Abstract

We have made what we believe is the first observation of phase-dependent temporal correlations in the fluorescent field emitted by coherently driven two-level atoms in free space. We measured the temporal fluctuations of the fluorescent field when the resonant driving field was in phase and out of phase with the local-oscillator field.

© 2005 Optical Society of America

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References

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  1. D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
    [CrossRef]
  2. L. Mandel, Phys. Rev. Lett. 49, 136 (1982).
    [CrossRef]
  3. Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
    [CrossRef]
  4. S. Bali, J. Opt. B: Quantum Semiclassical Opt. 6, S706 (2004).
    [CrossRef]
  5. H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
    [CrossRef] [PubMed]
  6. G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
    [CrossRef] [PubMed]
  7. S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
    [CrossRef] [PubMed]
  8. There is a close connection between the h?(?) function measured in Refs. [5, 6] and the phase-dependent correlation measured in this Letter, but a discussion of this connection is omitted owing to lack of space. See Ref. [4] for details.
  9. H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
    [CrossRef]
  10. A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
    [CrossRef] [PubMed]
  11. H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
    [CrossRef]
  12. A. Heidmann and S. Reynaud, J. Phys. (Paris) 46, 1937 (1985).
    [CrossRef]

2004 (1)

S. Bali, J. Opt. B: Quantum Semiclassical Opt. 6, S706 (2004).
[CrossRef]

2000 (2)

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

1998 (2)

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
[CrossRef]

1997 (1)

H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
[CrossRef]

1995 (1)

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

1993 (1)

S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
[CrossRef] [PubMed]

1985 (1)

A. Heidmann and S. Reynaud, J. Phys. (Paris) 46, 1937 (1985).
[CrossRef]

1982 (1)

L. Mandel, Phys. Rev. Lett. 49, 136 (1982).
[CrossRef]

1981 (1)

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[CrossRef]

Bacon, A.

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

Bacon, A. M.

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Bali, S.

S. Bali, J. Opt. B: Quantum Semiclassical Opt. 6, S706 (2004).
[CrossRef]

Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
[CrossRef]

S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
[CrossRef] [PubMed]

Carmichael, H. J.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

Castro-Beltran, H. M.

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

Foster, G. T.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

Heidmann, A.

A. Heidmann and S. Reynaud, J. Phys. (Paris) 46, 1937 (1985).
[CrossRef]

Lu, Z.

H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
[CrossRef]

Lu, Z. H.

Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
[CrossRef]

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Mandel, L.

S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
[CrossRef] [PubMed]

L. Mandel, Phys. Rev. Lett. 49, 136 (1982).
[CrossRef]

Narducci, F. A.

S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
[CrossRef] [PubMed]

Orozco, L. A.

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

Reynaud, S.

A. Heidmann and S. Reynaud, J. Phys. (Paris) 46, 1937 (1985).
[CrossRef]

Thomas, J.

H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
[CrossRef]

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

Thomas, J. E.

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
[CrossRef]

Walls, D. F.

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[CrossRef]

Wang, L.

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

Wang, L. J.

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Zhao, H.

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
[CrossRef]

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

Zoller, P.

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

S. Bali, J. Opt. B: Quantum Semiclassical Opt. 6, S706 (2004).
[CrossRef]

J. Phys. (Paris) (1)

A. Heidmann and S. Reynaud, J. Phys. (Paris) 46, 1937 (1985).
[CrossRef]

Phys. Rev. A (2)

S. Bali, F. A. Narducci, and L. Mandel, Phys. Rev. A 47, 5056 (1993).
[CrossRef] [PubMed]

H. Zhao, Z. H. Lu, A. M. Bacon, L. J. Wang, and J. E. Thomas, Phys. Rev. A 57, 1427 (1998).
[CrossRef]

Phys. Rev. Lett. (7)

A. Bacon, H. Zhao, L. Wang, and J. Thomas, Phys. Rev. Lett. 75, 1296 (1995).
[CrossRef] [PubMed]

H. Zhao, Z. Lu, and J. Thomas, Phys. Rev. Lett. 79, 613 (1997).
[CrossRef]

H. J. Carmichael, H. M. Castro-Beltran, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 85, 1855 (2000).
[CrossRef] [PubMed]

G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000).
[CrossRef] [PubMed]

D. F. Walls and P. Zoller, Phys. Rev. Lett. 47, 709 (1981).
[CrossRef]

L. Mandel, Phys. Rev. Lett. 49, 136 (1982).
[CrossRef]

Z. H. Lu, S. Bali, and J. E. Thomas, Phys. Rev. Lett. 81, 3635 (1998).
[CrossRef]

Other (1)

There is a close connection between the h?(?) function measured in Refs. [5, 6] and the phase-dependent correlation measured in this Letter, but a discussion of this connection is omitted owing to lack of space. See Ref. [4] for details.

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Figures (3)

Fig. 1
Fig. 1

Outline of measurement of phase-dependent temporal correlations in resonance fluorescence by subtraction of transmitted power signals from two identically prepared atomic samples. Transit time τ 0 is the time taken by the atoms to pass through each of the two laser beams.

Fig. 2
Fig. 2

Voltage waveform V ( t ) emanating from the subtraction electronics yields no discernible information.

Fig. 3
Fig. 3

(a) In-phase (i.e., ϕ = 0 ° ) and (b) out-of-phase (i.e., ϕ = 90 ° ) two-time autocorrelation function C ( τ ) as a function of delay τ for on-resonance excitation ( Δ = 0 ) . Solid curves are data. Dashed curves are not best fits; they were obtained from Eq. (3) by use of the experimental parameters given in the text. Inset, autocorrelation C shot ( τ ) for the shot noise, i.e., when the atomic beam is gated off.

Equations (3)

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Δ P ̂ ( t ) E L O [ exp ( i ϕ ) E ̂ f l ( t ) + exp ( i ϕ ) E ̂ f l ( t ) ] ,
C ( τ ) = : Δ P ̂ ( t ) Δ P ̂ ( t + τ ) : t [ Δ P ̂ ( t ) ] 2 t .
C ( τ ) = ( 1 τ τ 0 ) [ Δ 2 Ω sin 2 ϕ sin Ω τ + cos 2 ϕ cos Ω τ + sin 2 ϕ ] ,

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