Download Abstract Rydberg atoms are promising candidates for quantum

Abstract
Rydberg atoms are promising candidates for quantum computing/simulations
due to its many useful properties such as long range interactions and
longevity. Magnetic trapping of Rydberg atoms in low angular momentum
states is treated, with a focus on Rubidium-87 atoms in a Ioffe-Pritchard
trap.
An introduction to Rydberg atoms is given by presenting the relevant Hamiltonian and its solutions as well as experimental data of the
Rubidium-87 atom.
The Hamiltonian of neutral groundstate atoms in a Ioffe-Pritchard
yields a simple potential for the atom that depends on the norm of the
magnetic field and some angular momentum quantum numbers. The Rydberg atom interacting with a magnetic field is studied by constructing
a two particle Hamiltonian which involves the minimal coupling scheme
and a model potential. After a change of coordinates and other steps
a final Hamiltonian emerges, which is valid for any Rydberg atom in a
static magnetic field and depends on two types of operators, electronic
and nuclear. This Hamiltonian contains the Rydberg Hamiltonian and a
myriad of perturbation terms.
To solve this Hamiltonian, the magnetic field must be inserted and is
only useful if it consist of polynomials of position operators. This can be
achieved by a Taylor expansion of the magnetic field which in this work is
up to second order. By invoking the Maxwell equations, a useful expression of the magnetic field is derived which yields the relevant magnetic
parameters. This theory is applied to the two types of magnetic traps
that are created in the laboratory, the Z-wire trap and the microtraps.
The specific values of the magnetic fields are derived by simulating these
traps.
Using a harmonic approximation of the groundstate atom, the derived
magnetic parameters and the nonzero temperature in the laboratory, relevant scales involving trapping can be derived.
With these ingredients, the two-particle Hamiltonian can be studied
further. First the Hamiltonian is expressed using the magnetic parameters and is partially solved by applying the Born-Oppenheimer approximation, where the outer electron instantaneously to the position of the
core. Within this approximation, the electronic operators are integrated
out by using degenerate perturbation theory, yielding potential energy
surfaces, PES, for the nucleus that depend on the electronic state.
Although the above method is partially based on previous literature.
A comparison shows that this work uses a different and more complete
approach.
The PES’s are compared to the that of the groundstate approach and
the difference is profound, justifying the more complex two particle approach for Rydberg atoms. It is found that the difference is mainly caused
by two factors, larger perturbation terms due to Rydberg excitation and
fine structure mixing, both grow larger with increasing n.
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