Tunnelling photons pose no challenge to Bohmian machanics

Abstract

Very recently, Sharoglazova et al. performed an experiment measuring the energy-velocity relationship and Bohmian velocity in coupled waveguides. Their data show a discrepancy between the semi-classical `speed' $v=\sqrt{2|Δ|/m}$ and Bohmian velocity $v_s$ for $Δ<-\hbar J_0$, leading them to claim a challenge to Bohmian mechanics. Here, we definitively demonstrate this experiment poses no challenge to Bohmian mechanics. First, $v$ and $v_S$ represent fundamentally distinct physical quantities -- comparing them is physically unjustified and cannot adjudicate between Copenhagen and Bohmian interpretations. Second, we rigorously show that both interpretations predict identical photon tunneling dynamics in coupled waveguides.

Figures (2)

• Figure 1: Quantum tunnelling between two coupled wavegiudes based on Schrödinger equation. a, Calculated wavefunctions $\psi_m$ and $\psi_a$ along $x$ direction. Three conditions are considered here with different $\Delta$. The upper panel shows two transmission modes, the middle panel presents one transmission and evanescent modes, and the lower panel displays two evanescent modes. b, Purple dots denotes and cyan line are experimental determined $v$ and fitted results in Ref. S25, respectively. Red line is our theoretical fitting to the experimental results in Ref. S25.
• Figure 2: Quantum tunnelling between two coupled waveguides based on Bohmian mechanics. Four group of velocities at $x$=5 $\mu$m (a), 10 $\mu$m (b), 20 $\mu$m (c) and 40 $\mu$m (d) are displayed. If $\Delta < -\hbar J_0$, both $v_m$ and $v_a$ along $x$ are zero. In the regime of $|\Delta| < \hbar J_0$, $v_m$ and $v_a$ are distinguished because of the different quantum potential. For $\Delta > \hbar J_0$, $v_m$ and $v_a$ are identical.