Cavity-enhanced photoionization of an ultracold rubidium beam for application in focused ion beams

A two-step photoionization strategy of an ultracold rubidium beam for application in a focused ion beam instrument is analyzed and implemented. In this strategy the atomic beam is partly selected with an aperture after which the transmitted atoms are ionized in the overlap of a tightly cylindrically focused excitation laser beam and an ionization laser beam whose power is enhanced in a build-up cavity. The advantage of this strategy, as compared to without the use of a build-up cavity, is that higher ionization degrees can be reached at higher currents. Optical Bloch equations including the photoionization process are used to calculate what ionization degree and ionization position distribution can be reached. Furthermore, the ionization strategy is tested on an ultracold beam of $^{85}$Rb atoms. The beam current is measured as a function of the excitation and ionization laser beam intensity and the selection aperture size. Although details are different, the global trends of the measurements agree well with the calculation. With a selection aperture diameter of 52 $\mu$m, a current of $\left(170\pm4\right)$ pA is measured, which according to calculations is 63% of the current equivalent of the transmitted atomic flux. Taking into account the ionization degree the ion beam peak reduced brightness is estimated at $1\times10^7$ A/(m$^2\,$sr$\,$eV).Comment: 13 pages, 9 figure

Direct magneto-optical compression of an effusive atomic beam for high-resolution focused ion beam application

An atomic rubidium beam formed in a 70 mm long two-dimensional magneto-optical trap (2D MOT), directly loaded from a collimated Knudsen source, is analyzed using laser-induced fluorescence. The longitudinal velocity distribution, the transverse temperature and the flux of the atomic beam are reported. The equivalent transverse reduced brightness of an ion beam with similar properties as the atomic beam is calculated because the beam is developed to be photoionized and applied in a focused ion beam. In a single two-dimensional magneto-optical trapping step an equivalent transverse reduced brightness of $(1.0\substack{+0.8-0.4})$ $\times 10^6$ A/(m$^2$ sr eV) was achieved with a beam flux equivalent to $(0.6\substack{+0.3-0.2})$ nA. The temperature of the beam is further reduced with an optical molasses after the 2D MOT. This increased the equivalent brightness to $(6\substack{+5-2})$$\times 10^6$ A/(m$^2$ sr eV). For currents below 10 pA, for which disorder-induced heating can be suppressed, this number is also a good estimate of the ion beam brightness that can be expected. Such an ion beam brightness would be a six times improvement over the liquid metal ion source and could improve the resolution in focused ion beam nanofabrication.Comment: 10 pages, 8 figures, 1 tabl

Optimization of Gutzwiller Wavefunctions in Quantum Monte Carlo

Gutzwiller functions are popular variational wavefunctions for correlated electrons in Hubbard models. Following the variational principle, we are interested in the Gutzwiller parameters that minimize e.g. the expectation value of the energy. Rewriting the expectation value as a rational function in the Gutzwiller parameters, we find a very efficient way for performing that minimization. The method can be used to optimize general Gutzwiller-type wavefunctions both, in variational and in fixed-node diffusion Monte Carlo.Comment: 9 pages RevTeX with 10 eps figure

Stripes and spin-incommensurabilities are favored by lattice anisotropies

Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions ($t_x \ne t_y$ and $J_x \ne J_y$). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are almost unaffected with respect to the isotropic case.Comment: accepted for publication on Physical Review Letters, one color figur

An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.Comment: 5 pages, 5 figures; to appear in Physical Review

Screening, Coulomb pseudopotential, and superconductivity in alkali-doped Fullerenes

We study the static screening in a Hubbard-like model using quantum Monte Carlo. We find that the random phase approximation is surprisingly accurate almost up to the Mott transition. We argue that in alkali-doped Fullerenes the Coulomb pseudopotential $\mu^\ast$ is not very much reduced by retardation effects. Therefore efficient screening is important in reducing $\mu^{\ast}$ sufficiently to allow for an electron-phonon driven superconductivity. In this way the Fullerides differ from the conventional picture, where retardation effects play a major role in reducing the electron-electron repulsion.Comment: 4 pages RevTeX with 2 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease

A recent technique, proposed to alleviate the ``sign problem disease'', is discussed in details. As well known the ground state of a given Hamiltonian $H$ can be obtained by applying the imaginary time propagator $e^{-H \tau}$ to a given trial state $\psi_T$ for large imaginary time $\tau$ and sampling statistically the propagated state $\psi_{\tau} = e^{-H \tau} \psi_T$. However the so called ``sign problem'' may appear in the simulation and such statistical propagation would be practically impossible without employing some approximation such as the well known ``fixed node'' approximation (FN). This method allows to improve the FN dynamic with a systematic correction scheme. This is possible by the simple requirement that, after a short imaginary time propagation via the FN dynamic, a number $p$ of correlation functions can be further constrained to be {\em exact} by small perturbation of the FN propagated state, which is free of the sign problem. By iterating this scheme the Monte Carlo average sign, which is almost zero when there is sign problem, remains stable and finite even for large $\tau$. The proposed algorithm is tested against the exact diagonalization results available on finite lattice. It is also shown in few test cases that the dependence of the results upon the few parameters entering the stochastic technique can be very easily controlled, unless for exceptional cases.Comment: 44 pages, RevTeX + 5 encaplulated postscript figure

Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model

We combine the Density Matrix Technique (DMRG) with Green Function Monte Carlo (GFMC) simulations. The DMRG is most successful in 1-dimensional systems and can only be extended to 2-dimensional systems for strips of limited width. GFMC is not restricted to low dimensions but is limited by the efficiency of the sampling. This limitation is crucial when the system exhibits a so-called sign problem, which on the other hand is not a particular obstacle for the DMRG. We show how to combine the virtues of both methods by using a DMRG wavefunction as guiding wave function for the GFMC. This requires a special representation of the DMRG wavefunction to make the simulations possible within reasonable computational time. As a test case we apply the method to the 2-dimensional frustrated Heisenberg antiferromagnet. By supplementing the branching in GFMC with Stochastic Reconfiguration (SR) we get a stable simulation with a small variance also in the region where the fluctuations due to minus sign problem are maximal. The sensitivity of the results to the choice of the guiding wavefunction is extensively investigated. We analyse the model as a function of the ratio of the next-nearest to nearest neighbor coupling strength. We observe in the frustrated regime a pattern of the spin correlations which is in-between dimerlike and plaquette type ordering, states that have recently been suggested. It is a state with strong dimerization in one direction and weaker dimerization in the perpendicular direction.Comment: slightly revised version with added reference

Helicity Modulus and Effective Hopping in the Two-Dimensional Hubbard Model Using Slave-Boson Methods

The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak- and strong ferromagnetism and antiferromagnetism, including all continuous and first-order transitions, is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about 3 along both the $t/U$ and density axes compared to the HFA. Using the spin-rotation invariant formulation of the slave-boson method the helicity modulus is computed and for half-filling is found to practically coincide with that found using variational Monte Carlo calculations using the Gutzwiller wave function. Off half-filling the results can be used to compare with Quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half-filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half-filling. (Submitted to: Journal of Physics: Condensed Matter)Comment: 27 pages, LaTeX2e, 7 figures available upon request, INLO-PUB-10/9