Abstract

Straightforward novel methods for stabilizing, tuning, and controlling a twin Mach–Zehnder interferometer for the purpose of observing a subtle dynamical quantum nonlocality effect in a recent optical experiment are presented and discussed. Weak measurements were required for observing a subtle quantum dynamical nonlocality effect that reveals itself in a change of a weak value. Consequently, emphasis is placed upon describing the approaches to apparatus stabilization and interaction strength control between photons and the apparatus. The details discussed in this paper should be of general interest to experimentalists engaging in weak measurement and weak value research.

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  1. Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
    [CrossRef]
  2. Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
    [CrossRef]
  3. S. Popescu, “Dynamical quantum non-locality,” Nat. Physics 6, 151–153 (2010).
    [CrossRef]
  4. S. Spence and A. Parks, “Experimental evidence for a dynamical non-locality induced effect in quantum interference using weak values,” Found. Phys. 42, 803–815 (2012).
    [CrossRef]
  5. J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
    [CrossRef]
  6. A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
    [CrossRef]
  7. Y. Aharonov and D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley, 2005), pp. 67–73.
  8. I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
    [CrossRef]
  9. A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
    [CrossRef]
  10. K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
    [CrossRef]
  11. F. McCormick, T. Cloonan, F. Tooley, A. Lentine, J. Sasian, J. Brubaker, R. Morrison, S. Walker, R. Crisci, R. Novotny, S. Hinterlong, H. Hinton, and E. Kerbis, “Six-stage digital free-space optical switching network using symmetric self-electro-optic-effect devices,” Appl. Opt. 32, 5153–5171 (1993).
    [CrossRef]
  12. Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
    [CrossRef]
  13. Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
    [CrossRef]
  14. J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
    [CrossRef]
  15. Y. Shikano, “Theory of ‘weak value’ and quantum mechanical measurements,” in Measurements in Quantum Mechanics M. R. Pahlavani, ed. (InTech, 2012), pp. 75–100.
  16. A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
    [CrossRef]

2012 (2)

S. Spence and A. Parks, “Experimental evidence for a dynamical non-locality induced effect in quantum interference using weak values,” Found. Phys. 42, 803–815 (2012).
[CrossRef]

A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

2011 (1)

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

2010 (2)

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

S. Popescu, “Dynamical quantum non-locality,” Nat. Physics 6, 151–153 (2010).
[CrossRef]

2004 (1)

K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
[CrossRef]

2002 (1)

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

1998 (1)

A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
[CrossRef]

1993 (1)

1989 (2)

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
[CrossRef]

1988 (1)

Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

1970 (1)

Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
[CrossRef]

1969 (1)

Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
[CrossRef]

Aharonov, Y.

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
[CrossRef]

Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
[CrossRef]

Y. Aharonov and D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley, 2005), pp. 67–73.

Albert, D.

Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

Ashhab, S.

A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Bamber, C.

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

Botero, A.

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Brubaker, J.

Casher, A.

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Cloonan, T.

Crisci, R.

Cullin, D.

A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
[CrossRef]

Duck, I.

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
[CrossRef]

Endo, J.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

Ezawa, H.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

Hinterlong, S.

Hinton, H.

Kaufherr, T.

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Kawasaki, T.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

Kerbis, E.

Kofman, A.

A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Lentine, A.

Lundeen, J.

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
[CrossRef]

Matsuda, T.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

McCormick, F.

Morrison, R.

Nori, F.

A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Novotny, R.

Nussinov, S.

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Parks, A.

S. Spence and A. Parks, “Experimental evidence for a dynamical non-locality induced effect in quantum interference using weak values,” Found. Phys. 42, 803–815 (2012).
[CrossRef]

A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
[CrossRef]

Patel, A.

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

Pendleton, H.

Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
[CrossRef]

Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
[CrossRef]

Petersen, A.

Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
[CrossRef]

Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
[CrossRef]

Popescu, S.

S. Popescu, “Dynamical quantum non-locality,” Nat. Physics 6, 151–153 (2010).
[CrossRef]

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Resch, K.

K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
[CrossRef]

Reznik, B.

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Rohrlich, D.

Y. Aharonov and D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley, 2005), pp. 67–73.

Sasian, J.

Shikano, Y.

Y. Shikano, “Theory of ‘weak value’ and quantum mechanical measurements,” in Measurements in Quantum Mechanics M. R. Pahlavani, ed. (InTech, 2012), pp. 75–100.

Spence, S.

S. Spence and A. Parks, “Experimental evidence for a dynamical non-locality induced effect in quantum interference using weak values,” Found. Phys. 42, 803–815 (2012).
[CrossRef]

Steinberg, A.

K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
[CrossRef]

Stevenson, P.

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
[CrossRef]

Stewart, C.

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

Stoudt, D.

A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
[CrossRef]

Sudarshan, E.

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
[CrossRef]

Sutherland, B.

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

Tollaksen, J.

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Tonomura, A.

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

Tooley, F.

Vaidman, L.

Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

Walker, S.

Am. J. Phys. (1)

A. Tonomura, J. Endo, T. Matsuda, T. Kawasaki, and H. Ezawa, “Demonstration of single-electron buildup of an interference pattern,” Am. J. Phys. 57, 117–120 (1989).
[CrossRef]

Appl. Opt. (1)

Found. Phys. (1)

S. Spence and A. Parks, “Experimental evidence for a dynamical non-locality induced effect in quantum interference using weak values,” Found. Phys. 42, 803–815 (2012).
[CrossRef]

Int. J. Theor. Phys. (2)

Y. Aharonov, H. Pendleton, and A. Petersen, “Modular variables in quantum theory,” Int. J. Theor. Phys. 2, 213–230 (1969).
[CrossRef]

Y. Aharonov, H. Pendleton, and A. Petersen, “Deterministic quantum interference experiments,” Int. J. Theor. Phys. 3, 443–448 (1970).
[CrossRef]

Nat. Physics (1)

S. Popescu, “Dynamical quantum non-locality,” Nat. Physics 6, 151–153 (2010).
[CrossRef]

Nature (1)

J. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature 474, 188–191 (2011).
[CrossRef]

New J. Phys. (1)

J. Tollaksen, Y. Aharonov, A. Casher, T. Kaufherr, and S. Nussinov, “Quantum interference experiments, modular variables and weak measurements,” New J. Phys. 12, 013023 (2010).
[CrossRef]

Phys. Lett. A (2)

K. Resch, J. Lundeen, and A. Steinberg, “Experimental realization of the quantum box problem,” Phys. Lett. A 324, 125–131 (2004).
[CrossRef]

Y. Aharonov, A. Botero, S. Popescu, B. Reznik, and J. Tollaksen, “Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values,” Phys. Lett. A 301, 130–138 (2002).
[CrossRef]

Phys. Rep. (1)

A. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre- and post-selected measurements,” Phys. Rep. 520, 43–133 (2012).
[CrossRef]

Phys. Rev. D (1)

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a ‘weak measurement’ of a spin-1/2 particle’s spin component yields a value 100,” Phys. Rev. D 40, 2112–2117 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Aharonov, D. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60, 1351–1354 (1988).
[CrossRef]

Proc. R. Soc. A (1)

A. Parks, D. Cullin, and D. Stoudt, “Observation and measurement of an optical Aharonov-Albert-Vaidman effect,” Proc. R. Soc. A 454, 2997–3008 (1998).
[CrossRef]

Other (2)

Y. Aharonov and D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley, 2005), pp. 67–73.

Y. Shikano, “Theory of ‘weak value’ and quantum mechanical measurements,” in Measurements in Quantum Mechanics M. R. Pahlavani, ed. (InTech, 2012), pp. 75–100.

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Figures (1)

Fig. 1.
Fig. 1.

Schematic of the twin Mach–Zehnder interferometer apparatus implementing the gedanken two-slit experiment. The schematic indicates with a double arrow the M1 mirror movement directions that changed the L2 interaction strength in the first Mach–Zehnder interferometer. The schematic indicates the phase shift window in path R5 that tuned the apparatus to the desired postselection state. The image of the beam exiting the second Mach–Zehnder interferometer is captured by a machine vision camera. The schematic indicates with a double arrow the image movement directions in the camera.

Equations (12)

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

ψ(x)=12{φ(x-)+eiαφ(x)}
ddte-ip^x=i[H^,e-ip^x]=iD(x,px,)e-ip^x,
D(x,px,)x|D(x^,p^x,)|x=V(x)-V(x-).
H^=γ(t)A^p^,
|Φ=e-iH^dt|ψi|ϕ=e-iγA^p^|ψi|ϕ.
|Ψ=ψf|Φψf|ψie-iγAwp^|ϕ,
Aw=ψf|A^|ψiψf|ψi
Δpγ|Aw|1andΔpmin(n=2,3,)γ|Aw(An)w|1n1.
H^dt=γ(x)N^p^,
γ(x)=1.5(xx0)1.5Δx
ρi(x)=γ(x)Nw,i=1.5ΔxNw,i
|Δx|200μm

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