Dipolar quantum solids emerging in a Hubbard quantum simulator.

Phase transition and field driven hysteresis evolution of a two-dimensional Ising grid consisting of ferroelectric–antiferroelectric multilayers that take into account the long range dipolar interactions were simulated by a Monte–Carlo method. Simulations were carried out for a 1 + 1 bilayer and a 5 + 5 superlattice. Phase stabilities of components comprising the structures with an electrostatic-like coupling term were also studied. An electrostatic-like coupling, in the absence of an applied field, can drive the ferroelectric layers toward 180° domains with very flat domain interfaces mainly due to the competition between this term and the dipole–dipole interaction. The antiferroelectric layers do not undergo an antiferroelectric-to-ferroelectric transition under the influence of an electrostatic-like coupling between layers as the ferroelectric layer splits into periodic domains at the expense of the domain wall energy. The long-range interactions become significant near the interfaces. For high periodicity structures with several interfaces, the interlayer long-range interactions substantially impact the configuration of the ferroelectric layers while the antiferroelectric layers remain quite stable unless these layers are near the Neel temperature. In systems investigated with several interfaces, the hysteresis loops do not exhibit a clear presence of antiferroelectricity that could be expected in the presence of anti-parallel dipoles, i.e., the switching takes place abruptly. Some recent experimental observations in ferroelectric–antiferroelectric multilayers are discussed where we conclude that the different electrical properties of bilayers and superlattices are not only due to strain effects alone but also due to long-range interactions. The latter manifests itself particularly in superlattices where layers are periodically exposed to each other at the interfaces.

We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.

Thermal fluctuations in crystalline membranes with long-range dipole interactions

Imagine you could produce an artificial crystal for quantum matter, defect free and with complete control over the periodic crystal potential. The shape of the periodic potential, its depth and the interactions between the underlying particles could be changed at will and the particles could be moved around in a highly controlled way, at essentially zero temperature. This sounds almost too good to be true, but it is in fact what optical lattices have made possible for cold and ultracold atoms.

We describe several numerical methods developed to analyze the behavior of spin polarized liquids in the presence of long-range magnetic dipolar interactions and external field gradients. Two of the methods use a discrete lattice of spins. In the first we calculate the magnetic field from the lattice of spins directly, either in the rotating frame, or in the lab frame. In the second method we include the dipolar fields from linear magnetization gradients analytically and calculate the dipolar fields from higher order gradients in Fourier space, where they are a local function of the magnetization. In the third method the magnetization is expanded in a Taylor series and the dipolar fields are calculated analytically for each term. The results of these calculations are compared to experimental data, in which we use two superconducting quantum interference device magnetometers adjacent to a spherical sample of hyperpolarized liquid 129Xe to detect the evolution of magnetization gradients. In particular, we observe an increase by a factor of 100 of the spin dephasing time in a longitudinal magnetic field gradient due to dipolar interactions of the spins. While each of the numerical techniques has certain limitations, they are generally in agreement with each other and with experimental data.

We investigate a spin model in which a ferromagnetic short-range interaction competes with a long-range antiferromagnetic interaction decaying spatially as \(\frac{1}{r^{d+\sigma}}\), d being the dimensionality of the lattice. For σ smaller than a certain threshold \(\hat{\sigma}\) (with \(\hat{\sigma}>1\)), the long-range interaction is able to prevent global phase separation, the uniformly magnetized state favored by the exchange interaction for spin systems. The ground state then consists of a mono-dimensional modulation of the order parameter resulting in a superlattice of domains with positive and negative magnetization. We find that the period of modulation shrinks with increasing temperature T and suggest that this is a universal property of the considered model. For d = 2 and σ= 1 (dipolar interaction) Mean-Field (MF) calculations find a striking agreement with experiments performed on atomically-thin Fe/Cu(001) films. Monte Carlo (MC) results for d = 1 also support the generality of our arguments beyond the MF approach.Keywordsfrustrated systemsmodulated systemslong-range interactionscompeting interactionsIsing model

Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions

The spin-squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis countertwisting mechanism, accelerating the spin-squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measurements.

Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations.

We present a many-body theory of the dipole-dipole interaction in three-dimensional optical lattices generated by a four-beam configuration, specializing to the case of ${J}_{g}=\frac{1}{2}\ensuremath{\rightarrow}{J}_{e}=$$\frac{3}{2}$ transitions. We construct a many-body interaction Hamiltonian in coordinate representation for an antiferromagnetic fcc optical lattice, the Schr\odinger field operators being expanded on a basis of Wannier functions. We discuss the main characteristics of the dipole-dipole matrix elements giving rise to bound-bound and bound-free atom interactions in the lattice. Because of the anisotropy of the dipole-dipole interaction, specific directions can be favored for transport and scattering processes. Furthermore, since the dipole-dipole interaction depends on atomic magnetic quantum numbers, the dipole-dipole potential resembles a spin-dependent potential, and can give rise to atomic hopping with simultaneous change in the magnetic quantum number.

Long-range and anisotropic dipolar interactions induce complex order in quantum systems, particularly interesting in 2D where superfluidity emerges via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. We observe a superfluid phase with algebraically decaying correlation in a quasi-2D dipolar Bose gas of erbium atoms and further identify the superfluid phase transition by monitoring extended coherence. We also measure equations of state with tunable dipolar interactions. Our findings show a transition point shift due to dipole orientation, aligning with BKT transition with effective short-range interaction. However, we observe that in-plane tilted dipoles show nonlocal effects in the superfluid regime, preventing the effective short-range interaction from revealing universal behavior near the BKT critical point. We also measure anisotropic atom number fluctuations in the superfluid regime, highlighting its dipolar nature. Our results provide a foundation for understanding dipolar bosons in 2D and pave the way for investigating complex orders in dipolar superfluids.

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.

We predict the magnitude of fluctuations of two-dimensional, supercrystal stripe phases of Langmuir monolayers, composed of polar molecules, in the low temperature regime. Our model includes both the microscopic line tension and the interdomain, long-range dipolar interactions. We calculate (in the long wavelength approximation) the elastic energy of the stripes and show that the stripes exhibit long-range orientational order. We predict that the stabilization of the stripe width by the dipolar interactions tends to decrease the thermal roughness of the domain walls compared with systems with only short-range interactions. In the case of crystalline stripes our results suggest a possible finite-temperature first-order roughening transition. \textcopyright{} 1996 The American Physical Society.

Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal phases in a new multi-step heating process en route towards the ultimate heat death. We discuss implications for experiments on ferromagnetic thin films and other driving induced phenomena in frustrated magnets.

A simulation study on the magnetic ordering in an artificial geometrically frustrated lattice