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Journal of Physics B Atomic Molecular and Optical Physics

Stark-induced anapole magnetic fields inn= 2 hydrogen

Robert R. Lewis, A. Góngora-T

Published Aug 28, 1998• 3 citations
Publisher

Abstract

This paper presents results for the anapole magnetic field moment due to the mixing of states with opposite parity in the n = 2 hydrogen atom in an external constant electric field. The evaluation of the current densities of the four n = 2 states is carried out to first order in the field strength. These current densities and their associated magnetic fields are expanded in multipoles, including both the ordinary poloidal and the toroidal fields. The dominant contribution to the toroidal dipole (anapole) magnetic field comes from the strong mixing of the degenerate 2S, 2P states within the n = 2 shell. A brief discussion is also presented of the electronic scattering from the anapole field of a Rydberg atom. The experimental conditions under which the atomic anapole field could be detected are critically considered, in particular, in terms of the quasi-resonant dependence of the anapole field on the applied electric field.

DOI
10.1088/0953-4075/31/16/010

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This paper presents results for the anapole magnetic field moment due to the mixing of states with opposite parity in the n = 2 hydrogen atom in an external constant electric field. The evaluation of the current densities of the four n = 2 states is carried out to first order in the field strength. These current densities and their associated magnetic fields are expanded in multipoles, including both the ordinary poloidal and the toroidal fields. The dominant contribution to the toroidal dipole (anapole) magnetic field comes from the strong mixing of the degenerate 2S, 2P states within the n = 2 shell. A brief discussion is also presented of the electronic scattering from the anapole field of a Rydberg atom. The experimental conditions under which the atomic anapole field could be detected are critically considered, in particular, in terms of the quasi-resonant dependence of the anapole field on the applied electric field.
A determination of all the state multipoles of the n=2 excited state of atomic hydrogen has been made. The kinematical conditions were a crossed electron-atom-beam geometry in which the incident electron energy was 350 eV and the scattering angle 3'. The experimental technique measures the scattered 10.2 eV energy loss electrons in coincidence with the 10.2 eV photons from either the 2P state or the delayed Stark-quenched 2S-state decay. An external electrostatic field mixes the S and P states, permitting the observation of their coherence by measuring the linear and circular photon polarisations, while in-plane angular correlations for a zero electric field determine the P-state multipoles. The state multipoles were deduced from a least-squares fit of the measured data to the quantum mechanical expressions determined for a model of an S-P (m j =1/2) superposition excited state with averages over the singlet and triplet spin states.
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.
In addition to electric and magnetic multipoles, the expansion of current density also yields toroidal terms, a lesser-known family of multipoles. A recent proposal, I. Kuprov et al.\textit{et al.}et al., Science Adv. 8 abq6751 (2022), explores the possibility of a direct observation of optical toroidal transitions in hydrogen and alkali atoms in the presence of a large magnetic field that decouples the spin and the angular momentum of the electron. However, the difficulty of observing these transitions against the nearby electric dipole (E1) transitions were underestimated because of extra admixture coming from diamagnetic coupling. Here, we revisit the toroidal coupling in atoms, taking diamagnetic contribution into account, and discuss the technical challenges of observing toroidal coupling in atomic physics. We show that toroidal transition should be searched in transitions with low principal quantum numbers. The remaining strong electric-dipole contribution could be removed using an appropriate differential measurement.
This paper reports on the evidence for large permanent electric-dipole moments of Rydberg atoms in crossed electric and magnetic fields. It was found that the dipole moments have a large value if the scaled electric-field strength \ensuremath{\epsilon}=${\mathit{EB}}^{\mathrm{\ensuremath{-}}4/3}$ has the value \ensuremath{\epsilon}\ensuremath{\approxeq}0.75 (with electric- and magnetic-field strengths E and B in atomic units). The experimental technique employed to determine the atomic dipole moment was to add a slight inhomogeneity to the electric field and to measure the deflection of the atoms, this deflection being proportional to the field inhomogeneity and the atomic dipole moment. In order to discuss the experimental results, different theoretical approaches to the E\ifmmode\times\else\texttimes\fi{}B problem are reviewed. The occurrence of Rydberg atoms with large dipole moments can be explained as being caused by a distinct type of classical orbit.
The results obtained by Pauli, in his 1926 article on the hydrogen atom, made essential use of the dynamical so(4) symmetry of the bound states. Pauli used this symmetry to compute the perturbed energy levels of an hydrogen atom in a uniform electric field (Stark effect) and in uniform electric and magnetic fields. Although the experimental check of the single Stark effect on the hydrogen atom has been studied experimentally, Pauli\'s results in mixed fields have been studied only for Rydberg states of rubidium atoms in crossedfields and lithium atoms in parallel fields.