Abstract

I report a paradoxical result in the resonant Jaynes–Cummings model, in which atomic excitation by photon absorption is accompanied by an increase of the number of photons. I show that this always holds in the short-time regime for initial fields with super-Poissonian photon statistics. I provide a purely dynamical explanation of the effect that holds in both the quantum and the semiclassical regimes, and I discuss the relation of this counterintuitive photon behavior with the bunching effect.

© 2007 Optical Society of America

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  1. E. T. Jaynes and F. W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proc. IEEE 51, 89-109 (1963).
    [CrossRef]
  2. C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 1, 106-121 (1970).
    [CrossRef]
  3. C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 2, 1613-1614 (1970).
    [CrossRef]
  4. B. W. Shore and P. L. Knight, "The Jaynes-Cummings model," J. Mod. Opt. 40, 1195-1238 (1993).
    [CrossRef]
  5. P. Meystre, "Repeated quantum measurements on a single-harmonic oscillator," Opt. Lett. 12, 669-671 (1987).
    [CrossRef] [PubMed]
  6. H. Ghosh and C. C. Gerry, "Measurement-induced nonclassical states of the Jaynes-Cummings model," J. Opt. Soc. Am. B 14, 2782-2787 (1997).
    [CrossRef]
  7. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  8. H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
    [CrossRef]
  9. S. S. Mizrahi and V. V. Dodonov, "Creating quanta with an 'annihilation' operator," J. Phys. A 35, 8847-8857 (2002).
    [CrossRef]
  10. C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge U. Press, 2005).
  11. A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
    [CrossRef]

2006

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

2002

S. S. Mizrahi and V. V. Dodonov, "Creating quanta with an 'annihilation' operator," J. Phys. A 35, 8847-8857 (2002).
[CrossRef]

1999

A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
[CrossRef]

1997

1993

B. W. Shore and P. L. Knight, "The Jaynes-Cummings model," J. Mod. Opt. 40, 1195-1238 (1993).
[CrossRef]

1987

1970

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 1, 106-121 (1970).
[CrossRef]

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 2, 1613-1614 (1970).
[CrossRef]

1963

E. T. Jaynes and F. W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Becker, T.

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

Cives-Esclop, A.

A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
[CrossRef]

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, 89-109 (1963).
[CrossRef]

Dodonov, V. V.

S. S. Mizrahi and V. V. Dodonov, "Creating quanta with an 'annihilation' operator," J. Phys. A 35, 8847-8857 (2002).
[CrossRef]

Englert, B.-G.

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

Gerry, C. C.

Ghosh, H.

Jaynes, E. T.

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 1, 106-121 (1970).
[CrossRef]

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 2, 1613-1614 (1970).
[CrossRef]

E. T. Jaynes and F. W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proc. IEEE 51, 89-109 (1963).
[CrossRef]

Knight, P. L.

B. W. Shore and P. L. Knight, "The Jaynes-Cummings model," J. Mod. Opt. 40, 1195-1238 (1993).
[CrossRef]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge U. Press, 2005).

Luis, A.

A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
[CrossRef]

Meystre, P.

Mizrahi, S. S.

S. S. Mizrahi and V. V. Dodonov, "Creating quanta with an 'annihilation' operator," J. Phys. A 35, 8847-8857 (2002).
[CrossRef]

Sánchez-Soto, L. L.

A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Shore, B. W.

B. W. Shore and P. L. Knight, "The Jaynes-Cummings model," J. Mod. Opt. 40, 1195-1238 (1993).
[CrossRef]

Stroud, C. R.

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 2, 1613-1614 (1970).
[CrossRef]

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 1, 106-121 (1970).
[CrossRef]

Varcoe, B. T. H.

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

Walther, H.

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

J. Mod. Opt.

B. W. Shore and P. L. Knight, "The Jaynes-Cummings model," J. Mod. Opt. 40, 1195-1238 (1993).
[CrossRef]

A. Cives-Esclop, A. Luis, and L. L. Sánchez-Soto, "Influence of field dynamics on Rabi oscillations: beyond the standard semiclassical Jaynes-Cummings model," J. Mod. Opt. 46, 639-655 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. A

S. S. Mizrahi and V. V. Dodonov, "Creating quanta with an 'annihilation' operator," J. Phys. A 35, 8847-8857 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 1, 106-121 (1970).
[CrossRef]

C. R. Stroud Jr. and E. T. Jaynes, "Long-term solutions in semiclassical radiation theory," Phys. Rev. A 2, 1613-1614 (1970).
[CrossRef]

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, 89-109 (1963).
[CrossRef]

Rep. Prog. Phys.

H. Walther, B. T. H. Varcoe, B.-G. Englert, and T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325-1382 (2006).
[CrossRef]

Other

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge U. Press, 2005).

Cited By

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Figures (5)

Fig. 1
Fig. 1

Evolution of n ̂ ( t ) g (dotted curve), n ̂ ( t ) (solid curve), and n ̂ ( t ) e (dashed curve) for an initial thermal state with n ̂ = 3 .

Fig. 2
Fig. 2

Evolution of n ̂ ( t ) g (dotted curve), n ̂ ( t ) (solid curve), and n ̂ ( t ) e (dashed curve) for an initial coherent state with n ̂ = 3 .

Fig. 3
Fig. 3

Evolution of n ̂ ( t ) g (dotted curve), n ̂ ( t ) (solid curve), and n ̂ ( t ) e (dashed curve) for an initial squeezed state with n ̂ = 3 and Q = 0.31 .

Fig. 4
Fig. 4

Evolution of Q g ( t ) (dotted curve), Q (solid curve), and Q e ( t ) (dashed curve) for an initial coherent state with n ̂ = 3 .

Fig. 5
Fig. 5

Evolution of Q g ( t ) (dotted curve), Q (solid curve), and Q e ( t ) (dashed curve) for an initial squeezed state with n ̂ = 3 and Q = 0.31 .

Equations (19)

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

H = χ ( a g e + a e g ) ,
U ( t ) = cos ( χ t n ̂ + 1 ) e e + cos ( χ t n ̂ ) g g i a sin ( χ t n ̂ ) n ̂ e g i sin ( χ t n ̂ ) n ̂ a g e ,
Ψ ( t ) = c g ψ g g + c e ψ e e ,
c g ψ g = cos ( χ t n ̂ ) ψ , c e ψ e = i a sin ( χ t n ̂ ) n ̂ ψ ,
n ̂ ( t ) e = ( n ̂ 1 ) sin 2 ( χ t n ̂ ) sin 2 ( χ t n ̂ ) ,
n ̂ ( t ) g = n ̂ cos 2 ( χ t n ̂ ) cos 2 ( χ t n ̂ ) ,
n ̂ ( t ) e n ̂ 2 n ̂ 1 χ 2 t 2 3 n ̂ 2 ( n ̂ 3 n ̂ n ̂ 2 2 ) ,
n ̂ ( t ) g n ̂ χ 2 t 2 ( Δ n ̂ ) 2 ,
n ̂ ( t ) n ̂ ( 1 χ 2 t 2 ) ,
n ̂ ( t ) e > n ̂ ( t ) Δ n ̂ > n ̂ .
n ̂ ( t ) g < n ̂ ( t ) Δ n ̂ > n ̂ .
Q = n 2 n 2 n 1
n ( t ) j = s j ( t ) n ( t ) s j ( t ) ,
n ( t ) e = n sn 2 ( χ t n ) dn 2 ( χ t n ) sn 2 ( χ t n ) ,
n ( t ) g = n cn 2 ( χ t n ) dn 2 ( χ t n ) cn 2 ( χ t n ) ,
n ( t ) e n 2 n χ 2 t 2 3 n 2 ( n 3 n + 3 n 2 n n 2 2 ) ,
n ( t ) g n χ 2 t 2 [ ( Δ n ) 2 + n ] ,
n ( t ) n ( 1 χ 2 t 2 ) .
n ( t ) e > n ( t ) , n ( t ) g < n ( t )

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