In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility—a static physical quantity—can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.

A minimal Weyl semimetal: Many compounds have now been identified as Weyl semimetals, materials with an unusual electronic band structure characterized by the so-called Weyl points. Weyl points always appear in pairs, but the solid-state materials studied so far have at least four. Wang et al. engineered a Weyl semimetallic state with the minimum number of Weyl points (two) in a gas of ultracold atoms trapped in an optical lattice (see the Perspective by Goldman and Yefsah). To do that, the researchers had to create three-dimensional spin-orbit coupling in this system. The relative simplicity of the resulting band structure will make it easier to observe the unusual effects associated with this state. Science , this issue p. 271 ; see also p. 234

We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to $L=512$, and estimate the percolation thresholds to be $p_c\left(\mathrm{bond}\right)=0.24881182\left(10\right)$ and $p_c\left(\mathrm{site}\right)=0.3116077\left(2\right)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1/\nu =1.1410\left(15\right)$, $\beta /\nu =0.47705\left(15\right)$, the leading correction exponent $y_i=-1.2\left(2\right)$, and the shortest-path exponent $d_{\min }=1.3756\left(3\right)$. Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent $\approx$ $-2$, rather than $y_i\approx -1.2$.

Lowering the entropy: Atoms loaded in an optical lattice can convincingly mimic the behavior of electrons in solids. However, reaching very low temperatures, where the most interesting quantum phases are expected to occur, is tricky. Yang et al. introduced a clever experimental technique to reduce the entropy of their sample. They created an array consisting of alternating rows of sample atoms and reservoirs. The entropy was transferred from the sample atoms to the adjacent reservoirs, which were then removed. The resulting low-entropy system can be used as a basis for quantum simulation and information. Science , this issue p. 550

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 2013, 87(5): 052107], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker finite-size corrections and are more sensitive to the deviation from percolation threshold p _c , and thus provide a powerful means for determining p _c . We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus significantly improved estimates of p _c are obtained.

Ground-state phase diagram of the toric code model in a parallel magnetic field has three distinct phases: topological, charge-condensed, and vortex-condensed states. To study it we consider an implicit local order parameter characterizing the transition between the topological and charge-condensed phases, and sample it using continuous-time Monte Carlo simulations. The corresponding second-order transition line is obtained by finite-size scaling analysis of this order parameter. Symmetry breaking between charges and vortices along the first-order transition line is also observed, and our numerical result shows that the end point of the first-order transition line is located at $h_x^{\left(c\right)}=h_z^{\left(c\right)}=0.418\left(2\right)$.