Analytical Expression for the RKKY Interaction in Doped Graphene

We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $J$ in electron or hole doped graphene for linear Dirac bands. The results agree very well with the numerical calculations for the full tight-binding band structure in the regime where the linear band structure is valid. The analytical result, expressed in terms of the Meijer G-function, consists of a product of two oscillatory terms, one coming from the interference between the two Dirac cones and the second coming from the finite size of the Fermi surface. For large distances, the Meijer G-function behaves as a sinusoidal term, leading to the result $J \sim R^{-2} k_F \sin (2 k_F R) {1 + \cos[(K-K').R]}$ for moments located on the same sublattice. The $R^{-2}$ dependence, which is the same for the standard two-dimensional electron gas, is universal irrespective of the sublattice location and the distance direction of the two moments except when $k_F =0$ (undoped case), where it reverts to the $R^{-3}$ dependence. These results correct several inconsistencies found in the literature.Comment: 5 pages, 5 figure

Operation of a Stark decelerator with optimum acceptance

With a Stark decelerator, beams of neutral polar molecules can be accelerated, guided at a constant velocity, or decelerated. The effectiveness of this process is determined by the 6D volume in phase space from which molecules are accepted by the Stark decelerator. Couplings between the longitudinal and transverse motion of the molecules in the decelerator can reduce this acceptance. These couplings are nearly absent when the decelerator operates such that only every third electric field stage is used for deceleration, while extra transverse focusing is provided by the intermediate stages. For many applications, the acceptance of a Stark decelerator in this so-called $s=3$ mode significantly exceeds that of a decelerator in the conventionally used ($s=1$) mode. This has been experimentally verified by passing a beam of OH radicals through a 2.6 meter long Stark decelerator. The experiments are in quantitative agreement with the results of trajectory calculations, and can qualitatively be explained with a simple model for the 6D acceptance. These results imply that the 6D acceptance of a Stark decelerator in the $s=3$ mode of operation approaches the optimum value, i.e. the value that is obtained when any couplings are neglected.Comment: 13 pages, 11 figure

Loading Stark-decelerated molecules into electrostatic quadrupole traps

Beams of neutral polar molecules in a low-field seeking quantum state can be slowed down using a Stark decelerator, and can subsequently be loaded and confined in electrostatic quadrupole traps. The efficiency of the trap loading process is determined by the ability to couple the decelerated packet of molecules into the trap without loss of molecules and without heating. We discuss the inherent difficulties to obtain ideal trap loading, and describe and compare different trap loading strategies. A new "split-endcap" quadrupole trap design is presented that enables improved trap loading efficiencies. This is experimentally verified by comparing the trapping of OH radicals using the conventional and the new quadrupole trap designs

Accurate effective pair potentials for polymer solutions

Dilute or semi-dilute solutions of non-intersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of ``soft'' particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by inverting the pair distribution function of the centers of mass of the original polymer chains, using integral equation techniques from the theory of simple fluids. The resulting effective pair potential is finite at all distances, has a range of the order of the radius of gyration, and turns out to be only moderately concentration-dependent. The dependence of the effective potential on polymer length is analyzed in an effort to extract the scaling limit. The effective potential is used to derive the osmotic equation of state, which is compared to simulation data for the full SAW segment model, and to the predictions of renormalization group calculations. A similar inversion procedure is used to derive an effective wall-polymer potential from the center of mass density profiles near the wall, obtained from simulations of the full polymer segment model. The resulting wall-polymer potential turns out to depend strongly on bulk polymer concentration when polymer-polymer correlations are taken into account, leading to a considerable enhancement of the effective repulsion with increasing concentration. The effective polymer-polymer and wall-polymer potentials are combined to calculate the depletion interaction induced by SAW polymers between two walls. The calculated depletion interaction agrees well with the ``exact'' results from much more computer-intensive direct simulation of the full polymer-segment model, and clearly illustrates the inadequacy -- in the semi-dilute regime -- of the standard Asakura-Oosawa approximation based on the assumption of non-interacting polymer coils.Comment: 18 pages, 24 figures, ReVTeX, submitted to J. Chem. Phy

Deceleration and electrostatic trapping of OH radicals

A pulsed beam of ground state OH radicals is slowed down using a Stark decelerator and is subsequently loaded into an electrostatic trap. Characterization of the molecular beam production, deceleration and trap loading process is performed via laser induced fluorescence detection inside the quadrupole trap. Depending on details of the trap loading sequence, typically $10^5$ OH ($X^2\Pi_{3/2}, J=3/2$) radicals are trapped at a density of around $10^7$ cm$^{-3}$ and at temperatures in the 50-500 mK range. The 1/e trap lifetime is around 1.0 second.Comment: 4 pages, 3 figure

Direct measurement of the radiative lifetime of vibrationally excited OH radicals

Neutral molecules, isolated in the gas-phase, can be prepared in a long-lived excited state and stored in a trap. The long observation time afforded by the trap can then be exploited to measure the radiative lifetime of this state by monitoring the temporal decay of the population in the trap. This method is demonstrated here and used to benchmark the Einstein $A$-coefficients in the Meinel system of OH. A pulsed beam of vibrationally excited OH radicals is Stark decelerated and loaded into an electrostatic quadrupole trap. The radiative lifetime of the upper $\Lambda$-doublet component of the $X ^2\Pi_{3/2}, v=1, J=3/2$ level is determined as $59.0 \pm 2.0$ ms, in good agreement with the calculated value of $57.7 \pm 1.0$ ms.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Multiple packets of neutral molecules revolving for over a mile

The level of control that one has over neutral molecules in beams dictates their possible applications. Here we experimentally demonstrate that state-selected, neutral molecules can be kept together in a few mm long packet for a distance of over one mile. This is accomplished in a circular arrangement of 40 straight electrostatic hexapoles through which the molecules propagate over 1000 times. Up to 19 packets of molecules have simultaneously been stored in this ring structure. This brings the realization of a molecular low-energy collider within reach