Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field

TL;DR

This paper investigates the rotational states and mutual alignment of coupled polar molecules in a magnetic field, revealing how entanglement and state crossings influence their orientation and providing an analytic model for their alignment behavior.

Contribution

It introduces a detailed analysis of pair-eigenstates of polar molecules in magnetic fields, including the effects of entanglement, state crossings, and an analytic model for mutual alignment.

Findings

Entangled pair-eigenstates are affected differently by magnetic fields.

Mutual alignment remains constant except at avoided crossings.

An analytic model estimates the mutual alignment cosine effectively.

Abstract

We examine the rotational states of a pair of polar $^2\Sigma$ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules $\Delta J_{i}=0,\pm 1$, $\Delta N_{i}=0,\pm 2$, and $\Delta M_{i}=0,\pm 1$ imposed by the electric dipole-dipole operator. Here $J_{i}$, $N_{i}$ and $M_{i}$ are the total, rotational and projection angular momentum quantum numbers of molecules $i=1,2$ in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the coupled rotors.