Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one-and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.

We consider fermionic polar molecules in a bilayer geometry where they are oriented perpendicularly to the layers, which permits both low inelastic losses and superfluid pairing. The dipole-dipole interaction between molecules of different layers leads to the emergence of interlayer superfluids. The superfluid regimes range from BCS-like fermionic superfluidity with a high Tc to Bose-Einstein (quasi-)condensation of interlayer dimers, thus exhibiting a peculiar BCS-BEC crossover. We show that one can cover the entire crossover regime under current experimental conditions. PACS numbers: 03.75.Ss, Ultracold gases of dipolar particles attract great interest because the dipole-dipole interaction drastically changes the nature of quantum degenerate regimes compared to ordinary short-range interacting gases [1,2]. This has been demonstrated in experiments with Bosecondensed chromium atoms which have a magnetic moment of 6µ B equivalent to an electric dipole moment of 0.05 D [3][4][5]. The recent experiments on creating polar molecules in the ground ro-vibrational state [6,7] and cooling them towards quantum degeneracy [6] have made a breakthrough in the field. For such molecules polarized by an electric field the dipole-dipole interaction is several orders of magnitude larger than for atomic magnetic dipoles. This opens fascinating prospects for the observation of new quantum phases [1,2,[8][9][10][11][12]. The main obstacle is the decay of the system due to ultracold chemical reactions, such as KRb+KRb⇒K 2 +Rb 2 found in JILA experiments [13]. These reactions are expected to be suppressed by the intermolecular repulsion in 2D geometries where the molecules are oriented perpendicularly to the plane of their translational motion [14].In this Letter we consider fermionic polar molecules in a bilayer geometry where the dipoles are oriented perpendicularly to the layers (Fig. 1), which leads to low inelastic losses and allows for the possibility of superfluid pairing. The interaction between dipoles of different layers may lead to the emergence of an interlayer superfluid, that is a superfluid 2D gas where Cooper pairs are formed by fermionic molecules of different layers. We show that the interlayer dipole-dipole interaction provides a higher superfluid transition temperature than that for 2D spin-1/2 fermions with attractive short-range interaction.Interestingly, an increase in the interlayer dipole-dipole coupling leads to a novel BCS-BEC crossover resembling that studied for atomic fermions near a Feshbach resonance [15,16]. The reason is that two dipoles belonging to different layers can always form a bound state [17]. As long as the binding energy ǫ b is much smaller than the Fermi energy E F , or equivalently the size of the interlayer two-body bound state greatly exceeds the intermolecular spacing in the {x, y} plane, the ground state of the system is the BCS-paired interlayer superfluid. Once a reduction of the interlayer spacing λ or an increase of the molecular dipole moment d by an electric field make ǫ b >> E...

Low-energy two-dimensional scattering is particularly sensitive to the existence and the properties of weakly bound states. We show that interaction potentials V (r) with vanishing zero-momentum Born approximation drrV (r) = 0 lead to an anomalously weak bound state which crucially modifies the two-dimensional scattering properties. This anomalous case is especially relevant in the context of polar molecules in bilayer arrangements.

Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case of spin models with short-range couplings. However, progress toward the development of a comparable understanding in long-range interacting models, in particular out-of-equilibrium, remains limited. In a recent work, we proposed a semiclassical numerical method to study spin models, the discrete truncated Wigner approximation (DTWA), and demonstrated its capability to correctly capture the dynamics of one-and two-point correlations in one-dimensional (1D) systems. Here we go one step forward and use the DTWA method to study the dynamics of correlations in two-dimensional (2D) systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. We compute spatial and time-dependent correlations for spin-couplings that decay with distance as a power-law and determine the velocity at which correlations propagate through the system. Sharp changes in the behavior of those velocities are found as a function of the power-law decay exponent. Our predictions are relevant for a broad range of systems including solid state materials, atom-photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. We validate the DTWA predictions for small 2D systems and 1D systems, but ultimately, in the spirt of quantum simulation, experiments will be needed to confirm our predictions for large 2D systems.

Diagnostic testing for the novel coronavirus is an important tool to fight the coronavirus disease (Covid-19) pandemic. However, testing capacities are limited. A modified testing protocol, whereby a number of probes are ‘pooled’ (i.e. grouped), is known to increase the capacity for testing. Here, we model pooled testing with a double-average model, which we think to be close to reality for Covid-19 testing. The optimal pool size and the effect of test errors are considered. The results show that the best pool size is three to five, under reasonable assumptions. Pool testing even reduces the number of false positives in the absence of dilution effects.