Doerte Blume

Monte Carlo hyperspherical description of helium cluster excited states

The J=0 many-body Schrodinger equation for 4HeN clusters with N=3–10 is solved numerically by combining Monte Carlo methods with the adiabatic hyperspherical approximation. We find ground state and excited state energies for these systems with an adiabatic separation scheme that reduces the problem to motion in a one-dimensional effective potential curve as a function of the hyperspherical radius R. We predict the number of J=0 bound states for these clusters, and also the He+HeN−1 elastic scattering lengths up to N=10. For N=5–10, these are the first such calculations reported.

Comparative study of He3, Ne3, and Ar3 using hyperspherical coordinates

We calculate the L=0 ground and excited state energies for the rare gas trimers He3, Ne3, and Ar3. An adiabatic representation is adopted to solve the nuclear Schrodinger equation, in which the Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.

Formation of Atomic Tritium Clusters and Bose-Einstein Condensates

We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m(F)>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870 G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.

Quantum corrections to the ground-state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities,

Vibrationally excited states and fragmentation geometries of NeN and ArN clusters, N=3–6, using hyperspherical coordinates

n(0)a^3 \le 2 \cdot 10^{-3}

Analytical coupled-channels treatment of two-body scattering in the presence of three-dimensional isotropic spin-orbit coupling

[n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.

Stability of inhomogeneous multicomponent Fermi gases

We calculate the ground state and a class of zero orbital angular momentum (L=0) vibrationally excited state energies for NeN and ArN clusters using an adiabatic hyperspherical representation to solve the nuclear Schrodinger equation. The Schrodinger equation in the hyperangular coordinates is solved for a sequence of fixed hyperradii by diffusion Monte Carlo techniques, which determines the lowest effective potential curve. We monitor structural properties such as the pair and angle distribution as a function of the hyperspherical radius. These structural studies allow us to identify configurational changes as the N atom cluster fragments into an (N−1)-atom cluster plus an atom. We also determine separately the ground state of the full 3N-dimensional nuclear Schrodinger equation for the ground state, and compare the resulting structural properties with those calculated in the adiabatic hyperspherical approximation.

Interaction-induced localization of an impurity in a trapped Bose-Einstein condensate

It is shown that the single-particle spin-orbit coupling terms, which---in the cold atom context---are associated with synthetic gauge fields, can significantly and non-trivially modify the phase accumulation at small interparticle distances even if the length scale

Occupation numbers of the harmonically trapped few-boson system

(k_{\text{so}})^{-1}

Lowest breathing mode of bosonic helium clusters

associated with the spin-orbit coupling term is significantly larger than the van der Waals length