Abstract

Simple and efficient λ-method and λ/2-method (λ is the resonant wavelength of laser radiation) based on a nanometric-thickness cell filled with rubidium (Rb) are implemented to study the splitting of hyperfine transitions of an Rb85 and Rb87 D1 line in an external magnetic field in the range of B=0.50.7T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in Rb85 (Rb87) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B>0.5T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). The expressions derived in the frame of completely uncoupled basis (J,mJ;I,mI) describe the experimental results extremely well for Rb85 transitions at B>0.6T (that is a manifestation of hyperfine Paschen–Back regime). A remarkable result is that the calculations based on the eigenstates of the coupled (F,mF) basis, which adequately describe the system for a low magnetic field, also predict reduction of the number of transition components from 20 to 6 for Rb85 and from 12 to 4 for Rb87 spectrum at B>0.5T. Also, the Zeeman transition frequency shifts, frequency intervals between the components and their slope versus B, are in agreement with the experiment.

© 2014 Optical Society of America

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  1. J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
    [CrossRef]
  2. J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
    [CrossRef]
  3. M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
    [CrossRef]
  4. P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
    [CrossRef]
  5. E. B. Aleksandrov, M. P. Chaika, and G. I. Khvostenko, Interference of Atomic States (Springer, 1993).
  6. D. Sarkisyan, A. Papoyan, T. Varzhapetyan, K. Blushs, and M. Auzinsh, “Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic field,” J. Opt. Soc. Am. B 22, 88–95 (2005).
    [CrossRef]
  7. B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
    [CrossRef]
  8. M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).
  9. L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).
  10. A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
    [CrossRef]
  11. A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
    [CrossRef]
  12. D. A. Steck, Rubidium 85 D linedata, http://steck.us/alkalidata/rubidium85numbers.pdf .
  13. D. A. Steck, Rubidium 87 D line data, http://steck.us/alkalidata/rubidium87numbers.pdf .
  14. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3mj Symbols (World Scientific, 1988).
  15. D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
    [CrossRef]
  16. A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
    [CrossRef]
  17. D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
    [CrossRef]
  18. C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
    [CrossRef]
  19. G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
    [CrossRef]

2012 (4)

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

2011 (2)

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

2008 (1)

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

2007 (2)

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

2005 (1)

2004 (1)

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

2003 (1)

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

2001 (1)

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

1990 (1)

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Adams, C. S.

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

Adams, Ch. S.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Aleksandrov, E. B.

E. B. Aleksandrov, M. P. Chaika, and G. I. Khvostenko, Interference of Atomic States (Springer, 1993).

Andreeva, C.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

Atvars, A.

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

Auzinsh, M.

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

D. Sarkisyan, A. Papoyan, T. Varzhapetyan, K. Blushs, and M. Auzinsh, “Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic field,” J. Opt. Soc. Am. B 22, 88–95 (2005).
[CrossRef]

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

Beaubien, J.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Bloch, D.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Blushs, K.

Breton, M.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Budker, D.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

Cartaleva, S.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

Chaika, M. P.

E. B. Aleksandrov, M. P. Chaika, and G. I. Khvostenko, Interference of Atomic States (Springer, 1993).

Cyr, N.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Ducloy, M.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Dutier, G.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

Fichet, M.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Gorza, M.-P.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Hakhumyan, G.

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

Hamdi, I.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Happer, W.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

Hughes, I. G.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Jau, Y.-Y.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

Keaveney, J.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

Khersonskii, V. K.

D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3mj Symbols (World Scientific, 1988).

Khvostenko, G. I.

E. B. Aleksandrov, M. P. Chaika, and G. I. Khvostenko, Interference of Atomic States (Springer, 1993).

Kleinbach, K. S.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Knappe, S.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Krohn, U.

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

Leroy, C.

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

Levesque, M.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Lezama, A.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Malakyan, Yu.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Maurin, I.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Michaud, A.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Mirzoyan, R.

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

Moskalev, A. N.

D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3mj Symbols (World Scientific, 1988).

Olsen, B. A.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

Papoyan, A.

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

D. Sarkisyan, A. Papoyan, T. Varzhapetyan, K. Blushs, and M. Auzinsh, “Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic field,” J. Opt. Soc. Am. B 22, 88–95 (2005).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Pashayan-Leroy, Y.

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

Patton, B.

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

Petrov, L.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

Rochester, S. M.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

Saltiel, S.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

Saltiel, S. M.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

Sargsyan, A.

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

Sarkisyan, A.

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Sarkisyan, D.

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

A. Sargsyan, G. Hakhumyan, C. Leroy, Y. Pashayan-Leroy, A. Papoyan, and D. Sarkisyan, “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012).
[CrossRef]

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

D. Sarkisyan, A. Papoyan, T. Varzhapetyan, K. Blushs, and M. Auzinsh, “Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic field,” J. Opt. Soc. Am. B 22, 88–95 (2005).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Thériault, S.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Todorov, P.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Tremblay, P.

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Varshalovich, D. A.

D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3mj Symbols (World Scientific, 1988).

Varzhapetyan, T.

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

D. Sarkisyan, A. Papoyan, T. Varzhapetyan, K. Blushs, and M. Auzinsh, “Fluorescence of rubidium in a submicrometer vapor cell: spectral resolution of atomic transitions between Zeeman sublevels in a moderate magnetic field,” J. Opt. Soc. Am. B 22, 88–95 (2005).
[CrossRef]

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

Weller, L.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Yarovitski, A.

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

Yarovitsky, A.

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

Zentile, M. A.

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Appl. Phys. B (1)

A. Sargsyan, Y. Pashayan-Leroy, C. Leroy, R. Mirzoyan, A. Papoyan, and D. Sarkisyan, “High contrast D 1 line electromagnetically induced transparency in nanometric-thin rubidium vapor cell,” Appl. Phys. B 105, 767–774 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

A. Sargsyan, G. Hakhumyan, A. Papoyan, D. Sarkisyan, A. Atvars, and M. Auzinsh, “A novel approach to quantitative spectroscopy of atoms in a magnetic field and applications based on an atomic vapor cell with L = λ,” Appl. Phys. Lett. 93, 021119 (2008).
[CrossRef]

Europhys. Lett. (2)

M. Fichet, G. Dutier, A. Yarovitsky, P. Todorov, I. Hamdi, I. Maurin, S. Saltiel, D. Sarkisyan, M.-P. Gorza, D. Bloch, and M. Ducloy, “Exploring the van der Waals atom-surface attraction in the nanometric range,” Europhys. Lett. 77, 54001 (2007).
[CrossRef]

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. 63, 35–41 (2003).
[CrossRef]

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

J. Phys. B (1)

L. Weller, K. S. Kleinbach, M. A. Zentile, S. Knappe, Ch. S. Adams, and I. G. Hughes, “Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime,” J. Phys. B 45, 215005 (2012).

Opt. Commun. (1)

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs vapour layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

D. Sarkisyan, T. Varzhapetyan, A. Sarkisyan, Yu. Malakyan, A. Papoyan, A. Lezama, D. Bloch, and M. Ducloy, “Spectroscopy in an extremely thin vapor cell: Comparing the cell-length dependence in fluorescence and in absorption techniques,” Phys. Rev. A 69, 065802 (2004).
[CrossRef]

C. Andreeva, S. Cartaleva, L. Petrov, S. M. Saltiel, D. Sarkisyan, T. Varzhapetyan, D. Bloch, and M. Ducloy, “Saturation effects in the sub-Doppler spectroscopy of cesium vapor confined in an extremely thin cell,” Phys. Rev. A 76, 013837 (2007).
[CrossRef]

B. A. Olsen, B. Patton, Y.-Y. Jau, and W. Happer, “Optical pumping and spectroscopy of Cs vapor at high magnetic field,” Phys. Rev. A 84, 063410 (2011).
[CrossRef]

P. Tremblay, A. Michaud, M. Levesque, S. Thériault, M. Breton, J. Beaubien, and N. Cyr, “Absorption profiles of alkali-metal D lines in the presence of a static magnetic field,” Phys. Rev. A 42, 2766 (1990).
[CrossRef]

Phys. Rev. Lett. (2)

J. Keaveney, A. Sargsyan, U. Krohn, D. Sarkisyan, I. G. Hughes, and C. S. Adams, “Cooperative Lamb shift in an atomic vapor layer of nanometer thickness,” Phys. Rev. Lett. 108, 173601 (2012).
[CrossRef]

J. Keaveney, I. G. Hughes, A. Sargsyan, D. Sarkisyan, and C. S. Adams, “Maximal refraction and superluminal propagation in a gaseous nanolayer,” Phys. Rev. Lett. 109, 233001 (2012).
[CrossRef]

Other (5)

E. B. Aleksandrov, M. P. Chaika, and G. I. Khvostenko, Interference of Atomic States (Springer, 1993).

D. A. Steck, Rubidium 85 D linedata, http://steck.us/alkalidata/rubidium85numbers.pdf .

D. A. Steck, Rubidium 87 D line data, http://steck.us/alkalidata/rubidium87numbers.pdf .

D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3mj Symbols (World Scientific, 1988).

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

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Figures (13)

Fig. 1.
Fig. 1.

Photograph of the NTC with vertically wedged vapor gap. Regions of L=λ/2=397.5nm and L=λ=795nm are marked. SA is the sapphire side-arm filled with metallic Rb.

Fig. 2.
Fig. 2.

Sketch of the experimental setup. ECDL, diode laser; FI, Faraday isolator; 1, λ/4 plate; 2, NTC in the oven; PBS, polarizing beam splitter; 3, permanent ring magnets; 4, photodetectors; 5, stainless steel Π-shape holder; 6, auxiliary Rb NTC with thickness L=λ/2; BD, beam dumper.

Fig. 3.
Fig. 3.

Transmission spectrum of Rb NTC with L=λ for B=0.52T and σ+ laser excitation. The VSOP resonances marked 4–9 belong to Rb85, resonances marked 1, 2, 3, 10 belong to Rb87. The lower curve is fluorescence spectrum of the reference NTC with L=λ/2, showing the positions of Rb87 Fg=1Fe=1,2 transitions for B=0, labeled as 11 and 12.

Fig. 4.
Fig. 4.

Transmission spectrum of Rb NTC with L=λ for B=0.677T and σ+ laser excitation. The labeling of VSOP resonances is the same as in Fig. 3. All the VSOP resonances are well resolved. The lower curve is the fluorescence spectrum of the reference NTC with L=λ/2, showing the positions of Rb87 Fg=1Fe=1,2 transitions for B=0.

Fig. 5.
Fig. 5.

(a) Diagram of the Rb85 D1 line transitions in the HPB regime for σ+ laser excitation. (b) Magnetic field dependence of the frequency shifts for the transition components 4–9. Red solid lines 4–9, calculation by the coupled basis theory; black solid lines (4)–(9), calculation by the HPB theory; symbols, experimental results (measurement inaccuracy is ±1%). Note that the curves 9 and (9) are completely overlapped.

Fig. 6.
Fig. 6.

Theoretical magnetic field dependence of Fg=2,3 ground hyperfine levels of Rb85. Red lines, calculations by the coupled basis theory; black lines, calculations as given by Eq. (12) (HPB regime). Ground levels for the transitions 4–9 are indicated as (4)g(9)g.

Fig. 7.
Fig. 7.

(a) Diagram of the Rb87 D1 line transitions in the HPB regime for σ+ laser excitation. (b) Magnetic field dependence of the frequency shifts for the transition components 1–3 and 10. Red solid lines 1–3, 10, calculation by the coupled basis theory; black solid lines (1)–(3), (10), calculation by the HPB theory; symbols, experimental results (measurement inaccuracy is ±1%). Note, that the red curve 10 and black curve (10) are completely overlapped.

Fig. 8.
Fig. 8.

Comparison of spectra obtained by the λ-method (upper graph) and λ/2-method (lower graph) for B=0.605T.

Fig. 9.
Fig. 9.

Probabilities of nine Zeeman components of Fg=2Fe=2,3 transitions of Rb85 D1 line labeled in the inset versus B for the case of σ+ excitation.

Fig. 10.
Fig. 10.

Probabilities of nine Zeeman components of Fg=3Fe=2,3 transitions of Rb85 D1 line labeled in the inset versus B for the case of σ+ excitation.

Fig. 11.
Fig. 11.

Diagram of Rb87 D1 line transitions in the frame of coupled basis for σ+ laser excitation; the selection rules, ΔF=0,1; ΔmF=+1.

Fig. 12.
Fig. 12.

Calculated probabilities of Zeeman transitions 1–3, 7 and 8 for σ+ laser excitation versus magnetic field.

Fig. 13.
Fig. 13.

Calculated probabilities of Zeeman transitions 16 and 10 for σ+ laser excitation versus magnetic field.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

|(JI)FmF,
|JmJ|ImI,
|(JI)FmF=(1)JI+mF2F+1×mJmI(JIFmJmImF)|JmJ|ImI,
|JmJ|ImI=(1)JI+mF2F+1×FmF(JIFmJmImF)|(JI)FmF,
H^=H^0+H^hfs+H^B,
H^hfs=AhfsI^J^+Bhfs3(I^J^)2+32(I^J^)I(I+1)J(J+1)2I(2I1)J(2J1),
H^B=μ^JB^μ^IB^=gJμBJ^B^+gIμBI^B^,
(JI)FimF|J|(JI)FkmF=(1)J+I+Fi+FkmF+1×(2Fi+1)(2Fk+1)J(J+1)(2J+1)×(Fi1FkmF0mF){JFiIFkJ1},
(JI)FimF|I|(JI)FkmF=(1)J+I+Fi+FkmF+1×(2Fi+1)(2Fk+1)I(I+1)(2I+1)×(Fi1FkmF0mF){IFiJFkI1},
Ehfs=12AhfsK+Bhfs32K(K+1)2I(I+1)J(J+1)4I(2I1)J(2J1),
K=F(F+1)I(I+1)J(J+1).
E|J,mJ,I,mI=AhfsmJmI+μB(gJmJ+gImI)B,
2(I^J^)=F^2I^2J^2,
JmJ|ImI|I^J^|JmJ|ImI=12F(1)2J2I+mJ+mJ+mI+mI(2F+1)×(JIFmJmImJmI)(JIFmJmImJmI)×[F(F+1)J(J+1)I(I+1)].
ΔE=gFμBBmF,
Δnk={Ahfs(P1/2)mJ[mI(n)mI(k)]+Ahfs(S1/2)mJ[mI(n)mI(k)]}.
S=[gJ(P1/2)mJ+gJ(S1/2)mJ]μB/B18.6MHz/mT,

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