Nematic-orbit coupling and nematic density waves in spin-1 condensates

We propose the creation of artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates, in analogy to spin-orbit coupling. Using a suitably designed microwave chip, the quadratic Zeeman shift, normally uniform in space, can be made to be spatio-temporally varying, leading to a coupling between spatial and nematic degrees of freedom. A phase diagram is explored where three quantum phases with the nematic order emerge: easy-axis, easy-plane with single-well and easy-plane with double well structure in momentum space. By including spin-dependent and spin-independent interactions, we also obtain the low energy excitation spectra in these three phases. Lastly, we show that the nematic-orbit coupling leads to a periodic nematic density modulation in relation to the period $\lambda_T$ of the cosinusoidal quadratic Zeeman term. Our results point to the rich possibilities for manipulation of tensorial degrees of freedom in ultracold gases without requiring Raman lasers, and therefore, obviating light-scattering induced heating.