Abstract

On the basis of density matrix equations, we theoretically investigated narrow sub-Doppler resonances in the spectral distribution of a number of atomic particles (atoms or molecules) optically excited in a metastable state in an ultrathin gas cell with the inner thickness less than or of the order of the wavelength λ1μm of the monochromatic light wave incident in the normal direction. Essential dependence of these resonances (on the center of the optical transition) was analyzed versus the inner thickness and transversal size of such a gas cell and also versus the intensity of the incident wave. Investigated resonances may be applied as references in high-accuracy optical frequency standards and for high precision measurements.

© 2011 Optical Society of America

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References

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  1. W. Demtröder, Laser Spectroscopy: Basic Concept and Instrumentation (Springer, 2003).
  2. F. Riehle, Frequency Standards-Basics and Applications(Wiley-VCH, 2004).
  3. A. Ch. Izmailov, “On the possibility of detecting the sub-Doppler structure of spectral lines of gas particles by a single traveling monochromatic wave,” Laser Phys. 2, 762–763(1992).
  4. A. Ch. Izmailov, “Manifestations of the sub-Doppler structure of spectral lines of gas particles in a radiation of a traveling monochromatic pumping wave,” Opt. Spectrosc. 74, 25–29(1993).
  5. S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
    [CrossRef]
  6. S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
    [CrossRef]
  7. A. Ch. Izmailov, “Sub-Doppler spectroscopy based on optical pumping and transit relaxation of atoms in a thin gas cell,” Proc. SPIE 6727, 67270B (2007).
    [CrossRef]
  8. 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]
  9. K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).
  10. S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
    [CrossRef]
  11. A. A. Radtsig and B. M. Smirnov, Reference Data on atoms, molecules and ions (Springer, 1985).
    [CrossRef]
  12. N. Beverini and A. Ch. Izmailov, “Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell,” Opt. Commun. 282, 2527–2531 (2009).
    [CrossRef]
  13. N. Beverini and A. Ch. Izmailov, “A proposal for optical high-accuracy atomic references using thin cell spectroscopy,” in Proceedings of the EFTF-IFCS 2009 Joint Conference(Besanson, 2009), pp. 1030–1034.
  14. S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (North-Holland, 1991).
  15. V. S. Letokhov, Laser Photoionization Spectroscopy(Academic, 1987).

2009 (3)

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

N. Beverini and A. Ch. Izmailov, “Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell,” Opt. Commun. 282, 2527–2531 (2009).
[CrossRef]

2007 (1)

A. Ch. Izmailov, “Sub-Doppler spectroscopy based on optical pumping and transit relaxation of atoms in a thin gas cell,” Proc. SPIE 6727, 67270B (2007).
[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]

1999 (1)

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

1996 (1)

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
[CrossRef]

1993 (1)

A. Ch. Izmailov, “Manifestations of the sub-Doppler structure of spectral lines of gas particles in a radiation of a traveling monochromatic pumping wave,” Opt. Spectrosc. 74, 25–29(1993).

1992 (1)

A. Ch. Izmailov, “On the possibility of detecting the sub-Doppler structure of spectral lines of gas particles by a single traveling monochromatic wave,” Laser Phys. 2, 762–763(1992).

Beverini, N.

N. Beverini and A. Ch. Izmailov, “Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell,” Opt. Commun. 282, 2527–2531 (2009).
[CrossRef]

N. Beverini and A. Ch. Izmailov, “A proposal for optical high-accuracy atomic references using thin cell spectroscopy,” in Proceedings of the EFTF-IFCS 2009 Joint Conference(Besanson, 2009), pp. 1030–1034.

Bloch, D.

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]

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
[CrossRef]

Briaudeau, S.

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
[CrossRef]

Cartaleva, S.

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

Demtröder, W.

W. Demtröder, Laser Spectroscopy: Basic Concept and Instrumentation (Springer, 2003).

Ducloy, M.

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]

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
[CrossRef]

Dutier, G.

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]

Izmailov, A. Ch.

N. Beverini and A. Ch. Izmailov, “Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell,” Opt. Commun. 282, 2527–2531 (2009).
[CrossRef]

A. Ch. Izmailov, “Sub-Doppler spectroscopy based on optical pumping and transit relaxation of atoms in a thin gas cell,” Proc. SPIE 6727, 67270B (2007).
[CrossRef]

A. Ch. Izmailov, “Manifestations of the sub-Doppler structure of spectral lines of gas particles in a radiation of a traveling monochromatic pumping wave,” Opt. Spectrosc. 74, 25–29(1993).

A. Ch. Izmailov, “On the possibility of detecting the sub-Doppler structure of spectral lines of gas particles by a single traveling monochromatic wave,” Laser Phys. 2, 762–763(1992).

N. Beverini and A. Ch. Izmailov, “A proposal for optical high-accuracy atomic references using thin cell spectroscopy,” in Proceedings of the EFTF-IFCS 2009 Joint Conference(Besanson, 2009), pp. 1030–1034.

Letokhov, V. S.

V. S. Letokhov, Laser Photoionization Spectroscopy(Academic, 1987).

Papoyan, 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]

Radtsig, A. A.

A. A. Radtsig and B. M. Smirnov, Reference Data on atoms, molecules and ions (Springer, 1985).
[CrossRef]

Rautian, S. G.

S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (North-Holland, 1991).

Riehle, F.

F. Riehle, Frequency Standards-Basics and Applications(Wiley-VCH, 2004).

Saltiel, S.

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[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]

Sargsyan, A.

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

Sarkisyan, D.

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[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]

Shalagin, A. M.

S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (North-Holland, 1991).

Slavov, D.

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

Smirnov, B. M.

A. A. Radtsig and B. M. Smirnov, Reference Data on atoms, molecules and ions (Springer, 1985).
[CrossRef]

Todorov, P.

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

Vaseva, K.

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

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]

Acta Phys. Pol. (1)

K. Vaseva, P. Todorov, S. Cartaleva, D. Slavov, and S. Saltiel, “Investigation of the fluorescence spectra of Cs-vapor layers with nanometric thickness,” Acta Phys. Pol. 116, 573–575(2009).

Europhys. Lett. (2)

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337 (1996).
[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. (1)

S. Cartaleva, S. Saltiel, A. Sargsyan, D. Sarkisyan, D. Slavov, P. Todorov, and K. Vaseva, “Sub-Doppler spectroscopy of cesium vapor layers with nanometric and micrometric thickness,” J. Opt. Soc. Am. 26, 1999–2006 (2009).
[CrossRef]

Laser Phys. (1)

A. Ch. Izmailov, “On the possibility of detecting the sub-Doppler structure of spectral lines of gas particles by a single traveling monochromatic wave,” Laser Phys. 2, 762–763(1992).

Opt. Commun. (1)

N. Beverini and A. Ch. Izmailov, “Sub-Doppler spectroscopy of atoms excited in the regime of Rabi oscillations in a thin gas cell,” Opt. Commun. 282, 2527–2531 (2009).
[CrossRef]

Opt. Spectrosc. (1)

A. Ch. Izmailov, “Manifestations of the sub-Doppler structure of spectral lines of gas particles in a radiation of a traveling monochromatic pumping wave,” Opt. Spectrosc. 74, 25–29(1993).

Phys. Rev. A (1)

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

Proc. SPIE (1)

A. Ch. Izmailov, “Sub-Doppler spectroscopy based on optical pumping and transit relaxation of atoms in a thin gas cell,” Proc. SPIE 6727, 67270B (2007).
[CrossRef]

Other (6)

A. A. Radtsig and B. M. Smirnov, Reference Data on atoms, molecules and ions (Springer, 1985).
[CrossRef]

W. Demtröder, Laser Spectroscopy: Basic Concept and Instrumentation (Springer, 2003).

F. Riehle, Frequency Standards-Basics and Applications(Wiley-VCH, 2004).

N. Beverini and A. Ch. Izmailov, “A proposal for optical high-accuracy atomic references using thin cell spectroscopy,” in Proceedings of the EFTF-IFCS 2009 Joint Conference(Besanson, 2009), pp. 1030–1034.

S. G. Rautian and A. M. Shalagin, Kinetic Problems of Nonlinear Spectroscopy (North-Holland, 1991).

V. S. Letokhov, Laser Photoionization Spectroscopy(Academic, 1987).

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Figures (5)

Fig. 1
Fig. 1

The gas cell having the shape of the rectangular parallelepiped, with the small thickness l Q .

Fig. 2
Fig. 2

The number N b of metastable atoms (in the whole volume of the cell) versus the frequency detuning δ = ( ω ω 0 ) of the monochromatic radiation, when g / ( k u ) = ( 1 , 2 ) 2.8 · 10 6 and (3) 5.6 · 10 6 , Q = ( 1 , 3 ) 20 mm and (2) 50 nm, l = 0.5 λ , λ = 657 nm .

Fig. 3
Fig. 3

The amplitude A b (a) and width W (b) of the resonance (Fig. 2) versus the Rabi frequency g, when l = ( 1 3 ) 0.5 λ and (4) λ, Q = ( 1 , 4 ) 20 mm , (2) 50 mm , and (3) ∞, λ = 657 nm .

Fig. 4
Fig. 4

The amplitude A b (a) and width W (b) of the resonance (Fig. 2) versus the transversal size Q of the gas cell (Fig. 1), when g / ( k u ) = ( 1 , 3 ) 2.8 · 10 6 and (2) 5.6 · 10 6 , l = ( 1 , 2 ) 0.5 λ , and (3) λ, λ = 657 nm .

Fig. 5
Fig. 5

The amplitude A b (a) and width W (b) of the resonance (Fig. 2) versus the inner thickness l of the gas cell, when g / ( k u ) = ( 1 , 2 , 4 ) 2.8 · 10 6 and (3) 5.6 · 10 6 , Q = ( 1 , 3 ) 20 mm , (2) 50 mm , and (4) ∞, λ = 657 nm .

Equations (6)

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Λ ( z , t ) = 0.5 E · exp [ i ( ω t k z ) ] + c . c . ,
ρ m ( a ) + ρ m ( b ) = n a ( 0 ) ( 2 j + 1 ) · F ˜ ( v ) , ρ m ( b ) t + v ρ m ( b ) r = 0.5 i g m ρ m m ( a b ) * exp [ i ( δ t k z ) ] + c . c . , ρ m m ( a b ) t + v ρ m m ( a b ) r = 0.5 i g m ( ρ m ( b ) ρ m ( a ) ) exp [ i ( δ t k z ) ] ,
ρ m ( b ) ( r , v ) = η ( 0.5 l | z | ) · η ( 0.5 Q | x | ) · η ( 0.5 Q | y | ) × α = ± 1 β = ± 1 σ = ± 1 η ( α · v x ) · η ( β · v y ) · η ( σ · v z ) × { ρ ˜ m ( b ) [ 0.5 Q + α x | v x | ] · η [ ( 0.5 Q + β y ) | v y | ( 0.5 Q + α x ) | v x | ] × η [ ( 0.5 l + σ z ) | v z | ( 0.5 Q + α x ) | v x | ] + ρ ˜ m ( b ) [ ( 0.5 Q + β y ) | v y | ] × η [ ( 0.5 Q + α x ) | v x | ( 0.5 Q + β y ) | v y | ] · η [ ( 0.5 l + σ z ) | v z | ( 0.5 Q + β y ) | v y | ] + ρ ˜ m ( b ) [ 0.5 l + σ z | v z | ] · η [ ( 0.5 Q + α x ) | v x | ( 0.5 l + σ z ) | v z | ] · η [ ( 0.5 Q + β y ) | v y | ( 0.5 l + σ z ) | v z | ] } ,
ρ ˜ m ( b ) ( ξ ) = n a ( 0 ) ( 2 j + 1 ) F ˜ ( v ) × g m 2 · sin 2 { 0.5 ξ · [ g m 2 + ( δ k v z ) 2 ] 1 / 2 } [ g m 2 + ( δ k v z ) 2 ] ,
N b = m = j j [ V ρ m ( b ) ( r , v ) d 3 r ] d 3 v ,
g l > | v z | , g Q > | v x | , g Q > | v y | .

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