The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated. The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one.
A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact
by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the
projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated
wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how
to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions nala-nblb of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good
agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys.
Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method
to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle.
Received 6 April 1999 相似文献
We have developed a simple model potential with a hard core and the correct large-r Coulombic behaviour, to describe the interaction of an electron with a closed shell. One has an exact, analytic ground state
wave function for this potential. This potential is used to develop two-electron perturbed and unperturbed wave functions,
with the correct asymptotic behaviour and cusp conditions. These wave functions allow us to obtain accurate values for the
two-electron energies, polarisabilities, hyperpolarisabilities, and dispersion coefficients of alkaline earth sequences. Many
of these results are the only ones available in the literature.
Received 29 July 1999 and Received in final form 16 November 1999 相似文献
The conventional Hartree and Hartree-Fock approaches for treating many-electron bound systems have been extended recently
to positive energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of
full self-consistency. Serious consequences of such a theory are that the target orbitals become energy dependent and the
asymptotic boundary conditions are satisfied only approximately, in lowest order. It is important therefore to test the theory
for its convergence under configuration mixing. This self-consistent field (SCF) theory for scattering has been tested here
for scattering from hydrogenic target as a model where the target function is determined dynamically. Penetration of the projectile
inside the bound target orbital is manifest through the SCF for the bound state. Our results show that the theory converges
to the correct amplitudes and to the exact boundary conditions as more configurations are added. The use of the amputated
functions and the weak asymptotic condition (WAC) upon which the SCF theory is based, is justified as the WAC converges to
the correct limit. It is then applied to the positron-helium and electron-helium scattering systems where the helium function
is calculated simultaneously together with the scattering function. The resulting phase shifts and the SCF target functions
are compared with those obtained with the pre-determined target functions in the conventional approaches.
Received 22 September 1999 相似文献
