Abstract

We study the role of atomic coherence in the propagation dynamics of two-color lasers in an autoionizing medium. By solving the coupled equations for atoms and fields simultaneously, it is found that the asymptotic value of the phase difference after a long propagation distance critically depends on the detuning from an autoionizing resonance and the asymmetry parameter, suggesting that inherent atomic coherence of an autoionizing system, which is absent in a bound state system, plays an important role during the propagation processes. Our numerical findings are consistent with our theoretical analysis using a series expansion method of the coupled equations.

© 2007 Optical Society of America

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  1. M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
    [CrossRef]
  2. M. Shapiro and P. Brumer, "Quantum control of chemical reactions," J. Chem. Soc. Faraday Trans. 93, 1263-1277 (1987).
    [CrossRef]
  3. Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
    [CrossRef] [PubMed]
  4. Ce  Chen and D.S . Elliott, "Measurements of optical-phase variations using interfering multiphoton ionization processes," Phys. Rev. Lett. 65, 1737-1740 (1990).
    [CrossRef] [PubMed]
  5. X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
    [CrossRef]
  6. E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
    [CrossRef]
  7. Takashi  Nakajima, "Possibility of direct determination of the quantum phase of continua utilizing the phase of lasers," Phys. Rev. A 61, 041403(R) (2000).
    [CrossRef]
  8. David  Petrosyan and P.  Lambropoulos, "Phase control of photoabsorption in Optically dense media," Phys. Rev. Lett. 85, 1843-1846 (2000).
    [CrossRef] [PubMed]
  9. David  Petrosyan andP.  Lambropoulos, "Coherent control of autoionization in optically dense media," J. Phys. B 34, 1711-1725 (2001).
    [CrossRef]
  10. Takashi  Nakajima, "Propagation of phase-controlled lasers in a two-level medium," Phys. Rev. A 64, 043406 (2001).
    [CrossRef]
  11. Takashi  Nakajima, "Influence of ac Stark shifts on the propagation of phase-controlled lasers in a two-level medium," J. Opt. Soc. Am. B 19, 261-267 (2002).
    [CrossRef]
  12. M.A. Bouchene, "Phase control of dispersion effects for an ultrashort pulse train propagating in a resonant medium," Phys. Rev. A 66, 065801 (2002).
    [CrossRef]
  13. H.G. Barros, B. Lozano, S.S. Vianna, and L.H. Acioli, "Influence of propagation and external phase in sequential two-photon absorption of femtosecond pulses," Opt. Lett. 30, 3081-3083 (2005).
    [CrossRef] [PubMed]
  14. K. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in threelevel Lambda-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
    [CrossRef]

2006 (1)

K. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in threelevel Lambda-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

2005 (1)

2002 (2)

Takashi  Nakajima, "Influence of ac Stark shifts on the propagation of phase-controlled lasers in a two-level medium," J. Opt. Soc. Am. B 19, 261-267 (2002).
[CrossRef]

M.A. Bouchene, "Phase control of dispersion effects for an ultrashort pulse train propagating in a resonant medium," Phys. Rev. A 66, 065801 (2002).
[CrossRef]

2001 (2)

David  Petrosyan andP.  Lambropoulos, "Coherent control of autoionization in optically dense media," J. Phys. B 34, 1711-1725 (2001).
[CrossRef]

Takashi  Nakajima, "Propagation of phase-controlled lasers in a two-level medium," Phys. Rev. A 64, 043406 (2001).
[CrossRef]

2000 (1)

David  Petrosyan and P.  Lambropoulos, "Phase control of photoabsorption in Optically dense media," Phys. Rev. Lett. 85, 1843-1846 (2000).
[CrossRef] [PubMed]

1999 (1)

E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
[CrossRef]

1996 (1)

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

1990 (2)

Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Ce  Chen and D.S . Elliott, "Measurements of optical-phase variations using interfering multiphoton ionization processes," Phys. Rev. Lett. 65, 1737-1740 (1990).
[CrossRef] [PubMed]

1988 (1)

M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
[CrossRef]

1987 (1)

M. Shapiro and P. Brumer, "Quantum control of chemical reactions," J. Chem. Soc. Faraday Trans. 93, 1263-1277 (1987).
[CrossRef]

Chen, Ce

Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Ce  Chen and D.S . Elliott, "Measurements of optical-phase variations using interfering multiphoton ionization processes," Phys. Rev. Lett. 65, 1737-1740 (1990).
[CrossRef] [PubMed]

Lambropoulos, P.

David  Petrosyan andP.  Lambropoulos, "Coherent control of autoionization in optically dense media," J. Phys. B 34, 1711-1725 (2001).
[CrossRef]

David  Petrosyan and P.  Lambropoulos, "Phase control of photoabsorption in Optically dense media," Phys. Rev. Lett. 85, 1843-1846 (2000).
[CrossRef] [PubMed]

Nakajima, Takashi

Petrosyan, David

David  Petrosyan andP.  Lambropoulos, "Coherent control of autoionization in optically dense media," J. Phys. B 34, 1711-1725 (2001).
[CrossRef]

David  Petrosyan and P.  Lambropoulos, "Phase control of photoabsorption in Optically dense media," Phys. Rev. Lett. 85, 1843-1846 (2000).
[CrossRef] [PubMed]

Acioli, L.H.

Barros, H.G.

Bersohn, R.

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

Bouchene, M.A.

M.A. Bouchene, "Phase control of dispersion effects for an ultrashort pulse train propagating in a resonant medium," Phys. Rev. A 66, 065801 (2002).
[CrossRef]

Brumer, P.

M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
[CrossRef]

M. Shapiro and P. Brumer, "Quantum control of chemical reactions," J. Chem. Soc. Faraday Trans. 93, 1263-1277 (1987).
[CrossRef]

Charalambidis, D.

E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
[CrossRef]

Elliott, D.S

Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Elliott,, D.S

Ce  Chen and D.S . Elliott, "Measurements of optical-phase variations using interfering multiphoton ionization processes," Phys. Rev. Lett. 65, 1737-1740 (1990).
[CrossRef] [PubMed]

Hepburn, J.W.

M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
[CrossRef]

Kawasaki, M.

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

Kim, H.-L.

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

Loiko, K.

K. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in threelevel Lambda-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

Lozano, B.

Papastathopoulos, E.

E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
[CrossRef]

Serrat, C.

K. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in threelevel Lambda-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

Shapiro, M.

M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
[CrossRef]

M. Shapiro and P. Brumer, "Quantum control of chemical reactions," J. Chem. Soc. Faraday Trans. 93, 1263-1277 (1987).
[CrossRef]

Takahashi, K.

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

Vianna, S.S.

Wang, X.

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

Xenakis, D.

E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
[CrossRef]

Yin, , Yi-Yian

Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

M. Shapiro, J.W. Hepburn, and P. Brumer, "Simplified laser control of unimolecular reactions - simultaneous (⌉1 −⌉3) excitation," Chem. Phys. Lett. 149, 451-454 (1988).
[CrossRef]

J. Chem. Phys. (1)

X. Wang, R. Bersohn, K. Takahashi, M. Kawasaki, and H.-L. Kim, "Phase control of absorption in large polyatomic molecules," J. Chem. Phys. 105. 2992-2997 (1996).
[CrossRef]

J. Chem. Soc. Faraday Trans. (1)

M. Shapiro and P. Brumer, "Quantum control of chemical reactions," J. Chem. Soc. Faraday Trans. 93, 1263-1277 (1987).
[CrossRef]

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

J. Phys. B (1)

David  Petrosyan andP.  Lambropoulos, "Coherent control of autoionization in optically dense media," J. Phys. B 34, 1711-1725 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

K. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in threelevel Lambda-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

M.A. Bouchene, "Phase control of dispersion effects for an ultrashort pulse train propagating in a resonant medium," Phys. Rev. A 66, 065801 (2002).
[CrossRef]

Takashi  Nakajima, "Propagation of phase-controlled lasers in a two-level medium," Phys. Rev. A 64, 043406 (2001).
[CrossRef]

E. Papastathopoulos, D. Xenakis, and D. Charalambidis, "Phase-sensitive ionization through multiphotonexcitation schemes involving even numbers of photons," Phys. Rev. A 59, 4840 (1999).
[CrossRef]

Phys. Rev. Lett. (3)

Ce  Chen, Yi-Yian Yin, and D.S . Elliott, "Interference between optical transitions," Phys. Rev. Lett. 64, 507-510 (1990).
[CrossRef] [PubMed]

Ce  Chen and D.S . Elliott, "Measurements of optical-phase variations using interfering multiphoton ionization processes," Phys. Rev. Lett. 65, 1737-1740 (1990).
[CrossRef] [PubMed]

David  Petrosyan and P.  Lambropoulos, "Phase control of photoabsorption in Optically dense media," Phys. Rev. Lett. 85, 1843-1846 (2000).
[CrossRef] [PubMed]

Other (1)

Takashi  Nakajima, "Possibility of direct determination of the quantum phase of continua utilizing the phase of lasers," Phys. Rev. A 61, 041403(R) (2000).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Level scheme. An area above the shaded line represents the ionization continuum. (b) Single-photon ionization spectrum by the third harmonic field only.

Fig. 2.
Fig. 2.

Variation of the fundamental (red line) and harmonic (blue line) fields and the phase difference (black line) for the different propagation depths, αζ = 0,20, and 160 as a function of local time τ. The detuning is chosen to be δ = - 0.5Γ2 as represented by A in Fig. 1(b). All necessary parameters are given in the text.

Fig. 3.
Fig. 3.

Same with Fig. 2 but for the detuning δ = 0.5Γ2 represented by B in Fig. 1(b).

Fig. 4.
Fig. 4.

Same with Fig. 2 but for the detuning δ = 1.5Γ2 represented by C in Fig. 1(b).

Fig. 5.
Fig. 5.

Asymptotic value of the phase difference, ϕ(ζ = ∞), as a function of laser detuning, δ, for the case of q = 1.

Equations (23)

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E ( z , t ) = 1 2 [ ε f ( z , t ) e i ( k f z ω f t ) + ε h ( z , t ) e i ( k h z ω h t ) ] + c . c . ,
u 1 τ = 1 2 Γ 1 f ( 3 ) f 3 + Γ 1 h h 2 u 1 + i [ Ω ͂ ( 3 ) * ( f * ) 3 + Ω ͂ * h * ] u 2 ,
u 2 τ = i [ ( δ S ͂ 2 ) ( S ͂ 2 f S ͂ 1 f ) f 2 ( S ͂ 2 h S ͂ 1 h ) h ] 2 u 2 + i ( Ω ͂ ( 3 ) f 3 + Ω ͂ h ) u 1 ,
f ζ = i [ S 1 f ͂ u 1 2 + s 2 f ͂ u 2 2 f + 3 m ͂ 3 ( f * ) 2 u 2 u 1 ] ,
h ζ = i [ ( s 1 h ͂ u 1 2 + s 2 h ͂ u 2 2 h + m 1 ͂ u 2 u 1 ) ] .
s kp ͂ s kp + i γ kp 2 2 N p ε p 0 2 ( S kp + i Γ kp 2 ) 2 N p ε p 0 2 S ͂ kp ( k = 1 or 2 , p = f or h )
m 3 ͂ N f μ 12 ( 3 ) ( 1 i q ( 3 ) ) ε f 0 3 N f Ω ͂ ( 3 ) ,
m ͂ 3 N h μ 12 ( 1 i q ) ε h 0 N h Ω ͂ ,
N p = ω p N 0 n p ( p = f or h ) ,
f ( ζ = 0 , τ ) f 0 ( τ ) = exp [ 4 ln 2 ( τ τ f ) 2 ] ,
h ( ζ = 0 , τ ) h 0 ( τ ) = exp ( i ϕ 0 ) exp [ 4 ln 2 ( τ τ h ) 2 ] ,
u 2 τ = i ( Ω ͂ ( 3 ) f 3 + Ω ͂ h ) i ( δ i Γ 2 2 ) u 2 .
u 2 ( ζ , τ ) = ( α 0 f 3 + α 1 f 3 τ + ) + ( β 0 h + β 1 h τ + )
α n = i n Ω ͂ ( 3 ) [ δ i Γ 2 2 ] n + 1 ( n = 0 , 1 , 2 , ) ,
β n = i n Ω ͂ [ δ i Γ 2 2 ] n + 1 ( n = 0 , 1 , 2 , ) .
f ζ = i s 1 f ͂ f ,
h ζ = i [ m 1 ͂ α 0 f 3 + ( s 1 h ͂ + m ͂ 1 β 0 ) h ] ,
f ( ζ , τ ) = f 0 ( τ ) e i s 1 f ͂ ζ ,
h ( ζ , τ ) = ( e i ϕ 0 + α 0 m ͂ 1 3 s 1 f ͂ + ( s 1 h ͂ + m 1 ͂ β 0 ) ) [ f 0 ( τ ) ] 3 e i ( s 1 h ͂ + m 1 ͂ β 0 ) ζ α 0 m ͂ 1 3 s 1 f ͂ + ( s 1 h ͂ + m 1 ͂ β 0 ) [ f 0 ( τ ) ] 3 e s 1 f ͂ ζ .
γ 1 h = 2 Re ( m 1 ͂ ) q Γ 1 h Γ 2 ,
Re Ω ͂ = q 2 Γ 1 h Γ 2 ,
i ( s 1 h ͂ + m 1 ͂ β 0 ) = i s 1 h + Re ( m 1 ͂ ) q Γ 1 h Γ 2 [ 1 + i 2 ( q 1 ) 2 Γ 2 δ i Γ 2 2 ] .
ϕ ( ζ = ) = arg ( α 0 m ͂ 1 3 s 1 f ͂ + ( s 1 h ͂ + m 1 ͂ β 0 ) ) ( δ q Γ 2 2 )

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