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Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap

Bernd Hezel

Published Jan 1, 2010• 0 citations
Publisher

Abstract

Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap — Subject of this thesis is a theoretical investigation of the quantum properties of highly excited atoms in an inhomogeneous magnetic field configuration. It is demonstrated how the large size of the Rydberg atoms alters the coupling to strong magnetic gradients. We find that Rydberg atoms can be tightly trapped in long-lived electronic states. This confinement permits the creation of a one-dimensional Rydberg gas stabilized against auto-ionization by a dipolar repulsion between the atoms, which is generated imposing a homogeneous electric field. This strongly anisotropic interaction is also responsible for a well controllable equilibrium configuration of two Rydberg atoms in the trap whose distance can be changed by tuning the electric field.

DOI
10.11588/heidok.00010919

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•Jan 1, 2013•0 citations
Interaction-induced stabilization of ultracold Rydberg atoms in a Ioffe-Pritchard trap — Subject of this thesis is a theoretical investigation of the quantum properties of highly excited atoms in an inhomogeneous magnetic field configuration. It is demonstrated how the large size of the Rydberg atoms alters the coupling to strong magnetic gradients. We find that Rydberg atoms can be tightly trapped in long-lived electronic states. This confinement permits the creation of a one-dimensional Rydberg gas stabilized against auto-ionization by a dipolar repulsion between the atoms, which is generated imposing a homogeneous electric field. This strongly anisotropic interaction is also responsible for a well controllable equilibrium configuration of two Rydberg atoms in the trap whose distance can be changed by tuning the electric field.
We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold Rydberg gas.
We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the required linear density of Rydberg atoms.
We discuss a candidate solution for the controlled trapping and manipulation of two individual Rydberg atoms by means of a magnetic Ioffe-Pritchard trap that is superimposed by a constant electric field. In such a trap Rydberg atoms experience a permanent electric dipole moment that can be of the order of several hundred debye. The interplay of electric dipolar repulsion and three-dimensional magnetic confinement leads to a well controllable equilibrium configuration with tunable trap frequency and atomic distance. We thoroughly investigate the trapping potentials and analyze the interaction-induced stabilization of two such trapped Rydberg atoms. Possible limitations and collapse scenarios are discussed.
We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived, and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schrödinger equation of the system within a given n manifold and show that for a sufficiently large Ioffe field strength the 2n;{2}-dimensional system of coupled Schrödinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center of mass and electronic states is undertaken. In particular, we discuss the situation of tight center of mass confinement outlining the procedure to generate a low-dimensional ultracold Rydberg gas.
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in the presence of external inhomogeneous magnetic fields. We discuss the behavior of ground state atoms inside typical magnetic field configurations. Such atoms can be approximately treated as neutral point-like particles which carry a certain spin. In particular we analyze the resonance spectrum and the density of states of both fermionic and bosonic atoms. We point out the existence of so-called quasi-bound states whose wave functions can be approximately calculated analytically. Moreover, we focus on studying quantum mechanical states of ultracold but electronically highly excited atoms - so-called Rydberg atoms - inside magnetic traps. In a first step we explore their internal dynamics by employing a fixed-nucleus approximation. The latter assumes the atomic nucleus to be fixed in the magnetic field minimum. Within this framework we analyze spectral properties as well as properties of the electronic spin and calculate electromagnetic transitions. Finally we present an adiabatic approach which allows for a thorough description of the coupled center of mass and electronic dynamics. We highlight ways to magnetically trap highly excited atoms and present novel quantum states in which the center of mass and the electronic wave function are equal in size. This finding shows that Rydberg atoms even in inhomogeneous fields with moderate gradients cannot be considered point-like.
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.