The recent experimental realization of optical tweezer arrays of ultracold molecules provides a versatile platform for exploring molecular phases of matter. Here we show that by programming tweezers, the dipolar interactions in an optical tweezer ladder could be tailored to implement a generalized Su-Schrieffer-Heeger model. Through calculating topological invariants, nonlocal string-order parameters, many-particle ground-state degeneracy, and entanglement spectrum, we demonstrate that this ladder at the single-particle level supports two different chiral topological phases and at the many-particle level features two different interacting topological phases and, respectively, possesses much richer topological edge states. We also discuss the detection of these topological phases and their robustness to systematic imperfections. Further generalization to a high dimension could offer opportunities for preparing diverse ultracold molecular topological phases.
The recent experimental realization of optical tweezer arrays of ultracold molecules provides a versatile platform for exploring molecular phases of matter. Here we show that by programming tweezers, the dipolar interactions in an optical tweezer ladder could be tailored to implement a generalized Su-Schrieffer-Heeger model. Through calculating topological invariants, nonlocal string-order parameters, many-particle ground-state degeneracy, and entanglement spectrum, we demonstrate that this ladder at the single-particle level supports two different chiral topological phases and at the many-particle level features two different interacting topological phases and, respectively, possesses much richer topological edge states. We also discuss the detection of these topological phases and their robustness to systematic imperfections. Further generalization to a high dimension could offer opportunities for preparing diverse ultracold molecular topological phases.
Ultracold atomic and molecular systems in the past years have significantly advanced the exploration of topological phases of matter. Notably, the recent experimental progress achieved in ultracold molecules, particularly within optical-tweezer lattices and leveraging long-range dipolar interactions, has opened up new avenues for this prospect. Here, we propose the creation of an ultracold-molecule trimerized Kagome optical-tweezer lattice to examine the topological phases induced by long-range dipolar interactions. Through a comparison of topological features in scenarios with and without long-range couplings, we find that the long-range interactions can induce higher-order topological phases with diverse topological corner modes at each corner, a phenomenon that can even emerge in nonstandard trimerized Kagome lattices. Furthermore, we develop a dynamic method to spectrally and spatially detect these topological corner modes. Our research not only underscores that long-range interactions can engender much richer topological phases but also suggests exciting possibilities for designing reconfigurable topological lattices.
Ultracold molecules are attractive candidates for various applications including ultracold chemistry, quantum information processing, quantum simulation and searches for physics beyond the standard model. Combined with optical tweezer techniques, an optical tweezer array of ultracold polar molecules holds promise for versatile quantum applications. Their long-lived molecular rotational states form robust qubits, while the long-range dipolar interaction between molecules provides quantum entanglement. In this thesis, we build a new generation experiment of optical tweezer array of ultracold CaF molecules. We optically transport the laser cooled and optically trapped molecules into a science glass cell using a hybrid method, where high numerical aperture optical access allows for tighter optical tweezers. In an array of these tight optical tweezers, we demonstrate dipolar spin-exchange interactions between single CaF molecules for the first time. We realize the spin-21 quantum XY model by encoding an effective spin-21 system into the rotational states of the molecules, and use it to generate a Bell state through an iSWAP operation. Conditioned on the verified existence of molecules in both tweezers at the end of the measurement, we obtain a Bell state fidelity of 0.89(6). Employing interleaved tweezer arrays, we demonstrate single site molecular addressability. To further improve the platform, cooling of the molecules to near the motional ground state is crucial for reducing various dephasings. We demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their 3-D motional ground state, with a 3-D motional ground state probability of 54±18% of the molecules that survive the RSC. This paves the way to increase molecular coherence times in optical tweezers for robust quantum information processing and simulation applications in the near future.
Ultracold atomic quantum systems offer an unprecedentedly powerful platform for exploring interacting symmetry-protected topological phases. Here, we show that their characteristic control over temperature provides a resource for engineering effective topological regimes with no zero-temperature counterpart. Employing finite-temperature matrix-product-state calculations, we investigate experimentally accessible Hamiltonians - the interacting bosonic Su-Schrieffer-Heeger and spin-1 XXZ chains - that host a topological phase at zero temperature, as well as a fermionic dipolar ladder model whose ground state exhibits no topological order. By tracking complementary topological markers, we identify an intriguing mechanism rooted in the structure of the zero-temperature phase diagrams: in finite-size systems, excitation gaps with different magnitudes define an intermediate-temperature window where the correlations associated with the lower gap are suppressed, while those protected by the larger gap persist. This enables the emergence of effective finite-temperature regimes exhibiting topological features that are either absent or qualitatively different from those at zero temperature. Our results establish a novel route toward exploring effective topological phases in ultracold atomic quantum systems.
We establish a general theoretical framework for realizing topological edge states in dimerized arrays of chiral dipolar molecules and demonstrate that molecular handedness provides a natural and tunable route to SSH-like topology in an interacting one-dimensional setting. Starting from an effective spin-21 model generated by Stark-dressed chiral molecules, we introduce bond dimerization and show that the chirality-induced Dzyaloshinskii--Moriya interaction amplifies the effective hopping amplitudes and enlarges the bulk topological gap relative to an achiral chain of equivalent dipole strength. Using self-consistent mean-field theory with periodic- and open-boundary calculations, we map out the trivial, critical, and topological regimes through bulk spectra, complex-plane winding, and boundary-localized probability densities. A central result is that the two in-gap boundary modes carry \emph{opposite molecular chirality}: the left edge state localizes on a left-handed molecule and the right edge state on a right-handed molecule, a stereochemical labeling with no analogue in conventional SSH implementations. The two-leg ladder extension supports a richer four-band bulk structure and a rung-split edge sector whose robustness is characterized by a continuous sweep of the interchain coupling. All results are expressed in dimensionless units of the reference hopping scale t0, making the framework directly applicable to any dipolar molecular platform -- from bialkali polar molecules at MHz coupling scales to future arrays of ultracold chiral polyatomic species. These findings establish dimerized chiral molecular arrays as a controllable and chirality-addressable platform for quasi-one-dimensional topological quantum matter.
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su–Schrieffer–Heeger model, the Hofstadter–Harper model, the Haldane model and the Kane–Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold-atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.
Owing to rapid recent progress, ultracold atomic lattice systems for simulating topological phases are now at a pivotal stage, evolving from established paradigms into increasingly versatile and programmable quantum simulators. In this review, we survey recent experimental advances across four major classes of platforms: optical lattices, including optical lattices with laser-assisted tunneling and optical Raman lattices; synthetic lattices in momentum or internal-state space; Floquet-engineered lattices; and optical tweezer arrays, all of which offer distinct capabilities for realizing and probing topological matter. For each class, we highlight representative experimental breakthroughs, the topological models that have been realized, and the advanced detection and characterization techniques employed, emphasizing how these complementary approaches collectively expand the frontier of quantum simulation. We also discuss emerging directions in strongly correlated and nonequilibrium topological phases, and conclude with an outlook on future prospects.