Magnetically generated spin-orbit coupling for ultracold atoms

We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip

Small ball probability for the condition number of random matrices

Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb P}\big\{s_{\max}(A)/s_{\min}(A)\leq n/t\big\}\leq 2\exp(-c t^2),\quad t\geq 1,$$ where $c>0$ may only depend on the subgaussian moment. Although the estimate can be obtained as a combination of known results and techniques, it was not noticed in the literature before. As a key step of the proof, we apply estimates for the singular values of $A$, ${\mathbb P}\big\{s_{n-k+1}(A)\leq ck/\sqrt{n}\big\}\leq 2 \exp(-c k^2), \quad 1\leq k\leq n,$ obtained (under some additional assumptions) by Nguyen.Comment: Some changes according to the Referee's comment

Smoothed Complexity Theory

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability). Furthermore, we discuss extensions and shortcomings of our model and relate it to semi-random models.Comment: to be presented at MFCS 201

Synthetic 3D Spin-Orbit Coupling

We describe a method for creating a three-dimensional analogue to Rashba spin-orbit coupling in systems of ultracold atoms. This laser induced coupling uses Raman transitions to link four internal atomic states with a tetrahedral geometry, and gives rise to a Dirac point that is robust against environmental perturbations. We present an exact result showing that such a spin-orbit coupling in a fermionic system always rise to a molecular bound state.Comment: 4 pages, 6 figure

A New Linear Inductive Voltage Adder Driver for the Saturn Accelerator

Saturn is a dual-purpose accelerator. It can be operated as a large-area flash x-ray source for simulation testing or as a Z-pinch driver especially for K-line x-ray production. In the first mode, the accelerator is fitted with three concentric-ring 2-MV electron diodes, while in the Z-pinch mode the current of all the modules is combined via a post-hole convolute arrangement and driven through a cylindrical array of very fine wires. We present here a point design for a new Saturn class driver based on a number of linear inductive voltage adders connected in parallel. A technology recently implemented at the Institute of High Current Electronics in Tomsk (Russia) is being utilized[1]. In the present design we eliminate Marx generators and pulse-forming networks. Each inductive voltage adder cavity is directly fed by a number of fast 100-kV small-size capacitors arranged in a circular array around each accelerating gap. The number of capacitors connected in parallel to each cavity defines the total maximum current. By selecting low inductance switches, voltage pulses as short as 30-50-ns FWHM can be directly achieved.Comment: 3 pages, 4 figures. This paper is submitted for the 20th Linear Accelerator Conference LINAC2000, Monterey, C

Evidence for 2k_F Electron-Electron Scattering Processes in Coulomb Drag

Measurements and calculations of Coulomb drag between two low density, closely spaced, two-dimensional electron systems are reported. The experimentally measured drag exceeds that calculated in the random phase approximation by a significant, and density dependent, factor. Studies of the dependence of the measured drag on the difference in density between the two layers clearly demonstrate that previously ignored q=2k_F scattering processes can be very important to the drag at low densities and small layer separations.Comment: 5 pages, 5 figure

Thin-film GaAs photovoltaic solar energy cells Final report

Thin film gallium arsenide photovoltaic solar cell