One of the intriguing mystery in modern physics is the quantum interference phenomena, which the behaviour of photons in double-slit experiment is still ambiguous.Instead of relying on the naive probabilistic point of view, Bohmian mechanics provides the ground base for interpreting quantum system in a deterministic way closely related to classical mechanics such as it constructs the photon trajectory for the double-slit set up.The appearance on the bending in the constructed photon trajectory seem to contravene the notable law of conservation of momentum.Here, we report on conservation of the transverse momentum of photon trajectories based on numerical solution of Bohmian mechanics in double-slit set up for single photon, pair of photons and ensemble of photons until interference pattern is produced.It is shown that the total transverse momentum in the system of Bohmian mechanics is invariance due to the non-local action of quantum potential.
One of the intriguing mystery in modern physics is the quantum interference phenomena, which the behaviour of photons in double-slit experiment is still ambiguous.Instead of relying on the naive probabilistic point of view, Bohmian mechanics provides the ground base for interpreting quantum system in a deterministic way closely related to classical mechanics such as it constructs the photon trajectory for the double-slit set up.The appearance on the bending in the constructed photon trajectory seem to contravene the notable law of conservation of momentum.Here, we report on conservation of the transverse momentum of photon trajectories based on numerical solution of Bohmian mechanics in double-slit set up for single photon, pair of photons and ensemble of photons until interference pattern is produced.It is shown that the total transverse momentum in the system of Bohmian mechanics is invariance due to the non-local action of quantum potential.
Abstract Young’s double slit experiments, which represent the mystery of quantum mechanics, have been described by either the classical wave, or quantum probability waves or pilot waves. Recently, the novel experiments show that the interference patterns of the double slit/cross-double slit experiments may be curved. The previous phenomena of the light bending contain the gravity bending and Airy beam curving transversely. The curved Airy beam is interpreted by the quantum Schrödinger’s wave equation and electromagnetic wave theory. To study the curved interference patterns of the comprehensive double slit experiments, we study the underlying physics first, namely, to study whether the light beam/photons behave as wave or as particle before forming the curved interference pattern. In this article, the comprehensive double slit experiments are performed, which show: (1) the fringes of the curved interference pattern are created independently and may be create partially; (2) the longitudinal shield and the metal tube inserted between the slide and the detector has no effect on the interference pattern. The experimental observations suggest that, before forming the curved interference pattern on the detector, photons behave as particles, which can be referred as “wave-particle-coexistence”. The phenomena provide the comprehensive information/data for the theoretical study.
This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.
Making a "which-way" measurement (WWM) to identify which slit a particle goes through in a double-slit apparatus will reduce the visibility of interference fringes. There has been a long-standing controversy over whether this can be attributed to an uncontrollable momentum transfer. Here, by reconstructing the Bohmian trajectories of single photons, we experimentally obtain the distribution of momentum change. For our WWM, the change we see is not a momentum kick that occurs at the point of the WWM, but rather one that nonclassically accumulates during the propagation of the photons. We further confirm a quantitative relation between the loss of visibility consequent on a WWM and the total (late-time) momentum disturbance. Our results emphasize the role of the Bohmian momentum in giving an intuitive picture of wave-particle duality and complementarity.
Young's double slit experiments, which represent the mystery of quantum mechanics, have been described by either the classical wave, or quantum probability waves or pilot waves. Recently, the novel experiments show that the interference patterns of the double slit/cross-double slit experiments may be curved. The previous phenomena of the light bending contain the gravity bending and Airy beam curving transversely. The curved Airy beam is interpreted by the quantum Schrödinger's wave equation and electromagnetic wave theory. To study the curved interference patterns of the comprehensive double slit experiments, we study the underlying physics first, namely, to study whether the light beam/photons behave as wave or as particle before forming the curved interference pattern. In this article, the comprehensive double slit experiments are performed, which show: (1) the fringes of the curved interference pattern are created independently and may be create partially; (2) the longitudinal shield and the metal tube inserted between the slide and the detector has no effect on the interference pattern. The experimental observations suggest that, before forming the curved interference pattern on the detector, photons behave as particles, which can be referred as "wave-particle-coexistence". The phenomena provide the comprehensive information/data for the theoretical study.
Abstract We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.
Interpretations of quantum mechanics (QM), or proposals for underlying theories, that attempt to present a definite realist picture, such as Bohmian mechanics, require strong non-local effects. Naively, these effects would violate causality and contradict special relativity. However if the theory agrees with QM the violation cannot be observed directly. Here, we demonstrate experimentally such an effect: we steer the velocity and trajectory of a Bohmian particle using a remote measurement. We use a pair of photons and entangle the spatial transverse position of one with the polarization of the other. The first photon is sent to a double-slit-like apparatus, where its trajectory is measured using the technique of Weak Measurements. The other photon is projected to a linear polarization state. The choice of polarization state, and the result, steer the first photon in the most intuitive sense of the word. The effect is indeed shown to be dramatic, while being easy to visualize. We discuss its strength and what are the conditions for it to occur.