Dynamical features of interference phenomena in the presence of entanglement

A strongly interacting, and entangling, heavy nonrecoiling external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized electric Aharonov-Bohm effect, which differs from the original one in a crucial way. We propose a gedanken interference experiment. The predicted shift of the interference pattern is due to a self-induced or “private” potential difference experienced while the particle is in vacuum. We show that all nontrivial Born-Oppenheimer potentials are “private” potentials. We apply the Born-Oppenheimer approximation to interference states. Using our approach, we calculate the relative phase of the external heavy particle as well as its uncertainty throughout an interference experiment or entanglement event. We thus complement the Born-Oppenheimer approximation for interference states.

Figure 1

Setup for the electric AB effect.

Figure 2

The internal particle, moving inside the tunnel, is reflected at either $x=0$ or $L$.

Figure 3

The external particle is in a superposition of two narrow, stationary wave packets ${\psi }_1$, ${\psi }_2$. The internal particle is initially in a very wide wave packet ${\varphi }_{\text{in}}$, moving with velocity $v_0$

Figure 4

Setup for the second paradox, where an additional infinitely heavy barrier has been introduced at $L_1$.

Figure 5

The external particle is in a superposition of the wave packets ${\psi }_1$ and ${\psi }_2$, contained in the Faraday cages $C_1$ and $C_2$, respectively. The dipole is at the origin.

Figure 6

Electric AB type interference experiment.

Figure 7

Definition of $\theta$, ${\sigma }_{\theta }$, and ${\sigma }_{\theta }^{\perp }$.