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Ferroelectric quantum phase transition with cold polar molecules

We analyze a system of polar molecules in a one-dimensional optical lattice. By controlling the internal structure of the polar molecules with static electric and microwave fields, we demonstrate the appearance of a quantum phase transition into a ferroelectric phase via spontaneous breaking of a $U(1)$ symmetry. The phase diagram is first analyzed within mean-field theory, while in a second step the results are verified by a mapping onto the Bose-Hubbard model for hard-core bosons. The latter is studied within the well-established bosonization procedure. We find that the ferroelectric phase is characterized by (quasi) long-range order for the electric dipole moments.