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DENSITY WAVES IN DIPOLAR BOSE-EINSTEIN CONDENSATES

Alexandru I. Nicolin

Published Jan 1, 2013• 3 citations
Publisher

Abstract

Density waves in cigar-shaped dipolar Bose-Einstein condensates are analysed by variational means and we show analytically how the dipole-dipole interaction between the atoms generates a rotonmaxon excitation spectrum. A simple model is used to derive the effective equations which describe the emergence of the density waves.
DOI
10.5072/zenodo.21520

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Cambridge University Press eBooks•Oct 4, 2018•0 citations
Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.
We study the emergence of density waves in quasi-one-dimensional dipolar Bose-Einstein condensates (BECs) when the strength of dipole-dipole atomic interactions is periodically varied in time. The proposed theoretical model based on the evolution of small perturbations of the background density allows one to calculate the instability growth rate for an arbitrary set of input parameters, thereby identifying instability regions with respect to density waves. We find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. The frequency of temporal oscillations of emerging density waves coincides with half of the driving frequency, which is the hallmark of the parametric resonance and is characteristic of Faraday waves. The possibility to create density waves in dipolar BECs, which can persist after emergence, is demonstrated. The existence of a standing-wave solution of the nonlocal Gross-Pitaevskii equation is revealed from numerical simulations. The effect of three-body atomic interactions, which is relevant to condensates with increased density, upon the properties of emerging waves is analyzed too. Significant modification of the condensate's excitation spectrum owing to three-body effects is shown.
We derive the effective Gross-Pitaevskii equation for a cigar-shaped dipolar Bose-Einstein condensate in one-dimensional lattices and investigate the band structures numerically. Due to the anisotropic and the long-ranged dipole-dipole interaction in addition to the known contact interaction, we elucidate the possibility of modifying the band structures by changing the alignment of the dipoles with the axial direction. With the considerations of the transverse parts and the practical physical parameters of a cigar-shaped trap, we show the possibility to stabilize an attractive condensate simply by adjusting the orientation angle of dipoles. Some interesting Bloch waves at several particle current densities are identified for possible experimental observations.
We present a theory for the emergence of a supersolid state in a cigar-shaped dipolar quantum Bose gas.Our approach is based on a reduced three-dimensional (3D) theory, where the condensate wave function is decomposed into an axial field and a transverse part described variationally.This provides an accurate fully 3D description that is specific to the regime of current experiments and efficient to compute.We apply this theory to understand the phase diagram for a gas in an infinite tube potential.We find that the supersolid transition has continuous and discontinuous regions as the averaged density varies.We develop two simplified analytic models to characterize the phase diagram and elucidate the roles of quantum droplets and of the roton excitation.
Selected topics on spinor-dipolar aspects of Bose-Einstein condensation are overviewed. Spinor aspects include spin correlations, fragmentation, dynamical symmetries, and quantum mass acquisition. Dipolar aspects include magnetostriction, d-wave collapse, roton-maxon spectrum, supersolidity, and ferrofluidity. Finally, spinor-dipolar aspects concern the Einstein–de Haas effect and spontaneous mass and spin currents in the ground state. Introduction Bose-Einstein condensation is a phenomenon in which a macroscopic number of particles occupy the same single-particle state as a consequence of symmetrization of a many-body wave function and thereby quantum effects are amplified to the macroscopic level. The amplified single-particle state serves as a complex order parameter whose phase behaves as an emergent thermodynamic quantity, with its temporal and spatial variations giving the chemical potential and the superfluid velocity, respectively. If the interparticle interaction is repulsive, a Bose-Einstein condensate (BEC) acquires stability against excitations out of the condensate because they would cost the Fock exchange energy. This rigidity of the order parameter or the condensate wave function endows a BEC with several remarkable transport properties which are collectively known as superfluidity. In particular, the superfluid fraction can be 100% at zero temperature even though the condensate fraction is depleted due to interparticle interactions. Interparticle interactions also make excited particles phase-locked to the condensate, leading to Bogoliubov quasiparticles, which are the manifestation of phase-coherent particle– hole excitations. When constituent particles have spin degrees of freedom, a BEC features magnetism and spin nematicity which conspire with superfluidity to produce a rich phase diagram. In the absence of an external magnetic field, the mean-field groundstate phase diagram includes two [1, 2], five [3, 4, 5], and eleven phases [6, 7] for spin-1, 2, and 3 BECs, respectively. BECs with spin degrees of freedom are called spinor condensates. Moreover, the magnetic dipole–dipole interaction (MDDI) between atoms lends distinct twists to spinor condensates because it is long-ranged and anisotropic in sharp contrast with other interactions, which are short-ranged and isotropic. In this chapter, we will present a brief overview on the spinordipolar aspects of BEC. An early experimental work of spinor BECs is reviewed in Ref. [8]. Later developments with an emphasis on theoretical aspects are described in Ref. [9]. Many-body physics of polarized dipolar gases is reviewed in Ref. [10].