The OH molecule is currently of great interest from the perspective of ultracold chemistry, quantum fluids, precision measurement, and quantum computation. Crucial to these applications are the slowing, guiding, confinement, and state control of OH, using electric and magnetic fields. In this article, we show that the corresponding eight-dimensional effective ground-state Stark-Zeeman Hamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analytical solution opens the way to insightful characterization of the magnetoelectrostatic manipulation of ground-state OH. Based on our results, we also discuss a possible application to the quantum simulation of an imbalanced Ising magnet.The OH molecule in its ground X 2 3/2 state is presently widely employed in investigations of ultracold chemistry [1-4], precision measurements [5,6], and quantum computation [7]. Particularly interesting is the recently implemented evaporative cooling of OH close to Bose-Einstein condensation [8]. With such experiments under way, the exploration of quantum degeneracy and molecular optics [9] with OH should shortly become reality.A substantial reason behind the suitability of OH as a workhorse for these experiments is the fact that it is a polar paramagnetic molecule; i.e., it carries both electric and magnetic dipole moments. Electric and magnetic fields can therefore be used to slow, guide, confine, and generally manipulate OH [10][11][12][13][14]. It follows that a quantitative as well as qualitative understanding of the corresponding Stark-Zeeman spectrum is of great relevance.In this article we present the exact solution of the eightdimensional Stark-Zeeman Hamiltonian of OH in its X 2 3/2 ground state [13] and identify the intriguing underlying symmetry. This molecular Hamiltonian is an effective one, neglects hyperfine structure, and has been used to numerically model experimental data accurately [8,12,13]. However, there is interest in analytic solutions also: during the preparation of this article, the field-dependent part of the Hamiltonian was diagonalized exactly in an insightful article by Bohn and Quemener [15].Based on our analysis, we suggest that the OH molecule may be used to simulate a mixed spin Ising magnet, which is of interest in condensed matter physics [16]. Another use for our results is a realistic theory of nonadiabatic processes in traps, which so far has relied on a simplified four-dimensional model of the OH ground state [17]. Our work may also be of relevance to atmospheric [18], interstellar [19], and combustion physics [20], where OH plays an important role. Lastly, we hope that our results will usefully add to the handful of exact solutions available for molecules, especially in strong fields [21].We begin with the Stark-Zeeman Hamiltonian for OH in the X 2 3/2 state, as presented earlier [13],where H o is the field-free Hamiltonian, μ e and μ b are the electric and magnetic dipole moments of the molecule, respectively, and E [ B] is the electric [magnetic] field impose...

The ground electronic, vibrational and rotational state of the OH molecule is currently of interest as it can be manipulated by electric and magnetic fields for experimental studies in ultracold chemistry and quantum degeneracy. Based on our recent exact solution of the corresponding effective Stark-Zeeman Hamiltonian, we present an analytical study of the crossings and avoided crossings in the spectrum. These features are relevant to non-adiabatic transitions, conical intersections and Berry phases. Specifically, for an avoided crossing employed in the evaporative cooling of OH, we compare our exact results to those derived earlier from perturbation theory.