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Thouless pumping of soliton under cyclic and slow modulation of potential opens a window to understand the interplay between topology and interaction. The dynamics of a soliton change from quantized displacement per pumping cycle to its breakdown to self-trap as time-independent nonlinearity increases. Since nonlinearity can be dynamically and flexibly tuned in ultracold atomic systems, time-dependent nonlinearity can be a new degree of freedom to control behaviors of solitons in a Thouless pump. Leveraging time-dependent nonlinearity, we can not only restore quantized displacement of soliton by avoiding self-crossing structures, but also combine topological pumping and self-trap to effectively realize fractional displacement of soliton per cycle. Surprisingly, even when time translation symmetry is broken by linearly changing nonlinearity, we can still achieve the topological transport of a soliton when the initial soliton is symmetrically distributed. Our work provides a new way for dynamical and topological control of solitons.

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.

Abstract Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio of the tunneling strengths can be independently adjusted to a wide range of values. We identify a certain regime of parameters where a hard-core boson approximation holds and the system realizes a frustrated triangular spin ladder with tunable flux. We study the properties of the effective spin Hamiltonian using the density-matrix renormalization-group method and determine the phase diagram at half-filling. It displays two phases: a uniform superfluid and a bond-ordered insulator. The latter can be stabilized only for low Raman detuning. Finally, we provide experimentally feasible trajectories across the parameter space of the SOC system that cross the predicted phase transition. Graphical abstract

Abstract Employing the external degrees of freedom of atoms as synthetic dimensions renders easy and new accesses to quantum engineering and quantum simulation. As a recent development, ultracold atoms suffering from two-photon Bragg transitions can be diffracted into a series of discrete momentum states to form a momentum lattice. Here we provide a detailed analysis on such a system, and, as a concrete example, report the observation of robust helical Floquet channels, by introducing periodic driving sequences. The robustness of these channels against perturbations is confirmed, as a test for their topological origin captured by Floquet winding numbers. The periodic switching demonstrated here serves as a testbed for more complicated Floquet engieering schemes, and offers exciting opportunities to study novel topological physics in a many-body setting with tunable interactions. Graphical abstract

The modulational instability associated with discrete breathers in 2D quantum ultracold atoms is studied by using the Glauber’s coherent state combined with a semi-discrete approximation and multiple-scale methods. The linear stability analysis exhibits an intriguing threshold amplitude and instability regions associated with modulational growth rate. In addition, we demonstrate a coexistence of two bright intrinsic localized modes namely, the radial symmetric and bilateral symmetric modes, at the center and at the edges of the Brillouin zone, respectively, by alternating the on-site parameter interaction. Numerical investigations reveal a good agreement with the theoretical analysis.

Abstract Supersolid phase is a phase of matter that is characterized by the combination of the off-diagonal long-range order of superfluid and the diagonal long-range order of solid. Cold atoms with spin–orbit-coupling, contact interaction and long-range interaction can provide systems for the research of supersolid phase. Under the effect of spin-dependent potential and spin–orbit-coupling, hard-core ultra-cold atoms with contact interaction can be shown to construct supersolid phase. The combination of soft-core long-range interaction and spin–orbit coupling can establish exotic supersolid phase with spontaneous breakdown of chiral symmetry. The optical Bragg scattering of cold atoms in optical lattices can be used to detect supersolid phase. The study of supersolid phase will be helpful to the researches of matter phases. Graphical abstract

Universal collisions describe the reaction of molecules and atoms as dominated by long-range interparticle interactions. Here, we calculate the universal inelastic rate coefficients for a large group of ultracold polar molecules in their lower ro-vibrational states colliding with one of their constituent atoms. The rate coefficients are solely determined by values of the dispersion coefficient and reduced mass of the collisional system. We use the ab initio coupled-cluster linear response method to compute dynamic molecular polarizabilities and obtain the dispersion coefficients for some of the collisional partners and use values from the literature for others. Our polarizability calculations agree well with available experimental measurements. Comparison of our inelastic rate coefficients with results of numerically exact quantum-mechanical calculations leads us to conjecture that collisions with heavier atoms can be expected to be more universal.

Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom–based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.

Strongly interacting topological matter 1 exhibits fundamentally new phenomena with potential applications in quantum information technology 2 , 3 . Emblematic instances are fractional quantum Hall (FQH) states 4 , in which the interplay of a magnetic field and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement and anyonic exchange statistics. Progress in engineering synthetic magnetic fields 5 – 21 has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light 22 , preparing FQH states in engineered systems remains elusive. Here we realize a FQH state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν  = 1/2 Laughlin state 4 , 23 with two particles on 16 sites. This minimal system already captures many hallmark features of Laughlin-type FQH states 24 – 28 : we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations and we measure a fractional Hall conductivity of σ H / σ 0  = 0.6(2) by means of the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field, we map out the transition point between the normal and the FQH regime through a spectroscopic investigation of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms 29 – 33 . Using ultracold atoms trapped in an optical lattice, a Laughlin-like fractional quantum Hall state is prepared and mapped out on a microscopic level.