Abstract

For a number of basic experiments on two-photon intensity correlations, it is pointed out that the results, which are usually explained in terms of the formalism of canonical field quantization, can also be explained in terms of quantum wavepackets, where reduction and entanglement are taken into account.

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References

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  1. A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
    [CrossRef]
  2. A. Jabs, “A conjecture concerning determinism and phases in quantum mechanics,” arXiv:1204.0614 (2012).
  3. A. Jabs, “Picturing wavepacket reduction,” arXiv:1305.5119 (2013).
  4. A. Jabs, “An interpretation of the formalism of quantum mechanics in terms of epistemological realism,” arXiv:1212.4687 [Br. J. Philos. Sci. 43, 405–421 (1992)].
  5. A. Jabs, “Quantum mechanics in terms of realism,” arXiv:quant-ph/9606017 [Phys. Essays 9, 35–95, 354 (1996)].
  6. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
    [CrossRef]
  7. L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
    [CrossRef]
  8. L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986).
    [CrossRef]
  9. H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209–231 (1986).
    [CrossRef]
  10. G. Richter, “Über Interferenzen und Intensitätskorrelationen bei Lichtstrahlen sehr geringer Intensität,” Ann. Phys. 45, 564–577 (1988).
    [CrossRef]
  11. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
    [CrossRef]
  12. Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
    [CrossRef]
  13. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
    [CrossRef]
  14. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
    [CrossRef]
  15. P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
    [CrossRef]
  16. Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
    [CrossRef]
  17. J. D. Franson, “Two-photon interferometry over large distances,” Phys. Rev. A 44, 4552–4555 (1991).
    [CrossRef]
  18. J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
    [CrossRef]

1993 (1)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[CrossRef]

1992 (1)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef]

1991 (2)

J. D. Franson, “Two-photon interferometry over large distances,” Phys. Rev. A 44, 4552–4555 (1991).
[CrossRef]

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
[CrossRef]

1990 (2)

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[CrossRef]

1988 (2)

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef]

G. Richter, “Über Interferenzen und Intensitätskorrelationen bei Lichtstrahlen sehr geringer Intensität,” Ann. Phys. 45, 564–577 (1988).
[CrossRef]

1987 (1)

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

1986 (2)

L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986).
[CrossRef]

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209–231 (1986).
[CrossRef]

1983 (1)

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[CrossRef]

1905 (1)

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

Arons, A. B.

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

Brendel, J.

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Einstein, A.

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

Franson, J. D.

J. D. Franson, “Two-photon interferometry over large distances,” Phys. Rev. A 44, 4552–4555 (1991).
[CrossRef]

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[CrossRef]

Ghosh, R.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

Hong, C. K.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Jabs, A.

A. Jabs, “A conjecture concerning determinism and phases in quantum mechanics,” arXiv:1204.0614 (2012).

A. Jabs, “Picturing wavepacket reduction,” arXiv:1305.5119 (2013).

A. Jabs, “An interpretation of the formalism of quantum mechanics in terms of epistemological realism,” arXiv:1212.4687 [Br. J. Philos. Sci. 43, 405–421 (1992)].

A. Jabs, “Quantum mechanics in terms of realism,” arXiv:quant-ph/9606017 [Phys. Essays 9, 35–95, 354 (1996)].

Kwiat, P. G.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Mandel, L.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef]

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986).
[CrossRef]

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[CrossRef]

Martienssen, W.

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
[CrossRef]

Mohler, E.

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
[CrossRef]

Nathel, H.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef]

Paul, H.

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209–231 (1986).
[CrossRef]

Peppard, M. B.

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

Richter, G.

G. Richter, “Über Interferenzen und Intensitätskorrelationen bei Lichtstrahlen sehr geringer Intensität,” Ann. Phys. 45, 564–577 (1988).
[CrossRef]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef]

Vareka, W. A.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

Wang, L. J.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

Zou, X. Y.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

Ann. Phys. (2)

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. 17, 132–148 (1905).English translation by A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—a translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965).
[CrossRef]

G. Richter, “Über Interferenzen und Intensitätskorrelationen bei Lichtstrahlen sehr geringer Intensität,” Ann. Phys. 45, 564–577 (1988).
[CrossRef]

Phys. Rev. A (5)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a “quantum eraser”: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef]

L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28, 929–943 (1983).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “High-visibility interference in a Bell-inequality experiment for energy and time,” Phys. Rev. A 47, R2472–R2475 (1993).
[CrossRef]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[CrossRef]

J. D. Franson, “Two-photon interferometry over large distances,” Phys. Rev. A 44, 4552–4555 (1991).
[CrossRef]

Phys. Rev. Lett. (5)

J. Brendel, E. Mohler, and W. Martienssen, “Time-resolved dual-beam two-photon interferences with high visibility,” Phys. Rev. Lett. 66, 1142–1145 (1991).
[CrossRef]

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65, 321–324 (1990).
[CrossRef]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef]

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[CrossRef]

Phys. Scr. (1)

L. Mandel, “Non-classical states of the electromagnetic field,” Phys. Scr. T12, 34–42 (1986).
[CrossRef]

Rev. Mod. Phys. (1)

H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58, 209–231 (1986).
[CrossRef]

Other (4)

A. Jabs, “A conjecture concerning determinism and phases in quantum mechanics,” arXiv:1204.0614 (2012).

A. Jabs, “Picturing wavepacket reduction,” arXiv:1305.5119 (2013).

A. Jabs, “An interpretation of the formalism of quantum mechanics in terms of epistemological realism,” arXiv:1212.4687 [Br. J. Philos. Sci. 43, 405–421 (1992)].

A. Jabs, “Quantum mechanics in terms of realism,” arXiv:quant-ph/9606017 [Phys. Essays 9, 35–95, 354 (1996)].

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Figures (3)

Fig. 1.
Fig. 1.

Geometry of the interference experiment [6].

Fig. 2.
Fig. 2.

Geometry of the interference experiment [11].

Fig. 3.
Fig. 3.

Outline of the experimental setup in [14].

Equations (44)

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

Pqo(x1,x2)δx1δx2=2K1K2δx1δx2{1+cos2π(x1x2)/L0}.
Pco(x1,x2)δx1δx2=2K1K2δx1δx2[1+2|aA|2|aB|2(|aA|2+|aB|2)2cos2π(x1x2)L0].
E(x1)=aAeikA1rA1+aBeikB1rB1+iδ,E(x2)=aAeikA2rA2+aBeikB2rB2+iδ
Vco=2|aA|2|aB|2|aA|2|aA|2+|aB|2|aB|2+2|aA|2|aB|2.
Pqoa=12sin2ϕwithout polarizers,
Pqob=14sin2ϕwith one polarizer,
Pqoc=14sin2ϕsin2(θ1θ2)with two polarizers.
Pc(I1H+I1V)(I2H+I2V)¯δ.
A1H=12Asei(ωst+ksrs+δ)cosϕ+12Aiei(ωit+kiri+π/2).
A1H=12Ascosϕeiδ+i2Ai.
A1V=12Assinϕeiδ.
A2H=i2Ascosϕeiδ+12Ai,A2V=i2Assinϕeiδ.
I1=I1H+I1V=|A1H|2+|A1V|2=12(As2+Ai2+2AsAicosϕsinδ),
I2=I2H+I2V=|A2H|2+|A2V|2=12(As2+Ai22AsAicosϕsinδ).
I1I2=14((As2+Ai2)24As2Ai2cos2ϕsin2δ),
Pco14(Is2+Ii2)+12IsIisin2ϕ.
PcoI1θ1(I2H+I2V)¯δI1θ1=|A1θ1|2A1θ1=i2Ascos(θ1ϕ)+12Aicosθ1eiδA2H=12Ascosϕ+i2AieiδA2V=(1/2)Assinϕ,
Pco14Is2cos2(θ1ϕ)+14Ii2cos2θ1+14IsIisin2ϕ.
Pco|A1|2|A2|2¯δ,
A1=12Ascos(θ1ϕ)+i2Aicosθ1eiδA2=i2Ascos(θ2ϕ)+12Aicosθ2eiδ
Pco14Is2cos2(θ1ϕ)cos2(θ2ϕ)+14Ii2cos2θ1cos2θ2+14IsIisin2ϕsin2(θ1θ2).
ts=ti,
ks+ki=kp,
ωs+ωi=ωp,
ψsψi=(ψsS+ψsL)(ψiS+ψiL)=ψsSψiS+ψsSψiL+ψsLψiS+ψsLψiL,
ψsS(xs,t)=ksψ˜(ks)ei(ksxsωst)d3ks.
ψsL(xs,t)=ksψ˜(ks)ei(ks(xsΔL)ωst)dks
ψsSψiS=kskiψ˜(ks)ψ˜(ki)ei(ksxsωst+kixiωit)dksdki.
ψsiSS=ei(kpxiωpt)ψ˜(ks)ψ˜(kpks)eiks(xsxi)dks
ψsiLL=eikpΔLψsiSS.
ψsiSL=ei(kp(xiΔL)ωpt)ψ˜(ks)ψ˜(kpks)eiks(xsxi+ΔL)dks,
ψsiSL=ψsiLS=0
Cqm(A)=|ψsi|2=|ψsiSS+ψsiLL|2=|ψsiSS|2|1eikpΔL|2=|ψsiSS|22(1+coskpΔL),
Cqm(B1)=|ψ˜(ks)ψ˜(kpks)dks|22(1+coskpΔL).
ψsiSS=ψsiLL=0.
ψsiSL=0.
|ψsiLS|2=|ψ˜(ki)ψ˜(kpki)dki|2|ψ˜(ks)ψ˜(kpks)dks|2.
Cqm(B2)=|ψsiLS|2=|ψ˜(ks)ψ˜(kpks)dks|2.
Cqm(B3)=Cqm(B2),
Cqm(B)=Cqm(B1)+Cqm(B2)+Cqm(B3)=|ψsiLS|24(1+12coskpΔL).
EsEi=(EsS+EsL)(EiS+EiL)=EsSEiS+EsSEiL+EsLEiS+EsLEiL,
EsS(xs,t)=ψ˜(ks)ei(ksxsωst)Δks,EsL(xs,t)=ψ˜(ks)ei(ks(xsΔL)ωst)Δks,
EsEi=EsSEiS(1+ei(kpks)ΔL+eiksΔL+eikpΔL)ΔksΔki.
|EsEi|2¯=|EsSEiS|2¯(4+e+ikpΔL+eikpΔL)=|EsEi|2¯4(1+12coskpΔL),

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