Ground State Properties And Collective Excitations Of A Spin-3/2 Fermi Gas

Large-spin Fermi liquid theory will be developed to comprehensively study the ground-state properties and collective excitations for large-spin(multicomponent)cold atomic fermions.There exist complicated interactions between different components,including the spin-mixing exchange interaction.Many novel phenomena could be induced and the Landau Fermi parameters should be redefined.We will develop quantum many-body theory and diagram techniques to calculate ground state properties,collective excitation modes,and other Landau parameters.Firstly,we develop a generalized spin-3/2 Fermi model with spin-dependent contact interactions.The diagram technique is employed to study ground state properties.The chemical potential,ground state energy,and effective mass are calculated after elaborately dealing with the effective interaction and the self-energy.Contributions of each interaction term are derived within the second-order perturbation.It is found that the spin-mixing term always strengthens the ground state energy and effective mass.Second,collective excitation modes of charge-density-wave and spin-densitywave are investigated by two-particle Green’s functions and random phase approximation.All spectra are gapless and linear in the small wave vector q,with their slopes dependent on the coupling of different interaction parameters.The spinmixing interaction has effects on the transverse spin-density waves,but not on the charge-density modes.Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained with balanced spin populations.However,with the imbalanced populations,the spin-density wave will occur at a finite wave vector Q for a mismatch of the Fermi surfaces while the charge-density wave excites from Q=0.When the system satisfies SU(4)symmetry,the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate,too.It is also found that susceptibilities are increasing with the enhancement of all interaction parameters,and become divergent at certain points.This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.Finally,we discuss the effects of interactions on Kondo ground state in the large-spin Fermi system with spin-3/2 from a single impurity model with strong correlation.It is found that the impurity resistance increases logarithmically with the decrease of temperature in the case of antiferromagnetic coupling similar to spin-1/2 system but has a larger resistance minimum value due to the increase of spin scattering channels.In the case of antiferromagnetic interaction,the ground state of the system is still the Kondo singlet state while the septuplet state has lowest energy for ferromagnetic coupling.And with the same antiferromagnetic s-d coupling parameter,the energy of Kondo singlet state is lower than spin-1/2,which indicate that the larger spin,the easier it is to enter the Kondo-screened phase.This provides some theoretical support for the realization of the Kondo effect by ultracold atoms in experiments.