Abstract

We study the following situation: A two-level atom interacts according to the Jaynes–Cummings model with a quantized cavity field prepared in a coherent state by a classical source. The atom is selectively ionized after exiting the cavity, and it is found that the field states are highly dependent, for a given interaction time, on the outcome of the measurement and are dramatically different from those in the case of no selective measurement. First we show how to obtain a bifurcated Poisson distribution for which the probability of finding the photon number at the center of the initial Poisson distribution vanishes. Then we study the generation of sub-Poissonian states and show that the cavity field can approach a number state with a sequence of properly prepared and measured atoms.

© 1997 Optical Society of America

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  1. L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
    [CrossRef] [PubMed]
  2. N. Zagury and A. F. R. de Toledo Piza, Phys. Rev. A 50, 2908 (1994).
    [CrossRef] [PubMed]
  3. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
    [CrossRef]
  4. P. Bogár and J. Bergou, Phys. Rev. A 51, 2381 (1995).
    [CrossRef]
  5. P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
    [CrossRef]
  6. P. Meystre, Opt. Lett. 12, 669 (1987).
    [CrossRef] [PubMed]
  7. J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987).
    [CrossRef] [PubMed]
  8. K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
    [CrossRef] [PubMed]
  9. B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
    [CrossRef] [PubMed]
  10. P. Filipowicz, J. Javanainen, and P. Meystre, J. Opt. Soc. Am. B 3, 906 (1986).
    [CrossRef]
  11. J. A. Wheeler, Lett. Math. Phys. 10, 201 (1985).
    [CrossRef]
  12. W. P. Schleich and J. A. Wheeler, J. Opt. Soc. Am. B 4, 1715 (1987).
    [CrossRef]
  13. G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
    [CrossRef] [PubMed]
  14. L. Susskind and J. Glogower, Physics 1, 49 (1964).
  15. W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
    [CrossRef] [PubMed]
  16. M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
    [CrossRef] [PubMed]
  17. J. Gea-Banacloche, Phys. Rev. A 44, 5913 (1991).
    [CrossRef] [PubMed]
  18. L. Mandel, Opt. Lett. 4, 205 (1979).
    [CrossRef] [PubMed]
  19. G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
    [CrossRef] [PubMed]
  20. P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
    [CrossRef] [PubMed]
  21. P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
    [CrossRef] [PubMed]

1996 (3)

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
[CrossRef] [PubMed]

1995 (3)

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
[CrossRef] [PubMed]

P. Bogár and J. Bergou, Phys. Rev. A 51, 2381 (1995).
[CrossRef]

P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
[CrossRef]

1994 (2)

N. Zagury and A. F. R. de Toledo Piza, Phys. Rev. A 50, 2908 (1994).
[CrossRef] [PubMed]

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
[CrossRef] [PubMed]

1992 (1)

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

1991 (2)

J. Gea-Banacloche, Phys. Rev. A 44, 5913 (1991).
[CrossRef] [PubMed]

W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
[CrossRef] [PubMed]

1990 (1)

G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
[CrossRef] [PubMed]

1987 (3)

1986 (1)

1985 (1)

J. A. Wheeler, Lett. Math. Phys. 10, 201 (1985).
[CrossRef]

1979 (1)

1964 (1)

L. Susskind and J. Glogower, Physics 1, 49 (1964).

1963 (1)

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

Akulin, V. M.

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
[CrossRef] [PubMed]

Bardroff, P. J.

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
[CrossRef] [PubMed]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
[CrossRef] [PubMed]

Bergou, J.

P. Bogár and J. Bergou, Phys. Rev. A 51, 2381 (1995).
[CrossRef]

Bergou, J. A.

P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
[CrossRef]

Bogár, P.

P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
[CrossRef]

P. Bogár and J. Bergou, Phys. Rev. A 51, 2381 (1995).
[CrossRef]

Brune, M.

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

Chaturvedi, S.

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Davidovich, L.

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

de Toledo Piza, A. F. R.

N. Zagury and A. F. R. de Toledo Piza, Phys. Rev. A 50, 2908 (1994).
[CrossRef] [PubMed]

Filipowicz, P.

Garraway, B. M.

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

Gea-Banacloche, J.

J. Gea-Banacloche, Phys. Rev. A 44, 5913 (1991).
[CrossRef] [PubMed]

Glogower, J.

L. Susskind and J. Glogower, Physics 1, 49 (1964).

Hagley, E.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

Haroche, S.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

Hillery, M.

P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
[CrossRef]

Javanainen, J.

Jaynes, E. T.

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Kien, F. L.

W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
[CrossRef] [PubMed]

Knight, P. L.

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

Krause, J.

J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987).
[CrossRef] [PubMed]

Kurizki, G.

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

Maali, A.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

Maitre, X.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

Mandel, L.

Mayr, E.

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
[CrossRef] [PubMed]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
[CrossRef] [PubMed]

Meystre, P.

Moya-Cessa, H.

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

Pernigo, M.

W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
[CrossRef] [PubMed]

Raimond, J. M.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

Rempe, G.

G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
[CrossRef] [PubMed]

Schleich, W.

W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
[CrossRef] [PubMed]

Schleich, W. P.

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
[CrossRef] [PubMed]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
[CrossRef] [PubMed]

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
[CrossRef] [PubMed]

W. P. Schleich and J. A. Wheeler, J. Opt. Soc. Am. B 4, 1715 (1987).
[CrossRef]

Schmidt-Kaler, F.

G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
[CrossRef] [PubMed]

Scully, M. O.

J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987).
[CrossRef] [PubMed]

Sherman, B.

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

Srinivasan, V.

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

Susskind, L.

L. Susskind and J. Glogower, Physics 1, 49 (1964).

Tara, K.

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

Vogel, K.

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
[CrossRef] [PubMed]

Walther, H.

G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
[CrossRef] [PubMed]

J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987).
[CrossRef] [PubMed]

Wheeler, J. A.

Wunderlich, C.

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

Zagury, N.

N. Zagury and A. F. R. de Toledo Piza, Phys. Rev. A 50, 2908 (1994).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

Lett. Math. Phys. (1)

J. A. Wheeler, Lett. Math. Phys. 10, 201 (1985).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (11)

B. M. Garraway, B. Sherman, H. Moya-Cessa, P. L. Knight, and G. Kurizki, Phys. Rev. A 49, 535 (1994).
[CrossRef] [PubMed]

J. Gea-Banacloche, Phys. Rev. A 44, 5913 (1991).
[CrossRef] [PubMed]

G. S. Agarwal, S. Chaturvedi, K. Tara, and V. Srinivasan, Phys. Rev. A 45, 4904 (1992).
[CrossRef] [PubMed]

W. Schleich, M. Pernigo, and F. L. Kien, Phys. Rev. A 44, 2172 (1991).
[CrossRef] [PubMed]

J. Krause, M. O. Scully, and H. Walther, Phys. Rev. A 36, 4547 (1987).
[CrossRef] [PubMed]

L. Davidovich, M. Brune, J. M. Raimond, and S. Haroche, Phys. Rev. A 53, 1295 (1996), and references therein.
[CrossRef] [PubMed]

N. Zagury and A. F. R. de Toledo Piza, Phys. Rev. A 50, 2908 (1994).
[CrossRef] [PubMed]

P. Bogár and J. Bergou, Phys. Rev. A 51, 2381 (1995).
[CrossRef]

P. Bogár, J. A. Bergou, and M. Hillery, Phys. Rev. A 51, 2396 (1995).
[CrossRef]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 51, 4963 (1995).
[CrossRef] [PubMed]

P. J. Bardroff, E. Mayr, and W. P. Schleich, Phys. Rev. A 53, 2736 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993).
[CrossRef] [PubMed]

M. Brune, E. Hagley, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996).
[CrossRef] [PubMed]

G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett. 64, 2783 (1990).
[CrossRef] [PubMed]

Physics (1)

L. Susskind and J. Glogower, Physics 1, 49 (1964).

Proc. IEEE (1)

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Layout of the proposed cavity QED experiment. S is a source of classical microwave fields and is used to prepare the cavity in a coherent state.

Fig. 2
Fig. 2

Photon probability distribution when the interaction time is chosen such that there is zero probability of finding 20 photons.

Fig. 3
Fig. 3

Phase distribution for the state with the bifurcated photon probability distribution.

Fig. 4
Fig. 4

Inversion for a second atom interacting with the modified cavity state [Eq. (19)].

Fig. 5
Fig. 5

Variation in the expectation value of the photon number as a function of the scaled interaction time. The atom starts out and is detected in the excited state.

Fig. 6
Fig. 6

Mandel's Q parameter for an atom initially in the excited state interacting with a coherent field state with n¯=5. No state-selective measurement is made of the atom.

Fig. 7
Fig. 7

Same as Fig. 6 but with state-selective measurement. The atom is detected in state |e.

Fig. 8
Fig. 8

Same as Fig. 6 but with n¯=20. No state-selective measurement is made.

Fig. 9
Fig. 9

Same as Fig. 8 but with state-selective measurement. The atom is detected in the excited state.

Fig. 10
Fig. 10

Mandel Q for a second atom interacting with the cavity field modified by the first atom. The atom starts and is detected in |e.

Fig. 11
Fig. 11

Value of Mandel's Q after interaction of the cavity field with N successive atoms. The interaction time T=1.4 is the same for all atoms. All atoms start and are detected in the excited state.

Fig. 12
Fig. 12

Probability of detecting a sequence of N atoms all in state |e.

Fig. 13
Fig. 13

Photon probability distributions when the interaction time is optimized for each atom to minimize Q each time.

Equations (25)

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

H=ω(aa+1/2σ3)+λ(aσ-+aσ+),
HI=λ(aσ-+aσ+).
|α=exp(-|α|2/2)n=0αnn!|n,
|ψf=n=0Cn|n,
Cn=exp(-|α|2/2)αnn!.
|ψaf(t)=|ψg(t)|g+|ψe(t)|e,
|ψg(t)=-in=0Cn-1 sin(Tn)|n(C-1=0),
|ψe(t)=n=0Cn cos(Tn+1)|n
|Φg(t)=1Pg(t)n=0Cn-1 sin(Tn)|n,
Pg(t)=n=0|Cn-1|2 sin2(Tn)
|Φe(t)=1Pe(t)n=0Cn cos(Tn+1)|n,
Pe(t)=n=0|Cn|2 cos2(Tn+1).
Png(t)=|Cn-1|2 sin(Tn)m=0|Cm-1|2 sin2(Tm).
|θ=n=0 exp(inθ)|n(-π<θπ).
P(θ, t)=12π|θ|Φg(t)|2.
|±|α|T=0exp(iT/n¯/2)||α ×exp(iT/2n¯).
|e|α12[exp(-iTn¯/2)|+|α exp(-iT/2n¯)+exp(iTn¯/2)|-|α exp(iT/2n¯)].
exp(-iTn¯/2)|α exp(-iT/2n¯)-exp(+iTn¯/2)|α exp(iT/2n¯).
W(T2)=n=0Png(T1)cos(2T2n+1),
n¯(T)=Φe(t)|aa|Φe(t)=1Pe(t)n=0n|Cn|2 cos2(Tn+1),
Q=σn2-n¯n¯,
|Φe(k)(Tk)=n=0Cn(k)|n,
Cn(k)=1[Pe(k)(Tk)]1/2Cn(k-1) cos(Tkn+1)
Pe(k)(Tk)=n=0|Cn(k-1)|2 cos2(Tkn+1)
PeN=k=1NPe(k)(Tk)=n=0|Cn(0)|2k=1N cos2(Tkn+1).

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