Consistent histories for tunneling molecules subject to collisional 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 $\ensuremath{\hbar}\ensuremath{\omega}$ the separation in energy of the levels in the isolated molecule and $\ensuremath{\gamma}$ a decoherence rate proportional to the rate of collisions, we find for $\ensuremath{\gamma}\ensuremath{\gg}\ensuremath{\omega}$ (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 $\ensuremath{\gamma}<\ensuremath{\omega}$ 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 $\ensuremath{\gamma}=\ensuremath{\omega}$. 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 $\ensuremath{\gamma}>\ensuremath{\omega}$ and for $\ensuremath{\gamma}<\ensuremath{\omega}$. 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.