Momentum transfer for momentum transfer-free which-path experiments

Bohr’s principle of complementarity constitutes the hallmark and one of the most intriguing features of quantum mechanics. On the basis of this principle [1, 2] it is indeed universally accepted that any devices capable of determining the path taken by a particle trough a Young like double-aperture must destroy the interference. The justification usually presented is based on Heisenberg’s uncertainty principle [3, 4] and involves an irremediable exchange of momentum between the system considered and the measuring apparatus. Over the last decades the primacy of such recoil arguments has been however contested in favor of a more general decoherence mechanism considering the entanglement of the observed system with its environment [5]. In particular Scully et al. emphasized [6] that an atom, after emitting a long wavelength photon in a “micromaser-cavity”, located close to one of the two pinholes, can generate a recordable whichpath information without transfer of significant momentum. The conclusions of [6] seem actually verified in experiments using entanglement with an internal degree of freedom to label the path with either neutrons [7], photons [8, 36], or atoms [10, 11]. This stirred-up considerable controversy and a debate [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] on the genuine meaning of momentum transfer in which-path experiments. The paradox comes from the fact that any far-field interference observed with a Young’s like double aperture experiment is a direct map of the transverse momentum distribution of the diffracted particle in the aperture plane. Any processes able to erase the interference should be then interpretable in term of a perturbation done on this momentum distribution. Such proposition was formally done [12, 13, 14] but the answer is far from being universally accepted [15, 16]. We found two reasons for that: Firstly, the momentum distribution of the particle in the single-aperture experiment is not affected by the detector (this intuitively implies a momentum transfer equal to zero [6]). Secondly, the momentum transfer defined in [12, 13] is in general “hidden” in the