Spin-Hall Effect in A Symmetric Quantum Wells by A Random Rashba Field

Changes dopant ion concentrations in the sides of a symmetric quantum well are known to create a random Rashba-type spin-orbit coupling. Here we demonstrate that, as a consequence, a finite size spin-Hall effect is also present. Our numerical algorithm estimates the result of the Kubo formula for the spin-Hall conductivity, by using a tight-binding approximation of the Hamiltonian in the framework of a time-dependent Green's function formalism, well suited for very large systems.Comment: 4 pages, 4 figures in eps forma

Spin Hall Effect in a Symmetric Quantum Well by a Random Rashba Field

Dopant ion concentrations in the sides of a symmetric quantum well are known to create a random Rashba-type spin-orbit coupling. Here, we demonstrate that, as a consequence, a finite size spin Hall effect is also present. Our numerical algorithm estimates the result of the Kubo formula for the spin Hall conductivity by using a tight-binding approximation of the Hamiltonian in the framework of a time-dependent Green’s function formalism well suited for very large systems

Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high tensor powers of the line bundle. This gives after integration weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities which we apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a multiplicative constant 1/2 ; v.2 is a final updat

Macrodimers: ultralong range Rydberg molecules

We study long range interactions between two Rydberg atoms and predict the existence of ultralong range Rydberg dimers with equilibrium distances of many thousand Bohr radii. We calculate the dispersion coefficients $C_{5}$, $C_{6}$ and $C_{8}$ for two rubidium atoms in the same excited level $np$, and find that they scale like $n^{8}$, $n^{11}$ and $n^{15}$, respectively. We show that for certain molecular symmetries, these coefficients lead to long range potential wells that can support molecular bound levels. Such macrodimers would be very sensitive to their environment, and could probe weak interactions. We suggest experiments to detect these macrodimers.Comment: 4 pages, submitted to PR

Low energy atomic collision with dipole interactions

We apply quantum defect theory to study low energy ground state atomic collisions including aligned dipole interactions such as those induced by an electric field. Our results show that coupled even ($l$) relative orbital angular momentum partial wave channels exhibit shape resonance structures while odd ($l$) channels do not. We analyze and interpret these resonances within the framework of multichannel quantum defect theory (MQDT).Comment: 27 pages, 17 figures, an inadvertent typo correcte

High-precision calculations of dispersion coefficients, static dipole polarizabilities, and atom-wall interaction constants for alkali-metal atoms

The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states, are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from ultra-cold collisions and from studies of magnetic field induced Feshbach resonances in Na and Rb. For Cs we provide critically needed data for ultra-cold collision studies

Prospects for p-wave paired BCS states of fermionic atoms

We present theoretical prospects for creating p-wave paired BCS states of magnetic trapped fermionic atoms. Based on our earlier proposal of using dc electric fields to control both the strength and anisotropic characteristic of atom-atom interaction and our recently completed multi-channel atomic collision calculations we discover that p-wave pairing with $^{40}$K and $^{82,84,86}$Rb in the low field seeking maximum spin polarized state represent excellent choices for achieving superfluid BCS states; and may be realizable with current technology in laser cooling, magnetic trapping, and evaporative/sympathetic cooling, provided the required strong electric field can be applied. We also comment on the prospects of similar p-wave paired BCS states in $^{6}$Li, and more generally on creating other types exotic BCS states. Our study will open a new area in the vigorous pursuit to create a quantum degenerate fermionic atom vapor.Comment: to be publishe