Angular position and orbital angular momentum (OAM) states of photons are used to show that the uncertainty principle for an entangled photon passing through a ‘ghost’ slit has a finite limit which is source dependent.
Uncertainty relations are core to both classical and quantum physics, and lend themselves to tests across many degrees of freedom, with structured light emerging as a vibrant tool to harness these degrees of freedom. Here, we test Popper's conjecture by replacing the traditional spatial and momentum states with angular position and orbital angular momentum (OAM) states of photons, showing that the OAM spectrum for an entangled photon passing through a virtual slit differs from that of a photon passing through a physical slit. To achieve this, we produce two OAM entangled photons, one of which is sent to a slit encoded as a digital hologram, thereby localising its angular position, all the while measuring the OAM of the other. We show that the measured OAM spectrum is limited to that of the initial SPDC photons, independent of the OAM encoded into the slit, consistent with Popper's viewpoint. Our approach allows us to overcome prior limitations imposed by physical slits and linear momentum, and offers a versatile toolbox for further probes of quantum systems.
We propose a technique to characterize the dimensionality of entangled sources affected by any environment, including phase and amplitude masks or atmospheric turbulence. We illustrate this technique on the example of angular ghost diffraction using the orbital angular momentum (OAM) spectrum generated by a nonlocal double slit. We realize a nonlocal angular double slit by placing single angular slits in the paths of the signal and idler modes of the entangled light field generated by parametric down-conversion. Based on the observed OAM spectrum and the measured Shannon dimensionality spectrum of the possible quantum channels that contribute to Young's ghost diffraction, we calculate the associated dimensionality Dtotal. The measured Dtotal ranges between 1 and 2.74 depending on the opening angle of the angular slits. The ability to quantify the nature of high-dimensional entanglement is vital when considering quantum information protocols.
Quantum ghost diffraction harnesses quantum correlations to record diffraction or interference features using photons that have never interacted with the diffractive element. By designing an optical system in which the diffraction pattern can be produced by double slits of variable width either through a conventional diffraction scheme or a ghost diffraction scheme, we can explore the transition between the case where ghost diffraction behaves as conventional diffraction and the case where it does not. For conventional diffraction the angular extent increases as the scale of the diffracting object is reduced. By contrast, we show that no matter how small the scale of the diffracting object, the angular extent of the ghost diffraction is limited (by the transverse extent of the spatial correlations between beams). Our study is an experimental realisation of Popper's thought experiment on the validity of the Copenhagen interpretation of quantum mechanics. We discuss the implication of our results in this context and explain that it is compatible with, but not proof of, the Copenhagen interpretation.
Abstract In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit, and thereby its position becomes well-defined. This particle therefore diffracts into a large divergence angle; this effect can be understood as a consequence of the Heisenberg uncertainty principle. Popper further argued that its entangled partner would become comparably localized in position, and that, according to his understanding of the Copenhagen interpretation of quantum mechanics, the ‘mere knowledge’ of the position of this particle would cause it also to diffract into a large divergence angle. Popper recognized that such behavior could violate the principle of causality in that the slit could be removed and the partner particle would be expected to respond instantaneously. Popper thus concluded that it was most likely the case that, in an actual experiment, the partner photon would not undergo increased diffractive spreading and thus that the Copenhagen interpretation is incorrect. Here, we report and analyze the results of an implementation of Popper’s proposal. We find that the partner beam does not undergo increased diffractive spreading. Our work helps to clarify the issues raised in Popper’s proposal, and it provides further insight into the nature of entanglement and its relation to the uncertainty principle as applied to correlated particles.
Abstract An experiment to verify the adequacy of the Heisenberg uncertainty principle, as proposed by Karl Popper and implemented in practice, is considered. As in the Einstein–Podolsky–Rosen paradox, the quantum properties of an entangled pair of elementary particles are used. In this case, a ghost image of a narrow slit is actually formed. The results of the experiment, at first glance, support a violation of the uncertainty principle. However, analysis of the spatial resolution of the slit ghost image shows that this is not correct. A more correct description of diffraction in the case of spatially limited light beams, gives no violation of the uncertainty principle. The results can be also used to estimate the extreme quality of diffraction limited ghost images.
Heisenberg uncertainty principle (UP) holds that the nearly unlimited precise observation of linear momentum is for any states, and in complementarity, states with nearly infinite position space and vice versa for a particle by an lower bound h/4{\pi} on the product of two their underlying uncertainties [1]. In a cylindrical system, however, only the states with integral charges mh/2{\pi} allow the unlimitedly precise observation of orbital angular momentum (OAM), and in complementarity, angular position (AP) states with 2{\pi} range for round and doughnut light beams [2]. Moreover, the correlation of OAM and AP of entangled photon pairs is one order of magnitude stronger that those with independent particles [3]. Here we propose a UP of demonstrating arbitrary states of unlimitedly precise mean OAM refer to the azimuthal phase-gradient (PG), and in complementarity, states with infinite range AP, observed in a set of numerous singular light beams with simultaneously helical wavefront and phase-shift-front associated with three natures of wave, discrete OAM eigenmode and linear optics. These arbitrary OAM states of arbitrary phase-jump are extended by discrete precisions that consist of not only the OAM eigenstates but also the states with the max phase-jump. Furthermore, we theoretically demonstrate the double resolution limit of OAM eigenmodes and the super-2{\pi} angle period for two overlap probabilities of n-sectional fractional OAM state with one and two PGs, respectively, which is used to illustrate the quantum nonlocality in the spontaneously parametric down-conversion (SPDC) process.