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Chemical Physics Letters

Quantum interference by non-interacting classical trajectories evolving on a quasi-classical potential

Craig Brooksby, Oleg V. Prezhdo

Published Sep 1, 2003• 18 citations
Publisher
DOI
10.1016/s0009-2614(03)01342-3

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We find that real and complex Bohmian quantum trajectories resulting from well-localized Klauder coherent states in the quasi-Poissonian regime possess qualitatively the same type of trajectories as those obtained from a purely classical analysis of the corresponding Hamilton-Jacobi equation. In the complex cases we treated the quantum potential results to a constant, such that the agreement is exact. For the real cases we provide conjectures for analytical solutions for the trajectories as well as the corresponding quantum potentials. The overall qualitative behavior is governed by the Mandel parameter determining the regime in which the wave functions evolve as solitonlike structures. We demonstrate these features explicitly for the harmonic oscillator and the P\"oschl-Teller potential.
Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02.
Young’s double slit experiment revived the wave theory of the light. The standard interpretation is that the light behaves as waves before and after passing through the diaphragm of the double slit. Feynman called the double slit experiment the only mystery in quantum mechanics. Recently, the photon chamber has been proposed and utilized to study the behavior of photons near the detecting screen. The experiments show that the light, near the screen, behaves as photons propagating along the straight-line trajectories, and the trajectories distribute as waves. Furthermore, the photon chamber experiments show that, withing a macroscopic distance from the double slit, the pattern is non-interference, which indicates that the standard double slit experiments violate the standard wave interpretations in the area near the diaphragm. In this article, we utilize two new methods to study how the non-interference pattern (near the double slit) evolving to the interference pattern (far from it). The experiments show, the first time, that (1) the shape of the pattern are distance-dependent, when the distance increases, the non-interference pattern evolves to the interference pattern, which indicates that the non-wave nature and the wave distribution coexist in the same wave experiment; (2) the light beams behave as photons near the double slit. The experiments: (1) provide novel phenomena/data for further theoretical development of the established optics and for understanding the nature of the light; (2) show the Feynman’s mystery in the different perspectives; (3) provide three methods that show the non-wave pattern in standard wave experiments and can be utilized to develop the classical optics further.