Quantum Effect In Ultracold Spin-Orbit Coupled Atomic Fermi Gases And Applications

Following unprecedented experimental development, spin-orbit coupled atomicgases have attracted much attention in recent years. Due to the spin-orbit coupling ef-fect, atomic gases exhibit many new important properties. Topological superfluid andMajorana fermions have been predicted in this system. Also, as spin-orbit atomic gasesare easy to control in experiment, they can be used to simulate other important phys-ical phenomena, such as topological insulators. They are also important resources fortopological quantum computing.In this thesis, we mainly study the quantum effect of ultracold spin-orbit atomicFermi gases. Some theoretical problems related to quantum computing in open quantumsystems will also be touched upon.Firstly, we study the validity of the single channel model for a spin-orbit-coupledatomicFermigasnearFeshbachresonances. Itiswidelyaccepted, incaseswithoutspin-orbitcoupling, that when the channel couplingbetweentheclosedandtheopenchannelsis strong, the two-channel model is equivalent to the single-channel model. However,in the presence of spin-orbit coupling, we find that the condition for the equivalencebecomes much more stringent and is related to the strength of the spin-orbit coupling.We give new criteria for the equivalence in the presence of spin-orbit coupling and givea scheme for experiment testing.Secondly, we study the momentum-resolved radio frequency spectroscopy of spin-orbit atomic Fermi gases in a two-dimension optical lattice. Momentum-resolved ra-dio frequency spectroscopy is a powerful tool to probe single-particle energies andeigenstates. We also find an interesting spin-momentum reversed symmetry from themomentum-resolved radio frequency spectroscopy and prove it theoretically.In the field of quantum computing in open quantum systems, we first study a circuitmodel, i.e., duality quantum computer model, and give it a unified description. Then westudy the properties of a Kraus operator as a linear combination of unitary matrices. Wefind the expansion with the maximum constructive interference and also the expansionrequiring the minimum number of unitary matrices. Finally, we study the measure of thedistance between a general quantum operation and the unitary operations, which we callthe non-unitarity of the quantum operation. This also qualifies the noise of the quantum operation. We propose a new measure for the non-unitarity of a quantum operation andgivetheresultsforsomeimportantsinglequbitquantumchannels. Wealsostudythedis-tribution of the non-unitarity of quantum operations and the its relation to the dimensionof the environment.