The Study Of Polarons In Cold Atom

Since effective interactions between atoms can be tuned to essentially any value by Feshbach resonance,ultracold Fermi gases have become remarkably interesting systems for studying experimentally many-body physics.The Feshbach resonance can change the interaction between atoms to be attractive or repulsive,which can also tune the value of interaction strength.This method can make the Fermi atoms be molecules.and make the Fermi atoms be pairs in many-body physics,such as the crossover of the BEC-BCS.Landau's idea of mapping the behavior of impurity particles interacting with a complex environment into quasiparticle properties plays a fundamental role in physics and materials science,in the field of ultracold gases,the impurity problem and the associated concept of the polaron quasiparticle have attracted over the past decade a growing interest.Fermi polaron is a spin-down impurity im:mersed in a spin-up Fermi sea,with the interaction between them increasing,the spin-down and spin-up particles form a dimer.The recent experiments in polaron systems,provide a deep understanding in the many-body physics and make the impurity problem and the associated concept of the polaron quasiparticle a attracting topic.The main work of this particle is as follows:1.Considering one or few spin-down impurities immersed in a fully polarized spin-up Fermi sea,then the spin-down impurity will form a dressed state with the spin-up Fermi sea.This dilute limit system formed with polarized Fermi gas is called po-laron.By calculating the binding energy and effective mass,one can see that the polaron system is deeply dressed in strong attractive regime,which means the spin-down and spin-up fermions form a bounded dimer.On the other hand,the one-dimensional Fermi system can be solved by exact Bethe ansatz method.By comparing the resuts by these two different method,we find that the variational method is a good method for the ID polaron system.Also,we can get a clear momentum distribution by the wave function,instead of treating the momentum just as Fermi-Dirac distribution.More especially,we can get the Tan contact from three different aspects.At last,we calculate the density-density correlation.2.For the polaron system in repulsive interaction regime,it is a metastable state in the higher dimensional case.In the experiment imprecise negative effective mass was detected,and the energy can be above the Fermi energy EF.In the strong repulsive regime,the variational method can not give a good result.In the one-dimensional case,polaron is a stable state.We find that the polaron energy is always below EF by vari-ational method,and the effective mass becomes infinite which accords with the Bethe ansatz.We also find that the Tan contact calculated from different aspects still agree with each other in weak repulsive interaction regime,the Tan relation derived from the momentum distribution can still keep the same trend with the Tan relation derived from the adiabatic relation in strong repulsive regime.3.We calculte the properties of heavy polaron and explore the large influence of particle-hole excitation.In the polaron system,the hole momentum q is a small value compared with the momentum k out of Fermi sea.It is always neglected in the calculating of the binding energy,especially in the higher dimensional case.But in the study of one-dimensional polaron system,we find that the hole momentum has a large influence of the repulsive polaron energy.Even in the attractive interaction regime,it still has a large influence on the Tan relation,which means the hole term can not be neglected completely.