The Collapse Before a Quantum Jump Transition

Abstract

We may infer a transition $|n \rangle \to |m \rangle$ between energy eigenstates of an open quantum system by observing the emission of a photon of Bohr frequency $\omega_{mn} = (E_n-E_m) / \hbar$. In addition to the "collapses" to the state $|m\rangle$, the measurement must also have brought into existence the pre-measurement state $|n \rangle$. As quantum trajectories are based on past observations, the condition state will jump to $| m \rangle$, but the state $|n\rangle$ does not feature in any essential way. We resolve this paradox by looking at quantum smoothing and derive the time-symmetric model for quantum jumps.