Research On Novel Superfluid Phase In Spin Orbit Coupled Fermi Gas

In recent years,the superfluid pairing of ultra-cold Fermi gases has always been an important field of research.The superfluid properties of Fermi liquid at ultra-low temperature was discovered by scientists firestly through experiments.Subsequently,various model assumptions were put forward for this superfluid property by numerous theoretical physicists over a period of time.It was not until the Bardeen-Cooper-Schrieffer(BCS)theory was put forward that it provided a theoretical model for the superfluid properties of Fermi liquids.Being Different from the BCS theory,Feynman proposed the concept of quantum simulation in 1982,and people began to show great interest in unconventional aligned particle states Fulde-Ferrell(FF)states.By studying these quasi-particle bodies with novel structures,it could help us provide assistance for quantum computing of complex physical phenomena.In recent years,with the rapid development of physical experimental methods,people have found a way to control cold atomic gases,which provides an important method for us to study unconventional coordinated particle states in experiments.These included artificial gauge field,Feshbach resonance,controllable light lattice and other experimental methods to control the parameters of Fermi atoms.The realization of Feshbach resonance allowed people to freely control the interaction strength of cold atoms.The realization of the controllable lattice system meant that scientists could adjust the position and space between atoms to achieve certain specific crystal structures.The main forms of artificial gauge field was artificial spin-orbit coupling and artificial electromagnetic field.This meant that we could control the dispersion spectrum of the atoms in the system.These rich experimental methods made it easy for people to manipulate the cold atomic gas into some special states by changing various parameters in the experiment.Recently,since the NIST experimental team has achieved spin-orbit coupling in cold atom gases,which made the controllable Fermi gas containing artificial spin-orbit coupling an important research in the field of cold atom research.For Fermi gases with artificial spin-orbit coupling,there are still many unknowns that are worth exploring.In this article,we mainly conducted an in-depth study on the exotic pairing state of Fermi gas with artificial spin orbits.The specific work was as follows:First,we gave the experimental model of the NIST experimental team to achieve artificial spin-orbit coupling,at the same time studied the superfluid pairing in two-dimensional two-component Fermi gas containing spin-orbit coupling.The single-particle energy spectrum under this model was given,and the influence of the spin-orbit coupling effect on the energy spectrum was analyzed.Furthermore,by using the mean field theory,the thermodynamic potential equation in the many-body system was derived,and the self-consistent equations about the paired center-of-mass momentum were given.Finally,the pairing method of the system and the characteristics of the dispersion spectrum of quasiparticles(holes)in the system were analyzed.Then,the effect of adding a horizontal Zeeman field to the model of the NIST group on the two-component Fermi gas containing spin-orbit coupling was studied.Due to the spin-orbit coupling effect,the symmetry of the single-particle energy spectrum of the system cannot be changed alone.Therefore,adjusting the energy spectrum of a single particle by introducing a horizontal Zeeman field was considered.Therefore,the single-particle energy spectrum under the combined action of the horizontal Zeeman field and the spin-orbit coupling was changed.the pairing state of particles could be furthered studied in this model.As the single-particle energy spectrum was affected by the horizontal Zeeman field,it has shifted,which made us need to consider the pairing situation where the center-of-mass momentumwas not zero.For this reason,theoretical derivation and numerical calculation of the thermodynamic potential were carried out in the system,giving an image of the thermodynamic potential and intuitively analyzed the change of the ground state of the system.Through our research,we found that the FF state did exist in the system under the influence of the level Zeeman.According to the gapless excitation point profile of the FF state,the different FF states were distinguished and discussed.The different quasiparticle(hole)dispersion spectra of these FF states were an important sign to distinguish different FF states.Finally,the phase diagram of the horizontal Zeeman field and the spin-orbit coupling strength plane were gave,the influence of the inter-particle interaction strength on the horizontal Zeeman field inducing the formation of FF states with the spin-orbit coupling Fermi gas was discussed.Then,the pairing of two-dimensional three-component Fermi gas containing spin-orbit coupling were studied.Being Different from the two-component spin-orbit coupling Fermi gas,many new system pairing states were triggered through the combined effect of the different interaction strengths between the particles and the horizontal Zeeman field.Therefore,there will be fierce competition between different FF states.In this part,a three-component physical model of Fermi gas with spin-orbit coupling was established firstly.The single-particle energy spectrum of the model was given,and the binding energy self-consistent equation of the three-component Fermi gas with spin-orbit coupling was derived theoretically using the mean field theory and the self-consistent equation of bound energy to discuss the pairing of particles in the multi-particle system.This kind of different competition mechanism is studied.