Abstract
We propose a Quantum Field Theory description of beams on a Mach–Zehnder interferometer and apply the method to describe Interaction Free Measurements (IFMs), concluding that there is a change of momentum of the fields in IFMs. Analysing the factors involved in the probability of emission of low-energy photons, we argue that they do not yield meaningful contributions to the probabilities of the IFMs.
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Notes
Notice that if the detonation is detectable, these photons cannot be soft as soft photons have, by definition, such low energy that they evade detection. To avoid this semantic confusion, we shall refer to the detectable photons as low-energy photons.
The 4-momentum operator is
$$P^{\mu } = \int_\Sigma {T^{{0\mu }} d^{3} x} ,$$(6)where \(T^{\nu \mu }\) is the energy-momentum tensor [14].
References
Elitzur, A.C., Vaidman, L.: Quantum mechanical interaction-free measurements. Found. Phys. 23, 7 (1993)
Renninger, M.: Messungen ohne störung des meßobjekts. Z. Phys. 158, 417–421 (1960)
Paraoanu, G.S.: Interaction-free measurements with superconducting qubits. Phys. Rev. Lett. 97, 180406 (2006)
White, A.G., Mitchell, J.R., Nairz, O., Kwiat, P.G.: “Interaction-free imaging”. Phys. Rev. A 58, 605 (1998)
Paul, H., Pavic̆ić, M.: Nonclassical interaction-free detection of objects in a monolithic total-internal-reflection resonator. J. Opt. Soc. Am. B 14, 6 (1997)
Kwiat, P.G., White, A.G., Mitchell, J.R., Nairz, O., Weihs, G., Weinfurter, H., Zeilinger, A.: High-efficiency quantum interrogation measurements via the quantum Zeno effect. Phys. Rev. Lett. 83, 4725 (1999)
Namekata, N., Inoue, S.: High-efficiency interaction-free measurements using a stabilized Fabry–Perot cavity. J. Phys. B 39, 16 (2006)
Weinberg, S.: The Quantum Theory of Fields. Cambridge University Press, Cambridge (1995)
Weinberg, S.: Infrared photons and gravitons. Phys. Rev. 140, B516 (1965)
Bloch, F., Nordsieck, A.: Note on the radiation field of the electron. Phys. Rev 52, 54 (1937)
Simon, S.H., Platzman, P.M.: Fundamental limit on interaction-free measurements. Phys. Rev. A 61, 052103 (2000)
Vaidman, L.: The meaning of the interaction-free measurements. Found. Phys. 33, 491–510 (2003)
Karlsson, A., Björk, G., Forsberg, E.: “Interaction” (energy exchange) free and quantum nondemolition measurements. Phys. Rev. Lett. 80, 1198 (1998)
Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Perseus Books, New York (1995)
Gerry, C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)
Cabrera, R., Strohecker, T., Rabitz, H.: The canonical coset decomposition of unitary matrices through Householder transformations. J. Math. Phys. 51, 082101 (2010)
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C. R. Barroso, F., Bertolami, O. A Quantum Field Theory View of Interaction Free Measurements. Found Phys 50, 764–771 (2020). https://doi.org/10.1007/s10701-020-00350-8
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DOI: https://doi.org/10.1007/s10701-020-00350-8