A detailed microscopic analysis of the dynamic structure function S(k,omega) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. We finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.
A detailed microscopic analysis of the dynamic structure function S(k,omega) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. We finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.
We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size a and simulations are performed for values of the gas parameter na3 ranging from the dilute regime up to densities n where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for na3=0.2138, which corresponds to superfluid 4He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.
The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of a quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from a gas to a solid phase when the density increases. In the gas phase, the condensate fraction is calculated as a function of the density. Using the Feynman approximation, the collective excitation branch is studied and the appearance of a roton minimum is observed. The results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindemann ratio at the transition point becomes gamma=0.230(6). The condensate fraction in the gas phase is estimated as a function of the density.
We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\mathrm{\ensuremath{\Lambda}}$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\mathrm{\ensuremath{\Sigma}}$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.
We present a method for calculating the dynamics of a bosonic mixture, the multicomponent correlated-basis-function (CBF) method. For a single component, CBF results for the excitation energies agree quite well with experimental results, even for highly correlated systems like 4He, and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multicomponent CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider the case of strong coupling, leading to large positive interlayer correlations. We calculate the spectrum for a system of eight layers and show that the strong coupling can lead to a simpler spectrum than in the uncoupled case, with a single peak carrying most of the spectral weight.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
Recent experimental advances in creating stable dipolar systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Here we discuss our work on homogeneous 2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for non-zero tilt angles. Using Bogoliubov-de Gennes equations, we obtain T=0 excitation spectrum of the dipolar Bose gas, and explore instabilities at varying tilt angle, density and dipolar coupling. We map out a phase diagram a function of tilt angle, dipole strength and density. We find the development of maxon-roton behavior leading to roton instabilities at large densities for small tilt angles, and at low densities for large tilt angles. The behavior is anisotropic in k-space; accordingly the roton instabilities occur in the k y direction, suggestive of inhomogeneity and stripe phase, with density mode becoming soft in the y direction. Our results compare favorably with existing Quantum Monte Carlo calculations for non-zero tilt angles.