We propose a scheme to realize a pseudospin-
1/2 model of the ${}^{1}\mathrm{\ensuremath{\Sigma}}(v=0)$ bialkali polar molecules with the spin states corresponding to two sublevels of the first excited rotational level. We show that the effective dipole-dipole interaction between two spin-
1/2 molecules couples the rotational and orbital angular momenta and is highly tunable via a microwave field. We also investigate the ground-state properties of a spin-
1/2 molecular condensate. A variety of nontrivial quantum phases, including the doubly quantized vortex states, are discovered. Our scheme can also be used to create spin-1 model of polar molecules. Thus we show that the ultracold gases of bialkali polar molecules provide a unique platform for studying the spinor condensates of rotating molecules.
We present a method to design a finite decay rate for excited rotational states in polar molecules. The setup is based on a hybrid system of polar molecules with atoms driven into a Rydberg state. The atoms and molecules are coupled via the strong dipolar exchange interaction between two rotation levels of the polar molecule and two Rydberg states. Such a controllable decay rate opens the way to optically pump the hyperfine levels of polar molecules and it enables the application of conventional laser cooling techniques for cooling polar molecules into quantum degeneracy.
We analyze the possibility to exploit charge-dipole interaction between a single polar molecule or a one-dimensional (1D) molecular array and a single Rydberg atom to read out molecular rotational populations. We calculate the energy shift of a single
Rb(60s) atom interacting with a single KRb or RbYb molecule in their lowest two rotational states. At atom-molecule distances, relevant to trapping of molecules in optical lattices, the Rydberg electron energy shifts conditioned on the rotational states, are of the order of several MHz. Atom excitation to a Rydberg state and detection of atomic fluorescence conditioned on a rotational state preserves the molecule, making our scheme a nondestructive measurement of the rotational state. Similarly, a 1D array of polar molecules can shift the electron energy of a blockaded Rydberg superatom. We consider a scheme to read out the molecular array collective rotational states using the conditioned Rydberg energy shifts, and numerically analyze a system with three and five KRb or RbYb molecules interacting with
Rb(60s) superatom.