Abstract

Resonances of the six-wave mixing susceptibility χ(5)(ω1, ω1, ω1,-ω2,-ω2) at frequency 3ω1-2ω2 of a system of two-level atoms dissipating through the spontaneous emission and collisions and driven by a weak bichromatic external field of frequencies ω1 and ω2 in a finite Q cavity are analyzed. It is shown that the atomic collisions not only induce the usual Bloembergen resonances but that they also play a major role in enhancing the transitions among the higher-order dressed states, thereby bringing out some of the quantum resonances that are suppressed in the absence of collisions. The important contribution of collisions in this higher-order nonlinear process is the generation of the subharmonic resonances at ±1/2 times the hyperfine splitting of the first and the second excited manifolds.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. S. Agarwal, Advances in Atomic, Molecular and Optical Physics, Vol. 29, D. Bates and B. Bederson, eds. (Academic, San Diego, 1991).
  2. R. R. Puri and A. Ray, “Collision-induced quantum effects in four-wave mixing in a high-Q cavity,” J. Opt. Soc. Am. B 14, 1289–1294 (1997).
    [CrossRef]
  3. R. R. Puri and A. Ray, “Quantum effects in four-wave mixing in a cavity,” Phys. Rev. A 57, 4061–4064 (1998).
    [CrossRef]
  4. V. F. Lukinykh, S. A. Myslivets, A. Popov, and V. V. Slabko, “Nonlinear optical frequency mixing in dye vapors,” Appl. Phys. B 38, 143–146 (1985); A. V. Smith, “Four-photon resonant third-harmonic generation in Hg,” Opt. Lett. 10, 341–343 (1985).
    [CrossRef] [PubMed]
  5. R. Trebino and L. A. Rahn, “Subharmonic resonances in higher-order collision-enhanced wave mixing in a sodium-seeded flame,” Opt. Lett. 12, 912–914 (1987).
    [CrossRef] [PubMed]
  6. R. Trebino, “Alternative nonlinear-optical expansion and diagrammatic approach: Nth-order dephasing-induced effects,” Phys. Rev. A 38, 2921–2931 (1988).
    [CrossRef] [PubMed]
  7. G. S. Agarwal and N. Nayak, “Effect of collisions and saturation on multiphoton processes and nonlinear mixing in the field of two pumps,” Phys. Rev. A 33, 391–396 (1986).
    [CrossRef] [PubMed]
  8. N. Bloembergen, A. R. Bogdan, and M. W. Downer, “Collision-induced coherences in four-wave light mixing,” in Laser Spectroscopy V., A. R. W. McKeller, T. Oka, and B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), pp. 157–165.
  9. E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
    [CrossRef]

1998

R. R. Puri and A. Ray, “Quantum effects in four-wave mixing in a cavity,” Phys. Rev. A 57, 4061–4064 (1998).
[CrossRef]

1997

1988

R. Trebino, “Alternative nonlinear-optical expansion and diagrammatic approach: Nth-order dephasing-induced effects,” Phys. Rev. A 38, 2921–2931 (1988).
[CrossRef] [PubMed]

1987

1986

G. S. Agarwal and N. Nayak, “Effect of collisions and saturation on multiphoton processes and nonlinear mixing in the field of two pumps,” Phys. Rev. A 33, 391–396 (1986).
[CrossRef] [PubMed]

1963

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and N. Nayak, “Effect of collisions and saturation on multiphoton processes and nonlinear mixing in the field of two pumps,” Phys. Rev. A 33, 391–396 (1986).
[CrossRef] [PubMed]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
[CrossRef]

Jaynes, E. T.

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
[CrossRef]

Nayak, N.

G. S. Agarwal and N. Nayak, “Effect of collisions and saturation on multiphoton processes and nonlinear mixing in the field of two pumps,” Phys. Rev. A 33, 391–396 (1986).
[CrossRef] [PubMed]

Puri, R. R.

R. R. Puri and A. Ray, “Quantum effects in four-wave mixing in a cavity,” Phys. Rev. A 57, 4061–4064 (1998).
[CrossRef]

R. R. Puri and A. Ray, “Collision-induced quantum effects in four-wave mixing in a high-Q cavity,” J. Opt. Soc. Am. B 14, 1289–1294 (1997).
[CrossRef]

Rahn, L. A.

Ray, A.

R. R. Puri and A. Ray, “Quantum effects in four-wave mixing in a cavity,” Phys. Rev. A 57, 4061–4064 (1998).
[CrossRef]

R. R. Puri and A. Ray, “Collision-induced quantum effects in four-wave mixing in a high-Q cavity,” J. Opt. Soc. Am. B 14, 1289–1294 (1997).
[CrossRef]

Trebino, R.

R. Trebino, “Alternative nonlinear-optical expansion and diagrammatic approach: Nth-order dephasing-induced effects,” Phys. Rev. A 38, 2921–2931 (1988).
[CrossRef] [PubMed]

R. Trebino and L. A. Rahn, “Subharmonic resonances in higher-order collision-enhanced wave mixing in a sodium-seeded flame,” Opt. Lett. 12, 912–914 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

R. R. Puri and A. Ray, “Quantum effects in four-wave mixing in a cavity,” Phys. Rev. A 57, 4061–4064 (1998).
[CrossRef]

R. Trebino, “Alternative nonlinear-optical expansion and diagrammatic approach: Nth-order dephasing-induced effects,” Phys. Rev. A 38, 2921–2931 (1988).
[CrossRef] [PubMed]

G. S. Agarwal and N. Nayak, “Effect of collisions and saturation on multiphoton processes and nonlinear mixing in the field of two pumps,” Phys. Rev. A 33, 391–396 (1986).
[CrossRef] [PubMed]

Proc. IEEE

E. T. Jaynes and F. W. Cummings, “Comparison of quantum and semiclassical radiation theories with application to the beam maser,” Proc. IEEE 51, 89 (1963).
[CrossRef]

Other

G. S. Agarwal, Advances in Atomic, Molecular and Optical Physics, Vol. 29, D. Bates and B. Bederson, eds. (Academic, San Diego, 1991).

N. Bloembergen, A. R. Bogdan, and M. W. Downer, “Collision-induced coherences in four-wave light mixing,” in Laser Spectroscopy V., A. R. W. McKeller, T. Oka, and B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), pp. 157–165.

V. F. Lukinykh, S. A. Myslivets, A. Popov, and V. V. Slabko, “Nonlinear optical frequency mixing in dye vapors,” Appl. Phys. B 38, 143–146 (1985); A. V. Smith, “Four-photon resonant third-harmonic generation in Hg,” Opt. Lett. 10, 341–343 (1985).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the dressed states relevant to the 6WM process. Δm=2gm+1 represents the hyperfine splitting of the excited levels |ψ±m. (b) Transition channel between the states of an excited manifold |ψ±m and the ground state |0, -1/2〉. Two possible transitions are shown by the solid lines. (c) Transition channel between any two excited manifolds |ψ±m and |ψ±n. Four transition lines are shown.

Fig. 2
Fig. 2

Sn=|χ(5)(Ω)|/|χmax(5)(Ω)| as a function of δ/g (δ=ω2-ω1), for δ1=0, κ=0.01g, and γ=0.01g. The solid curve is for γc=0, and the dotted curve is for γc=0.05g.

Fig. 3
Fig. 3

(a) Sn=|χ(5)(Ω)|/|χmax(5)(Ω)| as a function of δ/g, in the range δ/g=-2.10.2, with δ1=0.1g, κ=0.01g, and γ=0.001g. The solid, dashed, and dotted curves represent the cases in which γc=0, γc=0.02g, and γc=0.05g, respectively. (b) Same as (a), but projecting the region δ/g=0.21.6. (c) Same as (a), but projecting the region δ/g=1.52.8.

Fig. 4
Fig. 4

Sn=|χ(5)(Ω)|/|χmax(5)(Ω)| as a function of δ/g, for δ1=0.1g, κ=0.01g, γ=0.001g, with γc=0.1g (solid curve) and γc=0.5g (dashed curve).

Equations (24)

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

dρdt=Lρ+Le(t)ρ,
Lρ=-i[H0, ρ]+Laρ+Lfρ+Lcρ,
Le(t)ρ=-i[He(t), ρ],
H0=ω0Sz+ω0aa+g(S+a+aS-),
Lfρ=κ(2aρa-aaρ-ρaa)
Laρ=γ(2S-ρS+-S+S-ρ-ρS+S-),
Lcρ=γc(2SzρSz-Sz2ρ-ρSz2)
He(t)=d[1 exp(-iω1t)+2 exp(-iω2t)]S++h.c.,
ρ(5)=ρ(5)(1)+ρ(5)(2)+ρ(5)(3)+ρ(5)(4),
ρ(5)(1)=d*2d3 1L+iΩ S+, 1L+2i(ω1-ω2)×S+, 1L+i(ω1-2ω2) S+, 1L-2iω2×S-, 1L-iω2[S-,ρ(0)]+1L+i(ω1-2ω2) S-, 1L+i(ω1-ω2)×S+, 1L-iω2[S-,ρ(0)]+1L+i(ω1-2ω2)S-, 1L+i(ω1-ω2)×S-, 1L+iω1[S+, ρ(0)],
ρ(5)(2)=d*2d3 1L+iΩ S+, 1L+2i(ω1-ω2)×S-,1L+i(2ω1-ω2)×S+, 1L+i(ω1-ω2) S-, 1L+iω1×[S+, ρ(0)]+1L+i(2ω1-ω2)×S+, 1L+i(ω1-ω2) S+, 1L-iω2×[S-, ρ(0)]+1L+i(2ω1-ω2)×S-, 1L+2iω1×S+, 1L+iω1[S+, ρ(0)],
ρ(5)(3)=d*2d3 1L+iΩ S-, 1L+i(3ω1-ω2)×S+, 1L+i(2ω1-ω2)×S+, 1L+i(ω1-ω2) S-, 1L+iω1×[S+, ρ(0)]+1L+i(2ω1-ω2)×S+, 1L+i(ω1-ω2) S+, 1L-iω2×[S-, ρ(0)]+1L+i(2ω1-ω2)×S-, 1L+2iω1×S+, 1L+iω1[S+, ρ(0)],
ρ(5)(4)=d*2d3 1L+iΩ S-, 1L+i(3ω1-ω2)×S-, 1L+3iω1 S+, 1L+2iω1×S+, 1L+iω1[S+, ρ(0)].
ρ(0)=|0,-1/20,-1/2|,
|ψ±m=12[|m,½±|m+1,-½],
m=0, 1, 2, 3 ,,
H0|ψ±m=λ±m|ψ±m,
λ±m=(m+½)ω0±gm+1.
(L+iα)X=A(α)X+BY,
(L+iα)-1X=A-1X-A-1·B·(L+iα)-1Y.
(L+iα)X=AX+BY,(L+iα)Y=CY+DZ,
(L+iα)Z=FZ,
(L+iα)-1X=EX-EY+EZ,
n(ω1-ω2)=±ωhfsm,or(ω1-ω2)=±ωhfsmn,

Metrics