Abstract

We show that the influence of quantum fluctuations in the electromagnetic field vacuum on a two level atom can be measured and consequently compensated by balanced homodyne detection and a coherent feedback field. This compensation suppresses the decoherence associated with spontaneous emissions for a specific state of the atomic system allowing complete control of the coherent state of the system.

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References

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  1. M. B. Plenio, V. Vedral, and P. L. Knight, "Quantum error correction in the presence of spontaneous emission ", Phys. Rev. A 55, 67 (1997).
    [CrossRef]
  2. C. W. Gardiner, Quantum Noise, (Springer-Verlag, Berlin 1991).
  3. H. Carmichael, An Open Systems Approach to Quantum Mechanics, (Springer-Verlag, Berlin 1993).
  4. M. Ueda and M. Kitagawa, "Reversibility in quantum measurement processes", Phys. Rev. Lett. 68, 3424 (1992).
    [CrossRef] [PubMed]
  5. H. P. Yuen and J. H. Shapiro, in Coherence and Quantum Optics IV, ed. by L. Mandel and E. Wolf (Plenum, New York 1978), pp. 719.
  6. S. L. Braunstein, "Homodyne Statistics", Phys. Rev. A 42, 474 (1990).
    [CrossRef] [PubMed]
  7. W. Vogel and J. Grabow, "Statistics of di’erence events in homodyne detection", Phys. Rev. A 47, 4227 (1993).
    [CrossRef] [PubMed]
  8. A. Luis and J. Perina, "Generalized measurements in 8-port homodyne detection" Quantum Semiclass. Opt. 8, 873 (1996).
    [CrossRef]
  9. H. F. Hofmann, G. Mahler, and O. Hess, "Quantum control of atomic systems by time resolved homodyne detection", Phys. Rev. A 57, in press (1998).
    [CrossRef]
  10. H. F. Hofmann and G. Mahler, "Measurement models for time-resolved spectroscopy: A comment", Quantum Semiclass. Opt. 7, 489 (1995).
    [CrossRef]
  11. H. Carmichael, "Stochastic Schroedinger equations: What they mean and what they can do." in Coherence and Quantum Optics VII, ed. by J. Eberly, L. Mandel, and E. Wolf, (Plenum, New York 1996), pp. 177.
  12. H. M. Wiseman, "Quantum theory of continuous feedback", Phys. Rev. A 49, 2133 (1994).
    [CrossRef] [PubMed]
  13. Y. Aharonov, D. Z. Albert, and L. Vaidman, "How the result of a measurement of a component of a spin-1/2 particle can turn out to be 100", Phys. Rev. Lett. 60, 1351 (1988).
    [CrossRef] [PubMed]

Other (13)

M. B. Plenio, V. Vedral, and P. L. Knight, "Quantum error correction in the presence of spontaneous emission ", Phys. Rev. A 55, 67 (1997).
[CrossRef]

C. W. Gardiner, Quantum Noise, (Springer-Verlag, Berlin 1991).

H. Carmichael, An Open Systems Approach to Quantum Mechanics, (Springer-Verlag, Berlin 1993).

M. Ueda and M. Kitagawa, "Reversibility in quantum measurement processes", Phys. Rev. Lett. 68, 3424 (1992).
[CrossRef] [PubMed]

H. P. Yuen and J. H. Shapiro, in Coherence and Quantum Optics IV, ed. by L. Mandel and E. Wolf (Plenum, New York 1978), pp. 719.

S. L. Braunstein, "Homodyne Statistics", Phys. Rev. A 42, 474 (1990).
[CrossRef] [PubMed]

W. Vogel and J. Grabow, "Statistics of di’erence events in homodyne detection", Phys. Rev. A 47, 4227 (1993).
[CrossRef] [PubMed]

A. Luis and J. Perina, "Generalized measurements in 8-port homodyne detection" Quantum Semiclass. Opt. 8, 873 (1996).
[CrossRef]

H. F. Hofmann, G. Mahler, and O. Hess, "Quantum control of atomic systems by time resolved homodyne detection", Phys. Rev. A 57, in press (1998).
[CrossRef]

H. F. Hofmann and G. Mahler, "Measurement models for time-resolved spectroscopy: A comment", Quantum Semiclass. Opt. 7, 489 (1995).
[CrossRef]

H. Carmichael, "Stochastic Schroedinger equations: What they mean and what they can do." in Coherence and Quantum Optics VII, ed. by J. Eberly, L. Mandel, and E. Wolf, (Plenum, New York 1996), pp. 177.

H. M. Wiseman, "Quantum theory of continuous feedback", Phys. Rev. A 49, 2133 (1994).
[CrossRef] [PubMed]

Y. Aharonov, D. Z. Albert, and L. Vaidman, "How the result of a measurement of a component of a spin-1/2 particle can turn out to be 100", Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef] [PubMed]

Supplementary Material (2)

» Media 1: MOV (416 KB)     
» Media 2: MOV (416 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

Visualization of the diffusion step on the Bloch sphere. The diffusion is represented by lines oriented parallel to the direction of the diffusion with a length proportional to the standard deviation of the step length. a) and b) show the projections into the sy, sz and the sx, sz plane, respectively.

Fig. 2.
Fig. 2.

Non-linear contribution to the diffusion step of the Bloch vector. The representation is in analogy to Fig. 1, with a) and b) showing the projections into the sy, sz and into the sx, sz planes, respectively.

Fig. 3.
Fig. 3.

Animation: Variation of the effective diffusion step with the feedback increasing from (cos Θ ¯ = -1) to (cos Θ ¯ = +1). (a) Projection into the sy,sz plane; (b) Projection into the sx, sz plane. [Media 1] [Media 2]

Equations (19)

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| P ( Δ n ) = ( 2 π α * α ) 1 / 4 exp [ Δ n 2 4 α * α ] ( | vacuum + Δ n α * | n in = 1 ) ,
| Φ β | vacuum + β | n in = 1 .
p β ( Δ n ) = P ( Δ n ) | Φ β 2 = 1 2 π α * α exp [ ( Δ n ( α * β + β * α ) ) 2 2 α * α ] .
| Ψ ( 0 ) = c E | E ˜ ; vacuum + c G | G ; vacuum ,
| Ψ ( τ ) = c E ( 1 Γ τ / 2 ) | E ˜ ; vacuum + c G | G ; vacuum + c E Γ τ | G ; n 0 = 1 .
| ψ ( τ ) = P ( Δ n ) | Ψ ( τ )
= ( 2 π α * α ) 1 4 exp [ Δ n 2 4 α * α ] ( c E ( 1 Γ τ 2 ) | E ˜ + ( c G + c E Γ τ Δ n α ) | G ) .
p ( Δ n ) 1 2 π α * α exp [ Δ n 2 2 α * α ] .
| δψ ( τ ) Γ τ Δ n α c E 2 ( c G * | E ˜ c E * | G ) .
s x = 2 Re ( ψ | E ˜ G | ψ )
s y = 2 Im ( ψ | E ˜ G | ψ )
s z = E ˜ | ψ 2 G | ψ 2 ,
δ s x δ s y δ s z = Γ τ Δ n α ( s z + 1 s x 2 s x s y s x s x s z ) .
δθ = Γ τ Δ n α ( 1 + cos θ ) .
f ( Δ n 0 ) = ( 1 + cos θ ̅ ) Δ n 0 2 α ,
Δ n next = Δ n qf + δ next
= Δ n qf + 2 α f ( Δ n 0 ) .
Δ n 2 α + f ( Δn ) = cos θ ̅ Δ n 2 α .
s x s y s z = Γ τ Δ n α cos Θ ̅ s z + 1 s x 2 s x s y + cos Θ ̅ s x - s x s z .

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