Nondestructive dispersive imaging of rotationally excited ultracold molecules

A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using $^{23}\text{Na}^{87}\text{Rb}$ and $^{87}\text{Rb}^{133}\text{Cs}$ as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for both bulk gases and individually trapped molecules, thus enabling high-fidelity nondestructive imaging of molecules.