We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the "activated complex" that mediates the collapse of the condensate. For a certain value of the s-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows to smoothly pass the bifurcation.
We investigate the rotational response of both non-dipolar and dipolar Bose-Einstein condensates confined in an annular potential. For the non-dipolar case we identify certain critical rotational frequencies associated with the formation of vortices. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms.
We investigate the stability properties and the dynamics of Bose-Einstein condensates with axial symmetry, especially with dipolar long-range interaction, using both simulations on grids and variational calculations. We present an extended variational ansatz which is applicable for axial symmetry and show that this ansatz can reproduce the lowest eigenfrequencies of the Bogoliubov spectrum, and also the corresponding eigenfunctions. Our variational ansatz is capable of describing the roton instability of pancake-shaped dipolar condensates for arbitrary angular momenta. After investigating the …
We consider the metastable dynamics of a flattened dipolar condensate. We develop an analytic model that quantifies the energy barrier to the system undergoing local collapse to form a density spike. We also develop a stochastic Gross-Pitaevskii equation (SGPE) theory for a flatted dipolar condensate, which we use to perform finite temperature simulations verifying the local collapse scenario. We predict that local collapses play a significant role in the regime where rotons are predicted to exist, and will be an important consideration for experiments looking to detect these excitations.
We investigate a multilayer stack of dipolar Bose-Einstein condensates in terms of a simple Gaussian variational ansatz and demonstrate that this arrangement is characterized by the existence several stationary states. Using a Hamiltonian picture we show that in an excited stack there is a coupled motion of the individual condensates by which they exchange energy. We find that for high excitations the interaction between the single condensates can induce the collapse of one of them. We furthermore demonstrate that one collapse in the stack can force other collapses, too. We discuss the possibi…
We put forward and discuss in detail a scheme to achieve Bose-Einstein condensation of stationary-light dark-state polaritons with dipolar interaction. To this end we have introduced a diamond-like coupling scheme in a vapor of Rydberg atoms under the frozen gas approximation. To determine the system's dynamics we employ normal modes and identify the dark-state polariton corresponding to one of the modes. We show that in contrast to atomic dipolar ultra-cold vapors dark-state polariton Bose-Einstein condensates proposed here can be stable for a negative dipolar interaction constant.
We explore spatial symmetry breaking of a dipolar Bose Einstein condensate in the thermodynamic limit and reveal a critical point in the phase diagram at which crystallization occurs via a second order phase transition. This behavior is traced back to the significant effects of quantum fluctuations in dipolar condensates, which moreover stabilize a new supersolid phase, namely a regular honeycomb pattern with maximal modulational contrast and near-perfect superfluidity.
Gases of doubly-dipolar particles, with both magnetic and electric dipole moments, offer intriguing novel possibilities. We show that the interplay between doubly-dipolar interactions, quantum stabilization, and external confinement results in a rich ground-state physics of supersolids and incoherent droplet arrays in doubly-dipolar condensates. Our study reveals novel possibilities for engineering quantum droplets and droplet supersolids, including supersolid-supersolid transitions and the realization of supersolid arrays of pancake droplets.
We apply a hyperspherical formulation to a trapped Bose-Einstein condensate with dipolar and contact interactions. Central to this approach is a general correspondence between K-harmonic hyperspherical methods and a suitable Gaussian ansatz to the Gross-Pitaevskii equation, regardless of the form of the interparticle potential. This correspondence allows one to obtain hyperspherical potential energies for a wide variety of physical problems. In the case of the dipolar Bose-Einstein condensate, this motivates the inclusion of a beyond-mean field term within the hyperspherical picture, which all…
We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several novel routes to induce vortex lattice formation i…
We propose a scheme to obtain the Heisenberg-limited parameter estimation precision by immersing atoms in a thermally equilibrated quasi-one-dimensional dipolar Bose-Einstein condensate reservoir. We show that the collisions between the dipolar atoms and the immersed atoms can result in a controllable nonlinear interaction through tuning the relative strength and the sign of the dipolar and contact interaction. We find that the repulsive dipolar interaction reservoir is preferential for the spin squeezing and the appearance of an entangled non-Gaussian state. As a useful resource for quantum m…
We develop finite temperature theory for a trapped dipolar Bose gas including thermal exchange interactions. Previous treatments neglected these, difficult to compute, terms. We present a methodology for numerically evaluating the thermal exchange contributions, making use of cylindrical symmetry. We then investigate properties of the dipolar gas, including calculating the excitation spectrum over the full range of trap anisotropy. We evaluate the contributions due to thermal exchange noting that, under some regimes, these effects can be at least as significant as the direct interaction. We th…
We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simula…
The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gr…
We have computed phase diagrams for rotating spin-1 Bose-Einstein condensates with long-range magnetic dipole-dipole interactions. Spin textures including vortex sheets, staggered half-quantum- and skyrmion vortex lattices and higher order topological defects have been found. These systems exhibit both superfluidity and magnetic crystalline ordering and they could be realized experimentally by imparting angular momentum in the condensate.
We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equat…
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
We experimentally show that dipolar interaction can stabilize otherwise unstable many-body systems like an attractive Bose gas. In a one dimensional lattice the repulsive dipolar on-site interaction balances negative scattering lengths up to -17 Bohr radii and stabilizes the chromium Bose-Einstein condensate. For reduced lattice depths, the dipolar stabilization turns into destabilization. We probe the full cross-over between the two regimes and our results are in excellent agreement with theoretical calculations, which reveal significant dipolar inter-site interactions.
We propose a two-dimensional model for a multilayer stack of dipolar Bose-Einstein condensates formed by a strong optical lattice. We derive effective intra- and interlayer dipole-dipole interaction potentials and provide simple analytical approximations for a given number of lattice sites at arbitrary polarization. We find that the interlayer dipole-dipole interaction changes the transverse aspect ratio of the ground state in the central layers depending on its polarization and the number of lattice sites. The changing aspect ratio should be observable in time of flight images. Furthermore, w…
The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the stationary states in the Thomas-Fermi limit, in the corotating frame, as well as direct numerical simulations in the Thomas-Fermi regime, explicitly accounting for the rotating polarization. The condensate is found to be inherently unstable due to the dynamical instability of collective modes. This ultimately prevents the realization of robust and long-lived rotat…
It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions, respectively. Our analytic results and the numerical simulations demonstrate that either of the two interactions can be suppressed to make the other dominate the spin dynamics; furthermore, both of th…
We study the evolution of correlations in a quasi-2D dipolar gas driven out-of-equilibrium by a sudden ramp of the interaction strength. For sufficiently strong ramps, the momentum distribution, excited fraction and density-density correlation function all display pronounced features that are directly related to the appearance of a roton minimum in the underlying spectrum. Our study suggests that the evolution of correlations following a quench can be used as a probe of roton-like excitations in a dipolar gas. We also find that the build up of density-density correlations following a quench oc…
We investigate effects of three-body contact interactions on a trapped dipolar Bose gas at finite temperature using the Hartree-Fock-Bogoliubov approximation. We analyze numerically the behavior of the transition temperature and the condensed fraction. Effects of the three-body interactions, anomalous pair correlations and temperature on the collective modes are discussed.
We present vortex solutions for the homogeneous two-dimensional Bose-Einstein condensate featuring dipolar atomic interactions, mapped out as a function of the dipolar interaction strength (relative to the contact interactions) and polarization direction. Stable vortex solutions arise in the regimes where the fully homogeneous system is stable to the phonon or roton instabilities. Close to these instabilities, the vortex profile differs significantly from that of a vortex in a nondipolar quantum gas, developing, for example, density ripples and an anisotropic core. Meanwhile, the vortex itself…
We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in phase plot of dipolar and contact interac…
We develop a theory of damping of low energy, collective excitations in a quasi-2D, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to the nature of the low energy spectrum of a quasi-2D dipolar gas, such processes cannot occur unless the momentum of the incoming quasi-particle exceeds a critical value k_{crit}. We find that as the dipolar interaction strength is increased, this critical value shifts to larger momenta. Our predictions can be directly verified in current experiments on dipola…
We systematically investigate the properties of three-dimensional dipolar binary Bose mixture at low temperatures. A set of coupled self-consistent equations of motion are derived for the two condensates. In the homogeneous case, useful analytical formulas for the condensate depletion, the anomalous density, the ground-state energy, and the equation of state are obtained. The theory is extended to the inhomogeneous case and the importance of the inhomogeneity is highlighted. Our results open up a new avenue for studying dipolar mixture droplets. Impacts of the dipole-dipole interaction on the …
Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, the atoms experience an overall dipolar repulsion and this fact sho…
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the post-expansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases, reducing error in expansion thermometry from tens of percent to only a few perce…
We report the measurement of collisions between two Bose-Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulation…
A homogeneous polarized dipolar Bose-Einstein condensate is considered in the presence of weak quenched disorder within mean-field theory at zero temperature. By first solving perturbatively the underlying Gross-Pitaevskii equation and then performing disorder ensemble averages for physical observables, it is shown that the anisotropy of the two-particle interaction is passed on to both the superfluid density and the sound velocity.
The long-range and anisotropic nature of the dipolar interaction provides the so-called supersolid phases in Bose-Einstein condensates (BECs) in an optical lattice. However, in a certain area of dipole interaction parameters, BECs can form into a droplet. In this paper, in order to qualitatively understand the droplet formations, we propose a toy model that allows us to estimate the size and shape of droplets in dipolar Bose-Hubbard system in the optical lattice. We compare results of the toy model with numerical solutions of the mean-field calculation.
Collapse in dipolar Bose-Einstein condensates may be arrested by quantum fluctuations. Due to the anisotropy of the dipole-dipole interactions, the dipole-driven collapse induced by soft excitations is compensated by the repulsive Lee-Huang-Yang contribution resulting from quantum fluctuations of hard excitations, in a similar mechanism as that recently proposed for Bose-Bose mixtures. The arrested collapse results in self-bound filament-like droplets, providing an explanation to recent dysprosium experiments. Arrested instability and droplet formation are novel general features directly linke…
The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the Schrödinger equation. In the present study we employ different Monte Carlo methods, that are stochastic techniques that allow to find numerical solutions to it.
We study the influence of dipole-dipole interaction on the formation of vortices in a rotating dipolar Bose-Einstein condensate (BEC) of $^{52}$Cr and $^{164}$Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross-Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices while a repulsive contact interaction increases the stability of the vortices. Further, an ordered vortex lattice of relatively large number of vortices is found in a strongly dipolar BEC.
We present a theory for the Landau damping of low energy quasi-particles in a collisionless, quasi-2D dipolar Bose gas and produce expressions for the damping rate in uniform and non-uniform systems. Using simple energy-momentum conservation arguments, we show that in the homogeneous system, the nature of the low energy dispersion in a dipolar Bose gas severely inhibits Landau damping of long wave-length excitations. For a gas with contact and dipolar interactions, the damping rate for phonons tends to decrease with increasing dipolar interactions; for strong dipole-dipole interactions, phonon…
We consider a rapidly rotating two-component Bose-Einstein condensate with short-range s-wave interactions as well as dipolar coupling. We calculate the phase diagram of vortex lattice structures as a function of the intercomponent s-wave interaction and the strength of the dipolar interaction. We find that the long-range interactions cause new vortex lattice structures to be stable and lead to a richer phase diagram. Our results reduce to the previously found lattice structures for short-range interactions and single-component dipolar gases in the corresponding limits.
We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitations spectrum, the correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial phy…
We consider a mixture of two-component Fermi and (one-component) dipolar Bose gases in which both dipolar interaction and s-wave scattering between fermions of opposite spins are tunable. We show that in the long wavelength limit, the anisotropy in the Fermi-Fermi interaction induced by phonons of the dipolar condensate can strongly enhance the scattering in the triplet channel. We investigate in detail the conditions for achieving optimal critical temperature at which the triplet superfluid begins to compete with the singlet superfluid.
We study the dynamics of vortex dipoles in erbium ($^{168}$Er) and dysprosium ($^{164}$Dy) dipolar Bose-Einstein condensates (BECs) by applying an oscillating blue-detuned laser (Gaussian obstacle). For observing vortex dipoles, we solve a nonlocal Gross-Pitaevskii (GP) equation in quasi two-dimensions in real-time. We calculate the critical velocity for the nucleation of vortex dipoles in dipolar BECs with respect to dipolar interaction strengths. We also show the dynamics of the group of vortex dipoles and rarefaction pulses in dipolar BECs. In the dipolar BECs with Gaussian obstacle, we obs…
We rigorously discuss the infrared behavior of the uniform three dimensional dipolar Bose systems. In particular, it is shown that low-temperature physics of the system is controlled by two parameters, namely isothermal compressibility and intensity of the dipole-dipole interaction. By using hydrodynamic approach we calculate the spectrum and damping of low-lying excitations and analyze infrared behavior of the one-particle Green's function. The low-temperature corrections to the anisotropic superfluid density as well as condensate depletion are found. Additionally we derive equations of the t…
We investigate long-range effects of the dipolar interaction in Bose-Einstein condensates by solving the time-dependent 3D Gross-Pitaevskii equation. We study the propagation of excitations between non-overlapping condensates when a collective mode is excited in one of the condensates. We obtain the frequency shifts due to the long-range character of the dipolar coupling for the bilayer and also the trilayer system when the dipolar mode is excited in one condensate. The propagation of the monopolar and quadrupolar modes are also investigated. The coupled-pendulum model is proposed to qualitati…
We study dipolar Bose-Einstein condensates for a realistic set of parameters close to actual experimental setups with dysprosium. Our analysis is based on the extended Gross-Pitaevskii equation, which we solve numerically exact on a three-dimensional grid. We present stability and phase diagrams, and study the expansion dynamics of dipolar condensates. Our calculations show signatures of the dipole-dipole interaction in terms of structured states and a deviation of the well-known inversion of the aspect ratio of the cloud during a time of flight.
Roton excitations constitute a key feature of dipolar gases, connecting these gases with superfluid helium. We show that the density dependence of the roton minimum results in a spatial roton confinement, particularly relevant in pancake dipolar condensates with large aspect ratios. We show that roton confinement plays a crucial role in the dynamics after roton instability, and that arresting the instability may create a trapped roton gas revealed by confined density modulations. We discuss the local susceptibility against density perturbations, which we illustrate for the case of vortices. Ro…
We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.
We study the Josephson oscillation and self trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of $^{52}$Cr atoms polarized along the symmetry axis of an axially-symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length a) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large number of atoms, whereas self trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self trapping to…
We report new results for the Thomas-Fermi groundstate and the quadrupolar modes of density oscillations of a spin- polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field is not orientated parallel to a principal axis of a harmonic anisotropic trap.
We demonstrate stable, robust, bright dipolar Bose-Einstein condensate (BEC) solitons, moving in a direction perpendicular to the polarization direction, formed due to dipolar interaction for repulsive contact interaction. At medium velocity the head on collision of two such solitons is found to be quasi elastic with practically no deformation. Upon small perturbation the solitons are found to exhibit sustained breathing oscillation. The findings are illustrated by numerical simulation using the 3D mean-field Gross-Pitaevskii equation and a reduced 2D model in three and two spatial dimensions …
With current magnetic field shielding and high precision detection in dipolar spinor Bose-Einstein condensates, it is possible to experimentally detect the low or zero field nonsecular dipolar dynamics. Here we analytically investigate the zero-field nonsecular magnetic dipolar interaction effect, with an emphasis on magnetization dynamics in a spin-1 Bose-Einstein condensate under the single spatial mode approximation within the mean field theory. Due to the biaxial nature of the dipolar interaction, a novel resonance occurs in the condensate magnetization oscillation, contrast to the previou…
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 counter-twisting mechanism, accelerating the spin squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measu…
Motivated by the recent experiments [H. Kadau et al., Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied using the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.
We study a simple model of interacting bosons on a d-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences of dipole conservation can be explored. As a function of chemical potential and hopping strength, the model can be tuned between gapped Mott insulating phases and various types of gapless condensates. The condensed phase realized at large hopping strengths, which we dub a Bose-Einstein insulator, is particularly interesting: despite having a Bose condensate, …
By solving the three-dimensional Gross-Pitaevskii equation we generate two-dimensional axially-symmetric and anisotropic dipolar Bose-Einstein condensate bright solitons, for repulsive atomic interaction, stabilized by only a weak one-dimensional optical lattice (OL) aligned along and perpendicular, respectively, to the dipole polarization direction. In the former case vortex solitons can also be created. We show that it is possible to make a stable array of small interacting axially-symmetric dipolar solitons put on alternate OL sites. Further, we demonstrate the elastic nature of the collisi…
We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two- dimensional anisotropic trap, for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles, and the size and the orientation of the deformation of the trapping potential.
We used the Gross--Pitaevskii equations to investigate ferromagnetic resonance in spin-1 Bose--Einstein condensates with a magnetic dipole-dipole interaction. By introducing the dipole interaction, we obtained equations similar to the Kittel equations used to represent ferromagnetic resonance in condensed matter physics. These equations indicated that the ferromagnetic resonance originated from dipolar interaction, and that the resonance frequency depended upon the shape of the condensate. Furthermore, spin currents driven by spin diffusions are characteristic of this system.
We calculate the mean-field phase diagram of a zero-temperature, binary Bose mixture on a square optical lattice, where one species possesses a non-negligible dipole moment. Remarkably, this system exhibits supersolidity for anomalously weak dipolar interaction strengths, which are readily accessible with current experimental capabilities. The supersolid phases are robust, in that they occupy large regions in the parameter space. Further, we identify a first-order quantum phase transition between supersolid and superfluid phases. Our results demonstrate the rich features of the dipolar Bose mi…
