The Influences Of Losses On The Wave-particle Duality And Discussion With Multiple Internal Degrees Of A Particle

Bohr proposed the important principle of complementarity, which lies at the heart of quantum mechanics and is paid attention since the beginning of the birth of quantum mechanics. This complementarity emphasizes that the quantum systems possess properties that are equally real but mutually exclusive, such as the wave-particle duality. Then the concept about the characteristic of a particle is changed from either wave behavior or particle behavior to wave-particle duality. The earlier discussion on the complementarity was based on Young’s double-slit experiment. One can observe wavelike or particlelike behavior of the particle through different measuring devices. If the particle goes through the double-slit, we will observe the interference fringe pattern. If we block one slit, we will not obtain the interference fringe pattern. With the progress of science, this famous experiment can be realized by a Mach-Zehnder interferometer with a single photon input. What’s more, the wave-particle duality is quantified by the inequality, P2+V2≤1, with P the predictability of the particle (photon) passing along the two paths and V the visibility of the interference pattern behind the standard Mach-Zehnder interferometer (MZI). This inequality has been demonstrated by many experiments. The study of the influences of losses on the wave-particle duality and discussion with multiple internal degrees of a particle on wave-particle can help us to understand the nature of optics deeply.The main works of this dissertation are as follows:(1) We introduced three different methods to quantify the wave-particle duality theoretically and experimentally. The definitions of visibility are the same, but the definitions of which-way information are different. If the variable beam splitter (VBS) is in front of the 50:50 beam splitter (BS), The predictability (P) is the difference between the probabilities that the particle takes one way and the other. For the distinguishability (D), the which-way information is stored in the which-way detector (WWD) and can be read out from the detector. If the BS is in front of the VBS, the which-way knowledge (K) is obtained by blocking one path. We find the results are the same for P and K when we don’t consider the losses. And we also introduced the definition of high-order wave-particle duality.(2) The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theoretically in a Mach-Zehnder interferometer. The famous duality relation K2+V2<1 is always valid in this situation, where K is the which-way information and V is the visibility. However, the sum of the particle information and the wave information, K2+V2 can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity K2+V2 is always equal to one when the internal degree of freedom of the particle is excluded.(3) We investigate the influence of losses on the wave-particle duality in a Mach-Zehnder interferometer theoretically and experimentally. Balanced losses (equal losses on the two paths) have no effect on the visibility and predictability (also the duality relation), while unbalanced losses do have influence on them. If the unbalanced losses occur inside the interferometer, the losses have an effect on both the visibility and predictability, while the losses have no effect on the duality relation. If the unbalanced losses occur after the interferometer, the losses have no effect on the visibility, but do have an effect on the predictability (also the wave-particle duality), which can lead to a result that the duality relation exceeds one P2+V2>1. The obtained P and V for the unbalanced losses in the two paths do not represent the original predictability and visibility. The influence of losses can be eliminated by exchanging the two detectors or the two inputs (one photon and the vacuum) of the interferometer and then averaging the two results. And we find the results are different from that above if the VBS and BS are switched.