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arXiv:2003.03360 · Physical Review A

Generalized excitation of atomic multipole transitions by twisted light modes

S. A.-L. Schulz, A. A. Peshkov, R. A. Müller, R. Lange, Nils Huntemann, Chr. Tamm, E. Peik, A. Surzhykov

Published Jul 21, 2020• 35 citations
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Abstract

A theoretical study is performed for the excitation of a single atom localized in the center of twisted light modes. Here we present the explicit dependence of excitation rates on critical parameters, such as the polarization of light, its orbital angular momentum projection, and the orientation of its propagation axis with respect to the atomic quantization axis. The effect of a spatial spread of the atom is also considered in detail. The expressions for transition rates obtained in this work can be used for any atom of arbitrary electronic configuration. For definiteness we apply them to the specific case of the $^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}^{2}F_{7/2}(F=3,M=0)$ electric octupole (E3) transition in ${^{171}\mathrm{Yb}}^{+}$ ion. Our analytical and numerical results are suitable for the analysis and planning of future experiments on the excitation of electric-dipole-forbidden transitions by twisted light modes in optical atomic clocks.

DOI
10.1103/physreva.102.012812

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A theoretical study is performed for the excitation of a single atom localized in the center of twisted light modes. Here we present the explicit dependence of excitation rates on critical parameters, such as the polarization of light, its orbital angular momentum projection, and the orientation of its propagation axis with respect to the atomic quantization axis. The effect of a spatial spread of the atom is also considered in detail. The expressions for transition rates obtained in this work can be used for any atom of arbitrary electronic configuration. For definiteness we apply them to the specific case of the 2S1/2(F=0)\ensuremath→2F7/2(F=3,M=0)^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}^{2}F_{7/2}(F=3,M=0)2S1/2​(F=0)\ensuremath→2F7/2​(F=3,M=0) electric octupole (E3) transition in 171Yb+{^{171}\mathrm{Yb}}^{+}171Yb+ ion. Our analytical and numerical results are suitable for the analysis and planning of future experiments on the excitation of electric-dipole-forbidden transitions by twisted light modes in optical atomic clocks.
We study the coherent excitation of the ^{2}S_{1/2}→^{2}F_{7/2} electric octupole (E3) transition by twisted light modes with a single ^{171}Yb^{+} ion in the dark center of a vortex beam. The intensity distribution of the beam is mapped as a function of the ion's position by measuring the light shift on an auxiliary electric quadrupole transition. In the center of the vortex beam, we observe excitation of the E3 transition with a fivefold reduced light shift in comparison to excitation by plane wave radiation for the same Rabi frequency. We measure the excitation probabilities for Laguerre-Gaussian twisted light modes of first and second order for different polarization patterns at various orientations of the ion quantization axis with respect to the beam propagation vector. We compare the experimental results with theoretical predictions and find good qualitative agreement.
Twisted light has received a lot of attention in recent years. And there are justified reasons for this. The properties of twisted light are unusual and differ fundamentally from the plane-wave properties. The phase fronts of these light beams have a helical structure, giving them the name twisted. This helical phase structure originates from the well-defined orbital angular momentum (OAM) that they carry along their propagation direction and in addition to the spin angular momentum (SAM). Moreover, they have a characteristic intensity profile, which consists of concentric rings with a central minimum, and a phase singularity in the beam center. This thesis is based on two main parts, each dealing with a different aspect of twisted light. These investigations are carried out using Bessel beams, one type of twisted light. Twisted light beams are cylindrically symmetrical. Therefore, they are defined on the basis of circularly polarized light. This fact leads to the first question: Is it possible to generate twisted light in other polarization states? In this work, we derive how this can be achieved by using the superposition principle and how this can be used to construct linearly, radially, or azimuthally polarized Bessel beams. The focus in the second part is on excitations of atoms by twisted Bessel beams. In particular, we analyze how the use of twisted light can modify individual atomic multipole transitions. The obtained results show that for an efficient modification a precise localization of the target atom is required. In the last chapter, both aspects are combined. We analyze transitions between magnetic hyperfine states in a single trapped atom (or ion), which is exposed to an additional external magnetic field. The presented calculations for these multipole excitations are based on a formalism that accounts for the alignment of the applied external magnetic field with respect to the light propagation direction, and additionally different polarization states of the radiation field are considered. The obtained results indicate that twisted light could be of particular interest for precision experiments. One possible application is the use in single-ion clocks. The work shows that high multipole orders of the vortex beams allow excitations in the intensity minimum in the center of these beams without causing large disturbances, and thus may enable a significant reduction of the light shift in atomic transitions.
We present a theoretical study of nondipole excitation of a single trapped atom by twisted light. Special emphasis is placed on effects that arise from the interplay between internal (electronic) and vibrational (center-of-mass) degrees of freedom of an atom. In order to provide a fully quantum mechanical understanding of the excitation, we used the density-matrix approach based on the Liouville--von Neumann equation. The developed theory has been applied to the particular case of the $4s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}3d\phantom{\rule{0.16em}{0ex}}^{2}D_{5/2}$ electric quadrupole (E2E2E2) transition in a 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion induced by Laguerre-Gaussian modes. It was found that the Rabi oscillations can show unconventional anharmonic behavior that is attributed to the strong coupling between vibrational levels of the trap. This effect is accompanied by the transfer of angular momentum to the center-of-mass motion and becomes most pronounced when the Rabi frequency is comparable to the trapping frequency.
Synopsis In this work, we present how the AC-Stark shift can be suppressed by using twisted light beams for photoexcitations. Twisted light beams carry a non-zero projection of orbital angular momentum (OAM) onto their propagation direction, have a helical phase front and an intensity minimum in the beam center. Atoms located in this minimum experience a reduced AC-Stark shift and, therefore, twisted beams may be considered as valuable tool to drive atomic clock transitions. In this contribution, particular emphasis is paid to the electric-octupole (E3) transition 2 S1/2 → 2 F7/2 in the 171 Yb+ ion.
Theoretical work has already established the existence of a light-induced torque acting on the centre of mass of an atom, ion or molecule immersed in twisted light, where the transition frequency is suitably detuned from that of the twisted light beam. The twisted beam carries l units of orbital angular momentum per photon, and the steady-state saturation form of the torque is also determined by the width of the upper state in the atomic transition. It has been shown that, to leading order, the transfer of orbital angular momentum can only occur between the twisted light and the centre of mass motion. We argue here that, for small linewidth, the full time-dependence of the torque is needed to account correctly for the dynamics of atoms in a twisted light beam. We outline the theoretical framework needed to derive this full time-dependence, applying the theory to the motion in a twisted light beam of Eu3+ ions, which possess a particularly narrow linewidth state. For relatively large linewidth, the steady-state forces and torque are appropriate, but the processes of cooling and trapping require the application of several suitably oriented twisted beams. The description of atomic motion in multiple twisted beams demands the application of special coordinate transformations. We show how to construct the appropriate transformation matrices to represent a twisted light beam propagating in an arbitrary direction, and we proceed to investigate the cooling and trapping of Mg+ ions in sets of pairs of counter-propagating twisted beams in two-dimensional and three-dimensional molasses configurations.
Photoexcitation of trapped ions by Hermite–Gaussian (HG) modes from guided beam structures is proposed and investigated theoretically. In particular, simple analytical expressions for the matrix elements of induced atomic transitions are derived that depend both on the parameters of HG beams and on the geometry of an experiment. By using these general expressions, the (Formula presented.) electric octupole (E3) transition is investigated in an Yb+ ion, localized in the low–intensity center of the HG10 and HG01 beams. It is shown how the corresponding Rabi frequency can be enhanced by properly choosing the polarization of incident light and the orientation of an external magnetic field, which defines the quantization axis of a target ion. The calculations, performed for experimentally feasible beam parameters, indicate that the achieved Rabi frequencies can be comparable or even higher than those observed for the conventional Laguerre–Gaussian (LG) modes. Since HG-like modes can be relatively straightforwardly generated with high purity and stability from integrated photonics, these results suggest that they may form a novel tool for investigating highly-forbidden atomic transitions.