Strings of ultracold molecules in a synthetic dimension

Abstract

We consider ultracold polar molecules trapped in a unit-filled one-dimensional chain in real space created with an optical lattice or a tweezer array and illuminated by microwaves that resonantly drive transitions within a chain of rotational states. We describe the system by a two-dimensional lattice model, with the first dimension being a lattice in real space and the second dimension being a lattice in a synthetic direction composed of rotational states. We calculate this system's ground-state phase diagram. We show that as the dipole interaction strength is increased, the molecules undergo a phase transition from a two-dimensional gas to a phase in which the molecules bind together and form a string that resembles a one-dimensional object living in the two-dimensional (i.e, one real and one synthetic dimensional) space. We demonstrate this with two complementary techniques: numerical calculations using matrix product state techniques and an analytic solution in the limit of infinitely strong dipole interaction. Our calculations reveal that the string phase at infinite interaction is effectively described by emergent particles living on the string and that this leads to a rich spectrum with excitations missed in earlier mean-field treatments.

8 pages main text + 3 pages Appendix + references; 7 figures

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Cited by in corpus (11)

• Topological quantum matter in synthetic dimensions
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• A comprehensive review on developments of synthetic dimensions
• Nonlinear dynamics in a synthetic momentum state lattice
• Particle exchange statistics beyond fermions and bosons
• Coherent Manipulation of the Internal State of Ultracold ${}^{87}$Rb${}^{133}$Cs Molecules with Multiple Microwave Fields
• Preparation of ${}^{87}$Rb and ${}^{133}$Cs in the motional ground state of a single optical tweezer
• Quantum Membrane Phases in Synthetic Lattices of Cold Molecules or Rydberg Atoms
• Building Flat-Band Lattice Models from Gram Matrices
• Long-lived multilevel coherences and spin-1 dynamics encoded in the rotational states of ultracold molecules
• Robust storage qubits in ultracold polar molecules