One-state vector formalism for the evolution of a quantum state through nested Mach-Zehnder interferometers

Abstract

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness producing seemingly contra-intuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well expected outcomes of the experiment. In quantum mechanics (QM) particles are assigned a wave function used to describe their properties [1]. This approach sometimes leads to conclusions about experimental results that seem to contradict intuitive estimations based on classical physics [2,3]. Despite this flaw, QM is currently widely accepted as a theory [1,4], that makes accurate predictions in agreement with the performed experiments. Therefore, it is considered valid regularly used for the interpretation of the results of the corresponding experiments.Recently, an experiment that contained counterintuitive features was proposed and realized by Danan et al. [5]. The authors used nested Mach-Zehnder interferometers (MZI), shown in Fig. 1, and mirrors (A, B, C, E, F) vibrating with different frequencies, in order to leave a mark on passing photons. At one selected output port of the interferometer, the photons were detected by a quad-cell detector D capable of tracing the spatial vibrations of the photon beam. After measurement, the collected signal was further processed and subjected to the Fourier transform. From the obtained frequencies of vibrations, the authors judged whether the detected photons have interacted with the mirror that was oscillating at this particular frequency.The results described in the article by Danan et al. ence inside the interferometer, the correct application of TSVF, the processing of the obtained data and its validity. Until now, no-one has managed to provide the theoretical calculations and the interpretation of the experimental results using only the standard one-state vec-

Experimental observation of anomalous trajectories of single photons

“…In particular, it rules out the option of a continuous trajectory. The results have stirred a lively discussion in the literature [22][23][24][25][26][27][28][29][30][31][32][33] including criticism on the use of classical light and the sensitivity of the experiment. Unfortunately, the clever technique used for obtaining the "which path" information, could not be applied to single photons.…”

Which-way information in a nested Mach-Zehnder interferometer

“…1) and measuring the time varying intensity difference across two halves of a quad-cell detector placed at one of the outputs. This has generated much interest in both theoretical [3,4] and experimental [5][6][7][8][9][10][11] contexts due mainly to the controversial conclusion that the photons follow disconnected paths in the interferometer.…”

“…Moreover, Danan et al, in the supplementary material appended to their paper [13], have themselves shown that there is a non-negligible leakage by blocking light from mirror F and observing the peaks corresponding to mirrors A and B disappear, although this was interpreted by them as evidence for the lack of electronic noise in the set-up. Bartkiewicz et al [11] have attempted to provide a minimal fully quantum treatment working in the frequency domain only. However they have assumed that the effect of the vibrating mirrors is to imprint the which-way information using mutually orthogonal (i.e.…”

Paradox of photons disconnected trajectories being located by means of “weak measurements” in the nested Mach–Zehnder interferometer

“…The surprising results of the experiment reported in [8] were actively discussed in [13][14][15][16][17][18][19], where their interpretation was criticized and various modifications of the experiment and methods of data processing were proposed. The authors of [8] also reported the calculation of detected signals according to the classical theory of electromagnetic waves but did not find any simple interpretation of the signals within this approach.…”

“…The authors of [8] also reported the calculation of detected signals according to the classical theory of electromagnetic waves but did not find any simple interpretation of the signals within this approach. The authors of [19] proposed to describe the evolution of the state of photons within a modified scheme according to traditional quantum mechanics. A numerical-analytical description of the discussed experiment was given in [17] on the basis of the paraxial optical approximation and angular spectrum.…”