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Register a new userQuantitative Wave-Particle Duality
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Authors
Tabish Qureshi
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The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is now described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these natures. These measures of wave and particle aspects are known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
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A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this contribution that neither the wave nor the particle description is sufficient to predict the outcomes of quantum-optical experiments. To show this, we derive correlation-based criteria that have to be satisfied when either particles or waves are fed into our interferometer. Using squeezed light, it is then confirmed that measured correlations are incompatible with either picture. Thus, within one single experiment, it is proven that neither a wave nor a particle model explains the observed phenomena. Moreover, we formulate a relation of wave and particle representations to two incompatible notions of quantum coherence, a recently discovered resource for quantum information processing.For such an information-theoretic interpretation of our method, we certify the nonclassicality of coherent states - the quantum counterpart to classical waves - in the particle picture, complementing the known fact that photon states are nonclassical in the typically applied wave picture.
We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, ${mathcal D}_1^2 + {mathcal V}_2^2 le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohrs principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brings back the interference fringes of the other.
The simplest single-photon entanglement is the entanglement of the vacuum state and the single-photon state between two path modes. The verification of the existence of single-photon entanglement has attracted extensive research interests. Here, based on the construction of Bells inequality in wave space, we propose a new method to verify single photon entanglement. Meanwhile, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure it. Strong violation of Bell inequality based on joint measurement of wave states indicates the existence of single photon entanglement with certainty. Wave state entanglement obtained from Fourier transform of single photon entanglement and the corresponding measurement protocols will provide us with more information-carrying schemes in the field of quantum information. The difference in the representation in photon-number space and wave space implies the wave-particle duality of single photon entanglement.
It is well known that in classical optics, the visibility of interference, in a two-beam light interference, is related to the optical coherence of the two beams. A wave-particle duality relation can be derived using this mutual coherence. The issue of wave-particle duality in classical optics is analyzed here, in the more general context of multipath interference. New definitions of interference visibility and path distinguishability have been introduced, which lead to a duality relation for multipath interference. The visibility is shown to be related to a new multi-point optical coherence function.
Bohrs principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relation ${mathcal D}^2+{mathcal V}^2 le 1$. Here ${mathcal D}$ is a measure of distinguishability of the two paths, and ${mathcal V}$ is the visibility of interference. It is shown that such a relation can be formulated for $N-$slit or $N-$path interference too, with the proviso that the wave nature is characterized by a measure of {em coherence} (${mathcal C}$). This new relation, ${mathcal D}^2+{mathcal C}^2 le 1$ is shown to be tight, and reduces to the known duality relation for the case $N=2$. A recently introduced similar relation (Bagan et al., 2016) is shown to be inadequate for the purpose.
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