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.

© 1998 Optical Society of America

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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, Berlin1991).
  3. H. Carmichael, An Open Systems Approach to Quantum Mechanics, (Springer-Verlag, Berlin1993).
  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 York1978), pp. 719.
  6. S. L. Braunstein, “Homodyne Statistics”, Phys. Rev. A 42, 474 (1990).
    [Crossref] [PubMed]
  7. W. Vogel and J. Grabow, “Statistics of difference 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 Schrödinger 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 York1996), 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]

1998 (1)

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]

1997 (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]

1996 (1)

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

1995 (1)

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

1994 (1)

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

1993 (1)

W. Vogel and J. Grabow, “Statistics of difference events in homodyne detection”, Phys. Rev. A 47, 4227 (1993).
[Crossref] [PubMed]

1992 (1)

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

1990 (1)

S. L. Braunstein, “Homodyne Statistics”, Phys. Rev. A 42, 474 (1990).
[Crossref] [PubMed]

1988 (1)

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]

Aharonov, Y.

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]

Albert, D. Z.

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]

Braunstein, S. L.

S. L. Braunstein, “Homodyne Statistics”, Phys. Rev. A 42, 474 (1990).
[Crossref] [PubMed]

Carmichael, H.

H. Carmichael, An Open Systems Approach to Quantum Mechanics, (Springer-Verlag, Berlin1993).

H. Carmichael, “Stochastic Schrödinger 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 York1996), pp. 177.

Gardiner, C. W.

C. W. Gardiner, Quantum Noise, (Springer-Verlag, Berlin1991).

Grabow, J.

W. Vogel and J. Grabow, “Statistics of difference events in homodyne detection”, Phys. Rev. A 47, 4227 (1993).
[Crossref] [PubMed]

Hess, O.

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]

Hofmann, H. F.

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]

Kitagawa, M.

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

Knight, P. L.

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]

Luis, A.

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

Mahler, G.

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]

Perina, J.

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

Plenio, M. B.

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]

Shapiro, J. H.

H. P. Yuen and J. H. Shapiro, in Coherence and Quantum Optics IV, ed. by L. Mandel and E. Wolf (Plenum, New York1978), pp. 719.

Ueda, M.

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

Vaidman, L.

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]

Vedral, V.

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]

Vogel, W.

W. Vogel and J. Grabow, “Statistics of difference events in homodyne detection”, Phys. Rev. A 47, 4227 (1993).
[Crossref] [PubMed]

Wiseman, H. M.

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

Yuen, H. P.

H. P. Yuen and J. H. Shapiro, in Coherence and Quantum Optics IV, ed. by L. Mandel and E. Wolf (Plenum, New York1978), pp. 719.

Phys. Rev. A (5)

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]

S. L. Braunstein, “Homodyne Statistics”, Phys. Rev. A 42, 474 (1990).
[Crossref] [PubMed]

W. Vogel and J. Grabow, “Statistics of difference events in homodyne detection”, Phys. Rev. A 47, 4227 (1993).
[Crossref] [PubMed]

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. M. Wiseman, “Quantum theory of continuous feedback”, Phys. Rev. A 49, 2133 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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]

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

Quantum Semiclass. Opt. (2)

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

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

Other (4)

H. Carmichael, “Stochastic Schrödinger 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 York1996), pp. 177.

H. P. Yuen and J. H. Shapiro, in Coherence and Quantum Optics IV, ed. by L. Mandel and E. Wolf (Plenum, New York1978), pp. 719.

C. W. Gardiner, Quantum Noise, (Springer-Verlag, Berlin1991).

H. Carmichael, An Open Systems Approach to Quantum Mechanics, (Springer-Verlag, Berlin1993).

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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