Single-particle trajectories and interferences in quantum mechanics

Takuya Mori, Izumi Tsutsui

The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore the physical significance provided by this “weak trajectory” by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.

Alex Kamenev

Junheng Pan, Shaoran Liu, Bozhou Zhang +2 more

Abstract In Copenhagen’s interpretation, a self-interference mechanism is assumed for a wave function to split and to pass through the slits simultaneously, then recombine and collapse to generate a dot signal on a detector. Its use of a single wave function to describe a whole ensemble without accounting for a particle’s individuality is incomplete. To better understand the single-electron double-slit interference, we use a wave-packet trajectory approach to track each electron’s dynamics and calculate the time-dependent interference intensity. We analyze the self-interference and cross-interference mechanisms to illustrate how an electron’s coherence length affects the self-interference and how it dictates the wave packet overlaps between adjacent electrons for the cross-interference mechanism to be effective. To circumvent a conflicting dilemma between the electron’s indivisibility and its wave-packet split while passing through the slits, we consider an alternate mechanism involving slit-induced quantized momentum. This mechanism preserves the electron’s indivisibility and avoids the illusive split, recombination and mysterious collapse of a single particle’s wave function.

Sayantan Das, Daniel S. Dahl, Daniel Peace +6 more

While the standard interpretation of quantum mechanics does not assign definite trajectories to particles, the Bohmian interpretation does. Only recently has an operational method for reconciling Bohmian mechanics with relativity been proposed. Here, we experimentally reconstruct relativistic Bohmian trajectories of a single photon in a Michelson-Sagnac interferometer, where counter-propagating probability amplitudes interfere head-on at the speed of light. As predicted by the relativistic Bohmian theory, we observe subluminal and superluminal features of the Bohmian trajectories of the photon traversing through the fringes. Our work provides experimental access to relativistic Bohmian mechanics and enables exploration of its unusual and counterintuitive properties.

Alex Kamenev

Urbasi Sinha, Debadrita Ghosh