Consistent histories for tunneling molecules subject to collisional decoherence

TL;DR

This paper analyzes how collisional decoherence affects tunneling molecules, revealing a phase transition between oscillatory and flipping behaviors, with implications for understanding chiral stability and quantum-classical transition.

Contribution

It introduces a consistent histories framework to describe tunneling molecules under collisional decoherence, identifying a phase transition in their behavior based on decoherence strength.

Findings

For strong decoherence, molecules flip randomly between chiral states.

For weak decoherence, molecules oscillate with phase changes, with a transition at  = .

Chiral information transfer rate relates to environmental decoherence.

Abstract

The decoherence of a two-state tunneling molecule, such as a chiral molecule or ammonia, due to collisions with a buffer gas is analyzed in terms of a succession of quantum states of the molecule satisfying the conditions for a consistent family of histories. With $\hbar \omega$ the separation in energy of the levels in the isolated molecule and $\gamma$ a decoherence rate proportional to the rate of collisions, we find for $\gamma \gg \omega$ (strong decoherence) a consistent family in which the molecule flips randomly back and forth between the left- and right-handed chiral states in a stationary Markov process. For $\gamma < \omega$ there is a family in which the molecule oscillates continuously between the different chiral states, but with occasional random changes of phase, at a frequency that goes to zero at a phase transition $\gamma = \omega$. This transition is similar to the behavior of the inversion frequency of ammonia with increasing pressure, but will be difficult to observe in chiral molecules such as D$_2$S$_2$. There are additional consistent families both for $\gamma > \omega$ and for $\gamma < \omega$. In addition we relate the speed with which chiral information is transferred to the environment to the rate of decrease of complementary types of information (e.g., parity information) remaining in the molecule itself.