K. D. Stokes, C. Schnurr, J. R. Gardner, M. Marable, G. R. Welch, and J. E. Thomad, “Precision position measurement of moving atoms using optical fields,” Phys. Rev. Lett. 67, 1997–2000 (1991).
[CrossRef]

Wilson-Gordon, A. D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Freidman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[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 standing waves: nanolithography at the Heisenberg limit,” Science 280, 1583–1586 (1998).
[CrossRef]

Zhang, D.-C.

Zhu, S.-Y.

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

Zoller, P.

M. Holland, S. Marksteiner, P. Marte, and P. Zoller, “Measurement induced localization from spontaneous decay,” Phys. Rev. Lett. 76, 3683–3686 (1996).
[CrossRef]

Zubairy, M. S.

M. Macovei, J. Evers, C. H. Keitel, and M. S. Zubairy, “Localization of atomic ensembles via super-fluorescence,” Phys. Rev. A 75, 033801 (2007).
[CrossRef]

J. Everes, 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]

M. Sahrai, H. Tajalli, K. 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. Kapalle, S. Qamar, and M. S. Zubairy, “Spectroscopic measurement of an atomic wave function,” Phys. Rev. A 67, 023805–023810 (2003).
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F. Ghafoor, S. Gamar, and M. S. Zubairy, “Atom localization via phase and amplitude control of the driving field,” Phys. Rev. A 65, 043819 (2002).
[CrossRef]

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

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]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Eur. Phys. J. D

M. Sahrai, A. Maleki, R. Hemmati, and M. Mahmoudi, “Transient dispersion and absorption in a V-shaped atomic system,” Eur. Phys. J. D 56, 105–112 (2010).
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[CrossRef]

J. Everes, 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]

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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S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Atom localization via resonance fluorescence,” Phys. Rev. A 61, 063806(2000).
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M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Standing-wave field is aligned in the x direction and a three-level moving atom enters in the z direction through the cavity. (b) V-shaped three-level system illuminated by two weak pulses with frequencies ωa and ωb, and phases φa and φb. The excited states are coupled by a strong microwave field.

Fig. 2.
Fig. 2.

Imaginary part of susceptibility, χ, as a function of kx for (a) Δ31=Δ21=1γ, (b) Δ31=Δ21=0.8γ, and (c) Δ31=Δ21=0.5γ. Other parameters are γ2=0.2γ, γ3=0.2γ, Ω23=1γ, Ω31=0.05γ, and Ω21=0.05γ.

Fig. 3.
Fig. 3.

Imaginary part of susceptibility, χ, as a function of kx for γ2=0.2γ, γ3=0.2γ, Ω23=50γ, Ω31=0.05γ, Ω21=0.05γ, and Δ31=Δ21=1γ.

Equations (25)

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H=H0+HI,
H0=ω1|11|+ω2|22|+ω3|33|
HI=[Ω12ei(ωat+φa)|12|+Ω13ei(ωbt+φb)|13|+Ω23sin(kx)eiωμt|23|]+H.C.
ρ˙21=(γ2+iω21)ρ21iΩ21ei(ωat+φa)(ρ22ρ11)+iΩ23eiωμtρ31iΩ31ei(ωbt+φb)ρ23,
ρ˙31=(γ3+iω31)ρ31iΩ31ei(ωbt+φb)(ρ33ρ11)+iΩ23eiωμtρ21iΩ21ei(ωat+φa)ρ32,
ρ˙32=(γμ+iω32)ρ32+iΩ32eiωμt(ρ22ρ33)+iΩ31ei(ωbt+φb)ρ12iΩ12ei(ωat+φa)ρ31.
ρ11(0)=1,ρ22(0)=ρ33(0)=ρ32(0)=0,
ρ31=ρ˜31ei(ωbt+φb),ρ21=ρ˜21ei(ωat+φa).
ρ˙˜31=(γ3+iΔ31)ρ˜31+iΩ32eiδφρ˜21+iΩ31,
ρ˙˜21=(γ2+iΔ21)ρ˜21+iΩ23eiδφρ˜31+iΩ21.
R˙(t)=MR+A,
R=(ρ˜31ρ˜21),A=(iΩ31iΩ21),
M=(iΩ32eiδφ(γ2+iΔ21)(γ3+iΔ31)iΩ23eiδφ).
R(t)=M1A.
ρ31=[iΩ31(γ2+iΔ21)Ω21Ω23sin(kx)eiδφ(γ2+iΔ21)(γ3+iΔ31)+|Ω23sin(kx)|2]eiωbt,
χ=N𝒫13ε0Eρ31eiωbt,
χ=N|𝒫13|22ε0z{A[Ω31γ2+Ω21Ω23sin(kx)sin(φ)]+B[Ω31Δ21+Ω21Ω23sin(kx)cos(φ)]},
z=A2+B2
A=(γ2γ3Δ21Δ31+|Ω23sin(kx)|2),B=(Δ21γ3+Δ31γ2).
Δ31=ω322±ω322+4|Ω23sin(kx)|22,
kx=sin1(2Δ31(Δ31+Δ21)Ω23)+nπ.
Heff=(ΔΩ23sinkxeiφΩ23sinkxeiφ0),
|+=eiφcosθ|3+sinθ|2,
|=sinθ|3+eiφcosθ|2,
λ±=Δ±Δ2+4Ω232sin2kx2.

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