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arXiv:1702.05969 · Journal of Physics B Atomic Molecular and Optical Physics

Interaction of a Laguerre–Gaussian beam with trapped Rydberg atoms

Koushik Mukherjee, Sonjoy Majumder, Pradip Kumar Mondal, Bimalendu Deb

Published Oct 4, 2017• 14 citations
arXivHTMLPDF

Abstract

Abstract Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.

DOI
10.1088/1361-6455/aa90d3

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Abstract Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.
We derive the interaction Hamiltonian between a diatomic molecule and a Laguerre-Gaussian beam under the assumption of a small spread of the center of mass wave function of the molecule in comparison with the beam waist. Considering the dynamical variables of the center of mass, vibrational, rotational, and electronic motion, we show that, within the electronic dipole approximation, the orbital angular momentum of the field couples with the rotational and electronic motion. The changes in the transition probabilities and selection rules induced by the field orbital angular momentum and the applicability of the derived interaction mechanisms for polyatomic molecules are discussed.
The exchange of orbital angular momentum between a Laguerre-Gaussian beam of light and the center-of-mass motion of an atom or molecule is well known. We show that the orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to the recoil limit, then an exchange of angular momentum between the quantized center-of-mass motion and the internal motion is possible during the interaction of cold atoms or molecules with the Laguerre-Gaussian beam. The orientation of the exchanged angular momentum is determined by the sign of the winding number of the Laguerre-Gaussian beam. We present selective results of numerical calculations for the quadrupole transition rates in the interaction of the Laguerre-Gaussian beam with an atomic Bose-Einstein condensate to illustrate the underlying mechanism of light orbital angular momentum transfer. We discuss how the alignment of diatomic molecules will facilitate exploration of the effects of light orbital angular momentum on the electronic motion of molecules.
Abstract We consider the excitation of Rydberg states through photons carrying an intrinsic orbital angular momentum degree of freedom. Laguerre–Gauss modes, with a helical wave-front structure, correspond to such a set of laser beams, which carry units of orbital angular momentum in their propagation direction, with ℓ 0 the winding number. We demonstrate that, in a proper geometry setting, this orbital angular momentum can be transferred to the internal degrees of freedom of the atoms, thus violating the standard dipole selection rules. Higher orbital angular momentum states become accessible through a single photon excitation process. We investigate how the spacial structure of the Laguerre–Gauss beam affects the radial coupling strength, assuming the simplest case of hydrogen-like wavefunctions. Finally we discuss a generalization of the angular momentum coupling, in order to include the effects of the fine and hyperfine splitting, in the context of the Wigner–Eckart theorem.
We derive the interaction Hamiltonian of a Laguerre–Gaussian beam with a simple atomic system, under the assumption of a small spread of the centre of mass wavefunction in comparison with the waist of the Laguerre–Gaussian beam and taking into account the centre of mass motion of the atomic system. Using the properties of regular spherical harmonics the internal and centre of mass dynamical variables are separated without making any multipolar expansion. The features of angular momentum exchange process assisted by Laguerre–Gaussian beams and the influence of their winding number on the selection rules and transition probability of internal and centre of mass motion are discussed.
This article investigates the quadrupole excitation of a trapped atom exposed to the tightly focused Laguerre-Gaussian (LG) beams with parallel and antiparallel spin angular momentum (SAM) and orbital angular momentum (OAM) under nonparaxial conditions. The Rabi frequency profile of allowed quadrupole transition channels, modified by SAM and OAM interaction, in the focal plane is provided. In the case of antiparallel SAM and OAM, the excitation probability undergoes substantial modification due to the considerable contribution of longitudinal intensity variations in tightly focused condition. The findings offer insights into controlling localized atom transition, including OAM transfer, with potential applications in qudit-based technologies.
A theory is developed that leads to the description of the internal and gross motions of an atom interacting with an arbitrary light field. The general results are then applied to the case of a Laguerre-Gaussian (LG) mode, one of a class of modes of electromagnetic radiation that possess orbital angular momentum. A number of effects are predicted, notably, an azimuthal shift in the atomic resonance, a modified radiation pressure force, and an associated torque on the atom. It is pointed out that the effects originate in the processes of the transfer of linear and orbital angular momentum from the field to the atomic gross motion. The strengths of the effects are assessed in relation to the normal axial Doppler shift and the linear light pressure force. The motion of atoms and ions subject to the LG pressure force is studied by solving the classical equation of motion. Trajectories clearly exhibiting the effects of orbital angular momentum are displayed for a free atom and for an ion in a two-dimensional trap and in a Paul trap.