Study On Anisotropic Dissipation In A Dipolar Bose-Einstein Condensate

The non-dissipative motion supported by superfluid is one of the manifestations of superfluidity.The critical velocity vc of the superfluid is determined by its elementary excitation energy spectrum.As long as the velocity of the impurity in the superfluid exceeds vc,energy dissipation will occur.In recent years,Bose-Einstein condensates(BEC)with anisotropic dipolar interactions have become a popular and new type of platform for the study of superfluidity.In experiments,there have been a lot of researches on measuring the isotropic critical velocity of various types of BEC,and the first experimental study to measure the anisotropic critical velocity was recently implemented by the T.Pfau group in a dipolar BEC.The energy dissipation in a dipolar BEC is further studied.The purpose of this thesis is to explain and generalize the conclusions of energy dissipation in the experiments theoretically.In this paper,the anisotropic dissipation in a dipolar BEC at zero temperature is studied by using the linear response theory.Firstly,the anisotropic dissipation in a dipolar BEC is considered in the Bogoliubov approximation.In the two principal directions of the parallel polarization axis and the vertical polarization axis measured in the experiment,an analytical expression of the energy dissipation rate is obtained as a function of reduced velocity u?v/vc,and the conclusion consistent with the experiment is obtained by comparing the analytical results:for any reduced velocity u>1,the energy dissipation rate is higher in the main axis direction of the parallel polarization axis with larger vc.In the direction of deviating from the principal axis,we generalize the above-mentioned anisotropic laws from three aspects,and give the asymptotic expressions about the dissipation rate near the high-velocity limit and vc,and from these two expressions it can be inferred that,for a given u,the dissipation rate is an increasing function of vc.In the case of medium dissipation,the analytical results can't be obtained,and the same conclusion is given by numerical results:the dissipation rate is higher in the direction of larger vc.Secondly,the influence of quantum fluctuation on energy dissipation in a dipolar BEC is considered.Regardless of the direction of the principal axis or the deviation from the principal axis,after the quantum fluctuation correction is taken into account,the analytical expression or asymptotic expression of the energy dissipation rate is consistent with the result form in the Bogoliubov approximation,and the energy dissipation is the same except that the corrected sound velocity is different.And the energy dissipation still has the same anisotropic law as that in the Bogoliubov approximation:the variation trend of the dissipation rate and the critical velocity with the direction angle is generally consistent.In the principal axis direction,when the dipolar interaction parameter ?dd?1,the dissipation rate results in the Bogoliubov approximation are still applicable after considering the quantum fluctuations,when ?dd=1,the dissipation rate results in the Bogoliubov approximation are different from that for ?dd<1,and the results are not reliable.In the direction of deviating from the principal axis,when ?dd is far away from 1,there is almost no difference between the energy dissipation rate considering the quantum fluctuation correction and the energy dissipation rate in the Bogoliubov approximation.When ?dd?1,the difference is gradually obvious.Finally,based on the study of single quasiparticle excitation,we study the critical velocity and energy dissipation rate when multiple quasiparticles are excited.The first thing that can be proved is that the critical velocity for exciting a single quasiparticle is less than or equal to the critical velocity for exciting multiple quasiparticles.Therefore,the excitation of a single quasiparticle must precede the excitation of multiple quasiparticles.On the other hand,in the Bogoliubov approximation,there are far more condensed atoms in the zero-momentum-occupied state than non-condensed atoms in the elementary excitation process caused by density perturbations,so the energy dissipation caused by the excitation of multiple quasiparticles can be ignored.