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arXiv:physics/0402109 · Physical Review A

Electronic structure of atoms in magnetic quadrupole traps

Igor Lesanovsky, Jörg Schmiedmayer, Peter Schmelcher

Published May 12, 2004• 14 citations
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Abstract

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin spatial as well as generalized time-reversal symmetries are established and shown to lead to a twofold degeneracy of the electronic states in the presence of the field. Low lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and, in particular, the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.

DOI
10.1103/physreva.69.053405

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We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin spatial as well as generalized time-reversal symmetries are established and shown to lead to a twofold degeneracy of the electronic states in the presence of the field. Low lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and, in particular, the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.
We investigate the electronic structure and properties of Rydberg atoms exposed to a magnetic quadrupole field. It is shown that the spatial as well as generalized time-reversal symmetries lead to a two-fold degeneracy of the electronic states in the presence of the external field. A delicate interplay between the Coulomb and magnetic interactions in the inhomogeneous field leads to an unusual weak field splitting of the energy levels as well as complex spatial patterns of the corresponding spin polarization density of individual Rydberg states. Remarkably, the magnetic quadrupole field induces a permanent electric-dipole moment of the atom.
We study electronically excited atoms exposed to a magnetic quadrupole field. In order to describe the electron dynamics, a one-body approach is employed. Due to the inhomogeneity of the field, the spatial and spin degrees of freedom become coupled in a unique way. The underlying unitary and anti-unitary symmetries are discussed in detail leading to remarkable features such as a two-fold degeneracy of any energy level. We analyse the energy level structure throughout a wide range of field gradients. An investigation of the electronic spin properties is performed by studying the spatially dependent spin-polarization which exhibits a rich nodal structure. We compute wavelengths and strengths for electromagnetic transitions and provide the selection rules. A discussion of the so-called ellipsoidal states which exhibit unique properties such as large mean orbital angular momenta and spatial compactness is provided. The property of magnetic field-induced permanent electric dipole moments is analysed in detail. Wherever reasonable, the results obtained for the quadrupole field are compared to the homogeneous field case.
We investigate electronically excited atoms in a magnetic guide. It turns out that the Hamiltonian describing this system possesses a wealth of both unitary as well as antiunitary symmetries that constitute an uncommon extensive symmetry group. One consequence is the twofold degeneracy of any energy level. The spectral properties are investigated for a wide range of field gradients and the spatial distributions of the spin polarization are analyzed. Wavelengths, oscillator strengths, and selection rules are provided for the corresponding electromagnetic transitions. The effects due to an additional homogeneous bias field constituting a Ioffe-Pritchard trap are explored equally.
In this work we present an investigation on the quantum dynamics of ultracold electronically excited atoms exposed to an external magnetic quadrupole field. We present a general Hamiltonian which describes the quantum dynamics of an atom in an arbitrary linear magnetic field. This makes our approach applicable to a wide range of atoms and magnetic field configurations. The system is solved by incorporating an adiabatic separation of the electronic and center-of-mass dynamics. We provide the adiabatic energy surfaces and discuss under which conditions trapped center-of-mass states can be achieved. We present energies and wave functions of the corresponding quantum states. By analyzing the properties of the combined center-of-mass and electronic quantum states we demonstrate that the extension of the electronic wave function can exceed that of the center-of-mass motion. Therefore such atoms cannot be considered as being pointlike. A discussion of electromagnetic transitions is also provided.
In this thesis I examine high-magnetic-field Rydberg spectra, with the goal of discerning the viability of using such states as an interaction mechanism for quantum computation processes. In the presence of a strong magnetic field of B0 = 2.6 T, high-lying states of E ~ -55 cm(-1) are non-degenerate and show a wide range of magnetic dipole moments. Near-degenerate pairs of states of the same mJ manifold but of different axial parity Pi_z will strongly interact in the presence of an applied weak parallel electric field F, generating a pair of highly polar states. I show experimental results that, in agreement with theoretical work presented here, illustrate the presence of strong permanent dipole moments p ~ 1500 ea0 under these conditions. Such Rydberg states can also be tuned into resonance through careful control of the magnetic field, and are suitable for developing quantum phase gates and performing Rydberg-Rydberg interaction experiments. In order to perform such high-field Rydberg excitation experiments, a stable, dense and well-controlled cold atom cloud is needed within a high-magnetic-field environment. Toward this end, I present a full characterization of the utilized high-field trapping apparatus, including measurements of the trapped atom sample size, shape, and temperature. Analysis of the loss rate from the high-magnetic-field atom trap, both as a function of the applied magnetic field B0 and transverse confinement are presented. Experimental results for the high-field confinement of 85Rb are presented, as well as the first demonstration of a high-field 87Rb trap. Current trap limitations and possible improvements to the trapping apparatus are discussed. Other applications of the high-magnetic-field trap, such as the investigation of ultracold two-component plasmas and three-body recombination experiments, are also presented.
We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schrödinger equation is solved by an adiabatic separation focusing on a fixed n -manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusp-like behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.