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arXiv:2109.10467 · Physical Review A

Hiding the which-path information of photons

Jinxian Guo, Qi-Zhang Yuan, Yuan Wu, Weiping Zhang

Published Aug 18, 2022• 2 citations

Abstract

Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.

DOI: 10.1103/physreva.106.022210

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Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.

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The two-state vector formalism (TSVF) describes a quantum system between two measurements, with a pre- and post-selected states evolving forward and backward in time, respectively. In this paper, we investigate the which-path information and the TSVF analysis considering the polarization and path states in a polarization-based nested Mach-Zehnder interferometer (NMZI). By adjusting photon polarization in the multipath via polarization optics, we can investigate the which-path information of the photons after the polarization beam splitter in the polarization-based NMZI under conditions of constructive or destructive interference conditions. Considering the incomplete polarization states of photons in the NMZI, the interpretation of our experimental results does not contradict the TSVF analysis.

Photons have been proved to hide their past, especially in interferometers. Recently, several surprising results have been shown in nested Mach-Zehnder interferometer(NMZI), proving that the 'weak trace' of photons can be hidden. This paper rearranges the three path interference problem which gives the general result of its output and the conditions for eliminating the weak trace. Surprisingly, such conditions strongly depend on the detection method of the output photon, as well as the phase differences and splitting ratios in the NMZI. Further analysis gives a new weak trace elimination phenomenon which is independent of the position sensitive detector. Moreover, we setup an experiment to verify the weak trace elimination conditions and demonstrate the new weak trace elimination phenomenon.

Complementarity of wave-like and particle-like properties in the Mach–Zehnder and Michelson interferometers is investigated by means of the exactly solvable model for a quantum measurement process. When the error-minimum measurement and unambiguous measurement are used for extracting the which-path information, the fringe visibility and which-path information are derived and their complementary relation is examined. It is shown that there is a possibility of the recovery of the quantum coherence in the Michelson interferometer since the which-path information can be erased by the propagating particle itself.