Abstract

We show that with an efficiency exceeding 99% one can use a monolithic total-internal-reflection resonator to ascertain the presence of an object without transferring a quantum of energy to it. We also propose an experiment on the probabilistic meaning of the electric field that contains only a few photons.

© 1997 Optical Society of America

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References

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  1. A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 23, 987–997 (1993).
    [CrossRef]
  2. L. Vaidman, “On the realization of interaction-free measurement,” Quantum Opt. 6, 119–126 (1994).
    [CrossRef]
  3. P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
    [CrossRef] [PubMed]
  4. The experiment of Kwiat et al. described in Ref. 3 as “an initial demonstration of the principle of interaction-free measurement” is, in effect, only a realization of the Elitzur–Vaidman 50% proposal.
  5. P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
    [CrossRef]
  6. H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
    [CrossRef]
  7. H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
    [CrossRef] [PubMed]
  8. K. Fiedler, S. Schiller, R. Paschotta, P. Kürz, and J. Mlynek, “Highly efficient frequency doubling with a doubly resonant monolithic total-internal-reflection resonator,” Opt. Lett. 18, 1786–1788 (1993).
    [CrossRef] [PubMed]
  9. S. Schiller, I. I. Yu, M. M. Fejer, and R. L. Byer, “Fused-silica monolithic total-internal-reflection resonator,” Opt. Lett. 17, 378–380 (1992).
    [CrossRef] [PubMed]
  10. S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
    [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  12. O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1993).
  13. M. Pavičić, “Resonance energy-exchange-free detection and ‘Welcher Weg’ detection,” Phys. Lett. A 223, 241–245 (1996).
    [CrossRef]

1996 (1)

M. Pavičić, “Resonance energy-exchange-free detection and ‘Welcher Weg’ detection,” Phys. Lett. A 223, 241–245 (1996).
[CrossRef]

1995 (4)

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
[CrossRef] [PubMed]

1994 (1)

L. Vaidman, “On the realization of interaction-free measurement,” Quantum Opt. 6, 119–126 (1994).
[CrossRef]

1993 (2)

1992 (1)

1986 (1)

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Byer, R. L.

Cook, R. J.

H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
[CrossRef] [PubMed]

Elitzur, A. C.

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 23, 987–997 (1993).
[CrossRef]

Fearn, H.

H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
[CrossRef] [PubMed]

Fejer, M. M.

Fiedler, K.

Hawly, D. W.

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Herzog, T.

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

Kasevich, M. A.

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

Kürz, P.

Kwiat, P.

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

Milonni, P. W.

H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
[CrossRef] [PubMed]

Mlynek, J.

Paschotta, R.

Pavicic, M.

M. Pavičić, “Resonance energy-exchange-free detection and ‘Welcher Weg’ detection,” Phys. Lett. A 223, 241–245 (1996).
[CrossRef]

Rarity, J. G.

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

Roy, R.

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Schiller, S.

Vaidman, L.

L. Vaidman, “On the realization of interaction-free measurement,” Quantum Opt. 6, 119–126 (1994).
[CrossRef]

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 23, 987–997 (1993).
[CrossRef]

Weinfurter, H.

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

Yu, A. W.

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Yu, I. I.

Zeilinger, A.

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

Zhu, S.

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Zukowski, M.

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

Am. J. Phys. (1)

S. Zhu, A. W. Yu, D. W. Hawly, and R. Roy, “Frustrated total internal reflection. A demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[CrossRef]

Ann. N.Y. Acad. Sci. (2)

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Experimental realization of interaction-free measurements,” Ann. N.Y. Acad. Sci. 755, 383–393 (1995).
[CrossRef]

H. Weinfurter, T. Herzog, P. Kwiat, J. G. Rarity, A. Zeilinger, and M. Żukowski, “Frustrated downconversion: virtual or real photons?,” Ann. N.Y. Acad. Sci. 755, 61–72 (1995).
[CrossRef]

Found. Phys. (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 23, 987–997 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

M. Pavičić, “Resonance energy-exchange-free detection and ‘Welcher Weg’ detection,” Phys. Lett. A 223, 241–245 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[CrossRef] [PubMed]

H. Fearn, R. J. Cook, and P. W. Milonni, “Sudden replacement of a mirror by a detector in cavity QED: are photons counted immediately?,” Phys. Rev. Lett. 74, 1327–1330 (1995).
[CrossRef] [PubMed]

Quantum Opt. (1)

L. Vaidman, “On the realization of interaction-free measurement,” Quantum Opt. 6, 119–126 (1994).
[CrossRef]

Other (3)

The experiment of Kwiat et al. described in Ref. 3 as “an initial demonstration of the principle of interaction-free measurement” is, in effect, only a realization of the Elitzur–Vaidman 50% proposal.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1993).

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Figures (4)

Fig. 1
Fig. 1

Setup of the proposed experiment. For the free round-trips shown within the total-internal-reflection resonator the incident laser beam tunnels in and out to yield the zero intensity of the reflected beam; i.e., detector Dr does not react even when the incoming FTIR approaches 1. However, when the bomb is immersed in the (index-matching) liquid practically the whole incoming beam is reflected into Dr.

Fig. 2
Fig. 2

Realistic values of η [ratio of the incoming and reflected powers, given by Eq. (9)] for R=0.98. For pulsed lasers the three upper curves represent sums from Eq. (9) [with Φ(j) =exp(-j2a-24-1)] as a function of n for a=100, a=200, and a=400 (top to bottom), where aτ/T is a ratio of the coherence time τ and the round-trip time T; filled circles represent the corresponding values of η obtained from Eq. (10). For cw lasers the lowest curve represents the sum given by Eq. (9) [with Φ(j)=1] as a function of the number of round trips n.

Fig. 3
Fig. 3

Realistic values of η [ratio of the incoming and reflected powers, Eq. (9)] for R=0.98, 0.99, 0.995, 0.997, and 0.998 (leftmost to rightmost curves) as functions of the number of round trips n.

Fig. 4
Fig. 4

The proposed virtual-or-real-path experiment. When Pockels cell c is on, it redirects the round-trip path through Rochon prism p into detector Dp, and therefore in most tests only detector Dr fires. When Pockels cell c is off, there is no influence on the round-trip path, and in most tests only detector Dt fires.

Equations (10)

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reiδ=1-2 sin δ1 sin δ2cosh 2bx-cos(δ1+δ2)×expsin δ1 sinh 2bxcos δ1 cosh 2bx-cos δ2,
η=1-c(x)1+2Fπsinδ(x)+ϕ22,
c(x)=(1-e2α)[1-|r(x)|2][1-e-α|r(x)|]2,
Bn(ω)=A(ω)R{-1+(1-R)eiψ[1+Reiψ+(Reiψ)2+]}=i=0n Bi(ω),
Br(ω)=limnBn(ω)=-A0R 1-eiψ1-Reiψ.
Ei(+)(z, t)=0 A(ω)exp[i(kz-ωt)]dω
Er(+)(z, t)=0 B(ω)exp[i(kz-ωt)]dω.
Ii=- Ei(+)(z, t)Ei(-)(z, t)dt=0 A(ω)A*(ω)dω.
ηn=IiIr;n=R1-1-R1+RR2n-1+2j=1n(1+R2n-2j+1)Rj-1Φ(j),
limnηn=0 Br(ω)Br*(ω)dω0 A(ω)A*(ω)dω=1-(1-R)2×0exp[-τ2(ω-ωres)2]dω1-2R cos[(ω-ωres)τ/a]+R20 exp[-τ2(ω-ωres)2]dω,

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