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Bulletin of the American Physical Society

Synthetic dimensions in ultracold molecules: quantum strings, membranes, and dissipation-induced topology

Kaden R. A. Hazzard

Published Mar 6, 2018• 0 citations
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Quantum matter based on ultracold molecules

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Bulletin of the American Physical Society•Mar 5, 2015•0 citations
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic dimensions have been engineered in ongoing experiments with ultracold matter. We show that rotational states of ultracold molecules can be used as synthetic dimensions extending to many - potentially hundreds of - synthetic lattice sites. Microwaves coupling rotational states drive fully controllable synthetic inter-site tunnelings, enabling, for example, topological band structures. Interactions leads to even richer behavior: when molecules are frozen in a real space lattice with uniform synthetic tunnelings, dipole interactions cause the molecules to aggregate to a narrow strip in the synthetic direction beyond a critical interaction strength, resulting in a quantum string or a membrane, with an emergent condensate that lives on this string or membrane. All these phases can be detected using local measurements of rotational state populations.