Abstract

In free space, where the vacuum mode density varies relatively slowly in the spectral region of an atomic transition, an atom’s real-field and vacuum interactions are effectively decoupled. Consequently, spontaneous decay and the Lamb shift are, for all practical purposes, independent of any real-field atomic perturbation. However, in a colored vacuum (i.e., a low-Q cavity) the vacuum mode density can change significantly in the vicinity of an atomic transition, so that a Stark shift will alter an atom’s vacuum environment and thereby couple real-field and vacuum effects. Since the ac Stark shift is an inherent aspect of multiphoton processes, this coupling is unavoidable for highly nonlinear field–atom interactions that occur in cavities. Here we consider this effect for 3+2 resonance-enhanced multiphoton ionization of xenon.

© 2002 Optical Society of America

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References

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  1. P. W. Milonni, The Quantum Vacuum (Academic, Boston, 1994).
  2. A. Kastler, “Displacement of energy levels of atoms by light,” J. Opt. Soc. Am. 53, 902–910 (1963).
    [CrossRef]
  3. M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
    [CrossRef] [PubMed]
  4. M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
    [CrossRef]
  5. D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. Lett. 59, 2623–2626 (1987).
    [CrossRef] [PubMed]
  6. J. C. Camparo, “Semiclassical random electrodynamics: spontaneous emission and the Lamb shift,” J. Opt. Soc. Am. B 16, 173–181 (1999).
    [CrossRef]
  7. J. C. Camparo, “Semiclassical description of spontaneous decay in a colored vacuum,” Phys. Rev. A 65, 013815–1–013815–12 (2002).
  8. A. T. Georges and P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191–240 (1980).
    [CrossRef]
  9. L. Allen and C. R. Stroud, Jr., “Broadening and saturation in n-photon absorption,” Phys. Rep. 91, 1–29 (1982).
    [CrossRef]
  10. C. M. Korendyke and D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
    [CrossRef]
  11. T. H. Boyer, “General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems,” Phys. Rev. D 11, 809–830 (1975).
    [CrossRef]
  12. W. Cheney and D. Kincaid, Numerical Mathematics and Computing (Brooks Cole, Monterey, Calif., 1985), Chap. 8.
  13. W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188–191 (1982).
    [CrossRef]
  14. J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
    [CrossRef]
  15. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), Chap. 2.
  16. M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
    [CrossRef] [PubMed]
  17. M. Lewenstein and T. W. Mossberg, “Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs,” Phys. Rev. A 37, 2048–2062 (1988).
    [CrossRef] [PubMed]

2002 (1)

J. C. Camparo, “Semiclassical description of spontaneous decay in a colored vacuum,” Phys. Rev. A 65, 013815–1–013815–12 (2002).

1999 (1)

1998 (1)

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

1994 (1)

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

1993 (1)

C. M. Korendyke and D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

1991 (1)

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

1988 (1)

M. Lewenstein and T. W. Mossberg, “Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs,” Phys. Rev. A 37, 2048–2062 (1988).
[CrossRef] [PubMed]

1987 (2)

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. Lett. 59, 2623–2626 (1987).
[CrossRef] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
[CrossRef] [PubMed]

1982 (2)

L. Allen and C. R. Stroud, Jr., “Broadening and saturation in n-photon absorption,” Phys. Rep. 91, 1–29 (1982).
[CrossRef]

W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188–191 (1982).
[CrossRef]

1980 (1)

A. T. Georges and P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191–240 (1980).
[CrossRef]

1975 (1)

T. H. Boyer, “General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems,” Phys. Rev. D 11, 809–830 (1975).
[CrossRef]

1963 (1)

Allen, L.

L. Allen and C. R. Stroud, Jr., “Broadening and saturation in n-photon absorption,” Phys. Rep. 91, 1–29 (1982).
[CrossRef]

Bernardot, F.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Boyer, T. H.

T. H. Boyer, “General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems,” Phys. Rev. D 11, 809–830 (1975).
[CrossRef]

Brune, M.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Camparo, J. C.

J. C. Camparo, “Semiclassical description of spontaneous decay in a colored vacuum,” Phys. Rev. A 65, 013815–1–013815–12 (2002).

J. C. Camparo, “Semiclassical random electrodynamics: spontaneous emission and the Lamb shift,” J. Opt. Soc. Am. B 16, 173–181 (1999).
[CrossRef]

Feld, M. S.

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. Lett. 59, 2623–2626 (1987).
[CrossRef] [PubMed]

Fleetwood, C. M.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Georges, A. T.

A. T. Georges and P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191–240 (1980).
[CrossRef]

Glauber, R. J.

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
[CrossRef] [PubMed]

Gum, J. S.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Haroche, S.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Heinzen, D. J.

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. Lett. 59, 2623–2626 (1987).
[CrossRef] [PubMed]

Herzig, H.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Kastler, A.

Keski-Kuha, R. A. M.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Korendyke, C. M.

C. M. Korendyke and D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Lambropoulos, P.

A. T. Georges and P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191–240 (1980).
[CrossRef]

Lewenstein, M.

M. Lewenstein and T. W. Mossberg, “Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs,” Phys. Rev. A 37, 2048–2062 (1988).
[CrossRef] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
[CrossRef] [PubMed]

Maali, A.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Marrocco, M.

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

Mossberg, T. W.

M. Lewenstein and T. W. Mossberg, “Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs,” Phys. Rev. A 37, 2048–2062 (1988).
[CrossRef] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
[CrossRef] [PubMed]

Nussenzveig, P.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Osantowski, J. F.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Press, W. H.

W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188–191 (1982).
[CrossRef]

Raimond, J. M.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Sang, R. T.

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

Schmidt-Kaler, F.

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

Socker, D. G.

C. M. Korendyke and D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Stroud Jr., C. R.

L. Allen and C. R. Stroud, Jr., “Broadening and saturation in n-photon absorption,” Phys. Rep. 91, 1–29 (1982).
[CrossRef]

Teukolsky, S. A.

W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188–191 (1982).
[CrossRef]

Toft, A. R.

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Walther, H.

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

Weidinger, M.

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

Adv. Electron. Electron Phys. (1)

A. T. Georges and P. Lambropoulos, “Aspects of resonant multiphoton processes,” Adv. Electron. Electron Phys. 54, 191–240 (1980).
[CrossRef]

Adv. Space Res. (1)

J. F. Osantowski, R. A. M. Keski-Kuha, H. Herzig, A. R. Toft, J. S. Gum, and C. M. Fleetwood, “Optical coating technology for the EUV,” Adv. Space Res. 11(11), 185–201 (1991).
[CrossRef]

Comput. Phys. (1)

W. H. Press and S. A. Teukolsky, “Adaptive stepsize Runge–Kutta integration,” Comput. Phys. 6, 188–191 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

C. M. Korendyke and D. G. Socker, “Measured optical performance of three Fabry–Perot interferometers for use in a tunable ultraviolet filter,” Opt. Eng. 32, 2281–2285 (1993).
[CrossRef]

Phys. Rep. (1)

L. Allen and C. R. Stroud, Jr., “Broadening and saturation in n-photon absorption,” Phys. Rep. 91, 1–29 (1982).
[CrossRef]

Phys. Rev. A (2)

J. C. Camparo, “Semiclassical description of spontaneous decay in a colored vacuum,” Phys. Rev. A 65, 013815–1–013815–12 (2002).

M. Lewenstein and T. W. Mossberg, “Spectral and statistical properties of strongly driven atoms coupled to frequency-dependent photon reservoirs,” Phys. Rev. A 37, 2048–2062 (1988).
[CrossRef] [PubMed]

Phys. Rev. D (1)

T. H. Boyer, “General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems,” Phys. Rev. D 11, 809–830 (1975).
[CrossRef]

Phys. Rev. Lett. (4)

M. Brune, P. Nussenzveig, F. Schmidt-Kaler, F. Bernardot, A. Maali, J. M. Raimond, and S. Haroche, “From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection,” Phys. Rev. Lett. 72, 3339–3342 (1994).
[CrossRef] [PubMed]

M. Marrocco, M. Weidinger, R. T. Sang, and H. Walther, “Quantum electrodynamic shifts of Rydberg energy levels between parallel metal plates,” Phys. Rev. Lett. 81, 5784–5787 (1998).
[CrossRef]

D. J. Heinzen and M. S. Feld, “Vacuum radiative level shift and spontaneous-emission linewidth of an atom in an optical resonator,” Phys. Rev. Lett. 59, 2623–2626 (1987).
[CrossRef] [PubMed]

M. Lewenstein, T. W. Mossberg, and R. J. Glauber, “Dynamical suppression of spontaneous emission,” Phys. Rev. Lett. 59, 775–778 (1987).
[CrossRef] [PubMed]

Other (3)

P. W. Milonni, The Quantum Vacuum (Academic, Boston, 1994).

W. Cheney and D. Kincaid, Numerical Mathematics and Computing (Brooks Cole, Monterey, Calif., 1985), Chap. 8.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962), Chap. 2.

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Figures (5)

Fig. 1
Fig. 1

Cavity geometry and the relevant Xe energy levels.

Fig. 2
Fig. 2

3+2 REMPI line shapes. The peak of the photoionization probability is P0, and the laser detuning corresponding to this peak is defined as the vacuum shift, δω.

Fig. 3
Fig. 3

Vacuum shift δω versus Δcav. Circles, complete computational results; dashed curve, fictitious case of κac=0 (referenced to the scale on the right), solid curve, fictitious case of δL(σ; t)=0.

Fig. 4
Fig. 4

Enhancement of Fig. 3 about Δcav=0. Circles, complete computational results; solid curve, fictitious case of δL(σ; t)=0; dashed line, an aid to guide the eye.

Fig. 5
Fig. 5

Peak photoionization probability P0 versus Δcav. Circles, complete computational results; dashed curve, fictitious case of κac=0; solid curve, fictitious case of δL(σ; t)=0.

Tables (1)

Tables Icon

Table 1 Parameters Used in the Density Matrix Calculationsa

Equations (14)

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

σ˙11=Γ1(σ; t)+Ω Im[σ12],
σ˙22=-Γ1(σ; t)-Ω Im[σ12]-γionσ22,
σ˙12=-γion2+i(Δ0-κacI)σ12+iΩ2(σ22-σ11)-Γ12(σ; t)+iδL(σ; t).
Γ1(σ; t)2ω212Δωsπc3|μ21|20tσ22(t)Re[F(t-t)]dt,
Γ2(σ; t)ω212Δωsπc3|μ21|20tσ12(t)×Re{F(t-t)exp[-iΔ0(t-t)]}dt,
δL(σ; t)-ω212Δωsπc3|μ21|20tσ12(t)×Im{F(t-t)exp[-iΔ0(t-t)]}dt.
F(t)=sηsωs exp[i(δs+Δcav)t].
ηs=23κs2-3(κs2-1)4cos(θc)+cos3(θc)3,
1κs=(1-R)1+4R(1-R)2sin2ωsdc1/2.
Γ1(σ; t)Δωs2π-Σ22(ω)Φ(ω)exp(iωt)dω,
Γ2(σ; t)Δωs2π-Σ12(ω)Φ(ω+Δ0)exp(iωt)dω.
Φ(ω)=πsηsωs{δ(δs+Δcav-ω)+δ(δs+Δcav+ω)}.
Γ1exp[iΔcavt]η(x)[x+Δcav+ω210]Σ22(x+Δcav)×exp(ixt)dx+c.c.,
Γ2exp[i(Δcav-κacIpeak)t]η(x)[x+Δcav+ω210]×Σ12(x+Δcav-κacIpeak)exp(ixt)dx+c.c.

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