A truncated photon

Abstract

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is not another photon or a mix of a photon and a vacuum. Instead it is a superposition and mix of photon numbers up to infinity. This state is rather complicated, but nevertheless locally equivalent to a single photon or vacuum in disjoint regions. Finally we demonstrate how the truncated photon may be illuminating and useful for the understanding of locality and equivalence in quantum field theory.

Figures (2)

• Figure 1: An incident photon propagating to the right gets reflected in $x=0$. The solid blue line is the expected energy density of the right-going part; the dashed line is the left-going part. At $t=0$ the reflector is removed. The quantum fields for $t<0$ are disconnected into the two regions $x<0$ and $x>0$ due to the reflector. The fields for $t>0$ are everywhere equal to the usual forward- and backward-propagating modes.
• Figure 2: Considering forward-propagating modes, the truncated photon state is locally equivalent to a single photon $a_\xi^\dagger| 0 \rangle$ to the left of the transition region, and vacuum $| 0 \rangle$ to the right. Equivalence means that all local observables give the same measurement statistics. In the main text we consider observables $L$ and $R$ on the left-hand side and right-hand side of the transition region, respectively.