Abstract

An electronic wave packet is excited in the Rydberg states of atomic calcium. The strong excitation of the remaining valence electron modifies the particular coherent superposition state associated with this Rydberg wave packet due to the electron-electron correlation. This modification is observed by a coherent pump-probe measurement in which the change of the global phase of the wave packet with respect to a local oscillator is found. The magnitude of the electron-electron correlation is varied experimentally and leads to sharp resonances in the phase. The coherence is maintained despite the open autoionization channel. The process also allows the manipulation of individual states within the wave packet.

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  1. W.S. Warren, and H. Rabitz, and M. Dahleh, "Coherent control of Quantum Dynamics: the Dream is Alive," Science 259, 1581-89 (1983).
    [CrossRef]
  2. I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve and Albert Stolow, "Wave Packet Isotope Separation," Phys. Rev. Lett. 77, 3518-3521 (1996).
    [CrossRef] [PubMed]
  3. B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwenter, R. M. Whitnell, and Y. Yan, "Quantum Control of Wave Packet Evolution with Tailored Femtosecond Pulses," Phys. Rev. Lett.74, 3360-3363 (1995).
    [CrossRef] [PubMed]
  4. A. P. Heberle, J. J. Baumberg, and K. Kohler, "Ultrafast coherent control and destruction of excitons in quantum wells," Phys. Rev. Lett. 75, 2598 (1995).
    [CrossRef] [PubMed]
  5. A. Ekert and R. Jozsa, "Quantum computation and Shor's factoring algorithm," Rev. Mod. Phys. 68, 733-53 (1996).
    [CrossRef]
  6. T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Measurement of the Amplitude and Phase of a Sculpted Rydberg Wave Packet," Phys. Rev. Lett. 80, 5508-5511 (1998).
    [CrossRef]
  7. T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wave function," Nature 397, 233-35 (1999).
    [CrossRef]
  8. G. Alber and P. Zoller, "Laser excitation of electronic wave packets in Rydberg atoms," Phys. Rep. 199, 231-280 (1991) and references therein.
    [CrossRef]
  9. M. W. Noel and C. R. Stroud, Jr., "Excitation of an Atomic Electron to a Coherent Superposition of Macroscopically Distinct States," Phys. Rev. Lett. 77, 1913-1916 (1996).
    [CrossRef] [PubMed]
  10. J. Parker and C.R. Stroud, Jr., "Coherence and decay of Rydberg wave Packets," Phys. Rev. Lett. 56, 716-719 (1986).
    [CrossRef] [PubMed]
  11. A. ten Wolde, L.D. Noordam, H.G. Muller, A. Lagendijk, and H.B. van Linden van den Heuvell,"Observation of radially localized atomic electron wave packets," Phys. Rev. Lett. 61, 2099-2101 (1988).
    [CrossRef]
  12. John A. Yeazell, Mark Mallalieu, and C. R. Stroud, Jr., "Observation of the collapse and revival of a Rydberg electronic wave packet," Phys. Rev. Lett. 64, 2007-2010 (1990).
    [CrossRef] [PubMed]
  13. W.E. Cooke, T.F. Gallagher, S.A. Edelstein, and R.M. Hill, "Doubly excited autoionizing Rydberg states of Sr," Phys. Rev. Lett. 40, 178-181 (1978).
    [CrossRef]
  14. X. Wang and W.E. Cooke, "Wave-front autoionization: Classical decay of two-electron atoms," Phys. Rev. Lett. 67, 976-979 (1991).
    [CrossRef] [PubMed]
  15. X. Wang and W.E. Cooke, "Wave-function shock waves," Phys. Rev. A46, 4347-4353 (1992).
  16. X. Wang and W.E. Cooke, "Amplitude modulation of atomic wave functions," Phys. Rev. A46, R2201-R2204 (1992).
  17. F. Robicheaux, "Atomic dynamics with photon-dressed core states,"Phys. Rev. A47, 1391-1402 (1993).
  18. Lars G. Hanson and P. Lambropoulos, "Nondispersing wave packets in two-electron atoms: Atomic mode locking by loss modulation," Phys. Rev.Lett. 74, 5009-5012(1995).
    [CrossRef] [PubMed]
  19. N.J. Druten and H.G. Muller, "Rydberg transitions induced by optical core dressing,"Phys. Rev. A52, 3047-3056 (1995).
  20. F. Robicheaux and W. T. Hill III, "Autoionizing Rydberg wave packets," Phys. Rev. A54, 3276-3289 (1996).
  21. O. Zobay and G. Alber,"Spontaneous photon emission in isolated-core excited Rydberg systems and dynamics of electronic wave packets" Phys. Rev. A54, 5361-5373 (1996).
  22. Xin Chen and John A. Yeazell, "Autoionization of a quasicontinuum: Population trapping, self- trapping, and stabilization," Phys. Rev. A58, 1267-1274 (1998).
  23. R. R. Jones, "Measurement of electronic radial probability distributions using time-resolved isolated core excitation," Phys. Rev. A57, 446-451 (1998).
  24. M. B. Campbell, T. J. Bensky and R. R. Jones, "Observation of oscillations between degenerate bound-state configurations in rapidly autoionizing two-electron atoms," Phys. Rev. A57, 4616- 4620 (1998).
  25. D. W. Schumacher, B. J. Lyons, and T. F. Gallagher , "Wave Packets in Perturbed Rydberg Systems," Phys. Rev. Lett. 78, 4359-4362 (1997).
    [CrossRef]
  26. B. J. Lyons, D. W. Schumacher, D. I. Duncan, R. R. Jones and T. F. Gallagher, "Temporal dynamics of a two-electron wave packet," Phys. Rev. A57, 3712-3718 (1998).
  27. Rev. A57, 3712-3718 (1998). 27. M.Strehle, U. Weichmann, and G. Gerber, "Femtosecond time-resolved Rydberg wave-packet dynamics in the two-electron system calcium," Phys. Rev. A58, 450-455 (1998).
  28. Xin Chen and John A. Yeazell, "Observation of a Nondecaying Wave Packet in a Two-Electron Atom" Phys. Rev. Lett. 81, 5772-5775 (1998).
    [CrossRef]
  29. L. D. Noordam, D. I. Duncan, and T. F. Gallagher, "Ramsey fringes in atomic Rydberg wave packets," Phys. Rev. A45, 4734-4737 (1992).
  30. S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien and F. Biraben, "Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity," Opt. Commun. 99, 89-94 (1993).
    [CrossRef]
  31. Xin Chen and John A. Yeazell, "Reconstruction of engineered atomic wave functions via phase- dependent population measurements," Phys. Rev.A 56, 2316-2320 (1997).
    [CrossRef]

Other

W.S. Warren, and H. Rabitz, and M. Dahleh, "Coherent control of Quantum Dynamics: the Dream is Alive," Science 259, 1581-89 (1983).
[CrossRef]

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve and Albert Stolow, "Wave Packet Isotope Separation," Phys. Rev. Lett. 77, 3518-3521 (1996).
[CrossRef] [PubMed]

B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwenter, R. M. Whitnell, and Y. Yan, "Quantum Control of Wave Packet Evolution with Tailored Femtosecond Pulses," Phys. Rev. Lett.74, 3360-3363 (1995).
[CrossRef] [PubMed]

A. P. Heberle, J. J. Baumberg, and K. Kohler, "Ultrafast coherent control and destruction of excitons in quantum wells," Phys. Rev. Lett. 75, 2598 (1995).
[CrossRef] [PubMed]

A. Ekert and R. Jozsa, "Quantum computation and Shor's factoring algorithm," Rev. Mod. Phys. 68, 733-53 (1996).
[CrossRef]

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Measurement of the Amplitude and Phase of a Sculpted Rydberg Wave Packet," Phys. Rev. Lett. 80, 5508-5511 (1998).
[CrossRef]

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wave function," Nature 397, 233-35 (1999).
[CrossRef]

G. Alber and P. Zoller, "Laser excitation of electronic wave packets in Rydberg atoms," Phys. Rep. 199, 231-280 (1991) and references therein.
[CrossRef]

M. W. Noel and C. R. Stroud, Jr., "Excitation of an Atomic Electron to a Coherent Superposition of Macroscopically Distinct States," Phys. Rev. Lett. 77, 1913-1916 (1996).
[CrossRef] [PubMed]

J. Parker and C.R. Stroud, Jr., "Coherence and decay of Rydberg wave Packets," Phys. Rev. Lett. 56, 716-719 (1986).
[CrossRef] [PubMed]

A. ten Wolde, L.D. Noordam, H.G. Muller, A. Lagendijk, and H.B. van Linden van den Heuvell,"Observation of radially localized atomic electron wave packets," Phys. Rev. Lett. 61, 2099-2101 (1988).
[CrossRef]

John A. Yeazell, Mark Mallalieu, and C. R. Stroud, Jr., "Observation of the collapse and revival of a Rydberg electronic wave packet," Phys. Rev. Lett. 64, 2007-2010 (1990).
[CrossRef] [PubMed]

W.E. Cooke, T.F. Gallagher, S.A. Edelstein, and R.M. Hill, "Doubly excited autoionizing Rydberg states of Sr," Phys. Rev. Lett. 40, 178-181 (1978).
[CrossRef]

X. Wang and W.E. Cooke, "Wave-front autoionization: Classical decay of two-electron atoms," Phys. Rev. Lett. 67, 976-979 (1991).
[CrossRef] [PubMed]

X. Wang and W.E. Cooke, "Wave-function shock waves," Phys. Rev. A46, 4347-4353 (1992).

X. Wang and W.E. Cooke, "Amplitude modulation of atomic wave functions," Phys. Rev. A46, R2201-R2204 (1992).

F. Robicheaux, "Atomic dynamics with photon-dressed core states,"Phys. Rev. A47, 1391-1402 (1993).

Lars G. Hanson and P. Lambropoulos, "Nondispersing wave packets in two-electron atoms: Atomic mode locking by loss modulation," Phys. Rev.Lett. 74, 5009-5012(1995).
[CrossRef] [PubMed]

N.J. Druten and H.G. Muller, "Rydberg transitions induced by optical core dressing,"Phys. Rev. A52, 3047-3056 (1995).

F. Robicheaux and W. T. Hill III, "Autoionizing Rydberg wave packets," Phys. Rev. A54, 3276-3289 (1996).

O. Zobay and G. Alber,"Spontaneous photon emission in isolated-core excited Rydberg systems and dynamics of electronic wave packets" Phys. Rev. A54, 5361-5373 (1996).

Xin Chen and John A. Yeazell, "Autoionization of a quasicontinuum: Population trapping, self- trapping, and stabilization," Phys. Rev. A58, 1267-1274 (1998).

R. R. Jones, "Measurement of electronic radial probability distributions using time-resolved isolated core excitation," Phys. Rev. A57, 446-451 (1998).

M. B. Campbell, T. J. Bensky and R. R. Jones, "Observation of oscillations between degenerate bound-state configurations in rapidly autoionizing two-electron atoms," Phys. Rev. A57, 4616- 4620 (1998).

D. W. Schumacher, B. J. Lyons, and T. F. Gallagher , "Wave Packets in Perturbed Rydberg Systems," Phys. Rev. Lett. 78, 4359-4362 (1997).
[CrossRef]

B. J. Lyons, D. W. Schumacher, D. I. Duncan, R. R. Jones and T. F. Gallagher, "Temporal dynamics of a two-electron wave packet," Phys. Rev. A57, 3712-3718 (1998).

Rev. A57, 3712-3718 (1998). 27. M.Strehle, U. Weichmann, and G. Gerber, "Femtosecond time-resolved Rydberg wave-packet dynamics in the two-electron system calcium," Phys. Rev. A58, 450-455 (1998).

Xin Chen and John A. Yeazell, "Observation of a Nondecaying Wave Packet in a Two-Electron Atom" Phys. Rev. Lett. 81, 5772-5775 (1998).
[CrossRef]

L. D. Noordam, D. I. Duncan, and T. F. Gallagher, "Ramsey fringes in atomic Rydberg wave packets," Phys. Rev. A45, 4734-4737 (1992).

S. Bourzeix, M. D. Plimmer, F. Nez, L. Julien and F. Biraben, "Efficient frequency doubling of a continuous wave titanium:sapphire laser in an external enhancement cavity," Opt. Commun. 99, 89-94 (1993).
[CrossRef]

Xin Chen and John A. Yeazell, "Reconstruction of engineered atomic wave functions via phase- dependent population measurements," Phys. Rev.A 56, 2316-2320 (1997).
[CrossRef]

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Figures (4)

Figure 1.
Figure 1.

Experimental setup. The pump and probe pulses interact with the calcium atoms in the thermal beam in the presence of the core laser field. The interference in the total population of the Rydberg states is observed by ionizing those states and counting the resulting electrons.

Figure 2.
Figure 2.

The global phase of the superposition as a function of κ. In (a) experimental measurements are shown. In (b) the results of a theoretical model are shown. The change in this phase probes the modification of the coherence due to the core laser field. The importance of synchronization is seen by the resonance-like structure near κ=0.5 and 0.25. The error bars are derived from the noise in the measured Rydberg atom population.

Figure 3.
Figure 3.

The change in relative phase of neighboring states of the superposition as a function of κ. The theoretical model that produced Fig. 2(b) yields this curve. Note the rapid change in phase near κ=0.5.

Figure 4.
Figure 4.

The radial probability distribution of three wave packet for three values of κ in the vicinity of κ=0.50. The three values are κ=0.48 (blue curve, circle), κ=0.50 (red curve, square), and κ=0.52 (green curve, triangle). The wave packets are shown at the same fixed delay time of 86 ps. Note the localization of the ‘red’ wave packet at the outer turning point.

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