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We design dipolar quantum many-body Hamiltonians that will facilitate therealization of exotic quantum phases under current experimental conditionsachieved for polar molecules. The main idea is to modulate both single-bodypotential barriers and two-body dipolar interactions on a spatial scale of tensof nanometers to strongly enhance energy scales and, therefore, relaxtemperature requirements for observing new quantum phases of engineeredmany-body systems. We consider and compare two approaches. In the first,nanoscale barriers are generated with standing wave optical light fieldsexploiting optical nonlinearities. In the second, static electric fieldgradients in combination with microwave dressing are used to writenanostructured spatial patterns on the induced electric dipole moments, andthus dipolar interactions. We study the formation of inter-layer and interfacebound states of molecules in these configurations, and provide detailedestimates for binding energies and expected losses for present experimentalsetups.

Quantum Many-Body Physics with Ultracold Polar Molecules: Nanostructured Potential Barriers and Interactions