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arXiv:2310.10197 · Physical Review A

Atomic photoexcitation as a tool for probing purity of twisted light modes

R. P. Schmidt, S. Ramakrishna, A. A. Peshkov, Nils Huntemann, E. Peik, S. Fritzsche, A. Surzhykov

Published Mar 4, 2024• 7 citations
arXivHTMLPDF

Abstract

The twisted light modes used in modern atomic physics experiments can be contaminated by small admixtures of plane-wave radiation. Although these admixtures hardly reveal themselves in the beam-intensity profile, they may seriously affect the outcome of high-precision spectroscopy measurements. In the present study we propose a method for diagnosing such a plane-wave contamination which is based on the analysis of the magnetic sublevel population of atoms or ions interacting with the ``twisted $+$ plane-wave'' radiation. In order to theoretically investigate the sublevel populations, we solve the Liouville--von Neumann equation for the time evolution of the atomic density matrix. The proposed method is illustrated for the electric dipole $5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\text{\ensuremath{-}}5p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}$ transition in Rb induced by (linearly, radially, or azimuthally polarized) vortex light with just a small contamination. We find that even tiny admixtures of plane-wave radiation can lead to remarkable variations in the populations of the ground-state magnetic sublevels. This opens up new opportunities for diagnostics of twisted light in atomic spectroscopy experiments.

DOI
10.1103/physreva.109.033103

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The twisted light modes used in modern atomic physics experiments can be contaminated by small admixtures of plane-wave radiation. Although these admixtures hardly reveal themselves in the beam-intensity profile, they may seriously affect the outcome of high-precision spectroscopy measurements. In the present study we propose a method for diagnosing such a plane-wave contamination which is based on the analysis of the magnetic sublevel population of atoms or ions interacting with the ``twisted +++ plane-wave'' radiation. In order to theoretically investigate the sublevel populations, we solve the Liouville--von Neumann equation for the time evolution of the atomic density matrix. The proposed method is illustrated for the electric dipole 5s2S1/2\ensuremath-5p2P3/25s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\text{\ensuremath{-}}5p\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2}5s2S1/2​\ensuremath-5p2P3/2​ transition in Rb induced by (linearly, radially, or azimuthally polarized) vortex light with just a small contamination. We find that even tiny admixtures of plane-wave radiation can lead to remarkable variations in the populations of the ground-state magnetic sublevels. This opens up new opportunities for diagnostics of twisted light in atomic spectroscopy experiments.
Electric and magnetic fields are inherently coupled in an electromagnetic wave. However, structured light beams enable their spatial separation. In particular, azimuthally polarized laser beams exhibit a localized magnetic field on-axis without the electric counterpart. A recent study by Martín-Domene [S. Martín-Domene , ] has shown that combining these beams enables the generation of locally isolated magnetic fields with a controllable direction and phase. In the present paper, we propose a method to probe and characterize such magnetic fields by studying their interaction with a single trapped atom. In order to theoretically investigate magnetic sublevel populations and their dependence on the relative orientation and phase—i.e., the —of the isolated magnetic field, we use a time-dependent density-matrix method based on the Liouville–von Neumann equation. As illustrative cases, we consider the 2 s 2 2 p 2 P 0 3 − 2 s 2 2 p 2 P 1 3 , 1 s 2 2 s 2 S 0 1 − 1 s 2 2 s 2 p P 2 3 , and 2 s 2 2 p P 1 / 2 2 − 2 s 2 2 p P 3 / 2 2 transitions in Ca 14 + 40 , Be 10 , and Ar 13 + 38 , respectively. Our results indicate that monitoring atomic populations serves as an effective tool for probing isolated vector magnetic fields, which opens avenues for studying laser-induced processes in atomic systems where electric-field suppression is critical.
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.
Recent studies have highlighted the frequent applications of structured light modes in optically pumped atomic magnetometers. In this work, we theoretically explore how a Poincaré beam probes an optically polarized atomic medium. Specifically, we consider atoms polarized by a plane wave with linear polarization, immersed in a constant external magnetic field. We analyze how the polarization of the pump and probe light fields, along with the external magnetic field, impact the absorption profile. To this end, we employ a density-matrix approach based on the Liouville–von Neumann equation. Our results reveal that the absorption profile exhibits an asymmetric pattern that depends on the magnetic-field strength and the mutual orientation of the pump and probe light propagation directions relative to the quantization axis. For illustration, we assume the incoming radiation drives an electric dipole transition, 5 s 2 S 1 / 2 ( F = 1 ) → 5 p 2 P 3 / 2 ( F = 0 ), in rubidium atoms subjected to a magnetic field. These findings may aid in designing future experiments on optically pumped atomic magnetometers utilizing structured light modes.
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.
We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.
A form of quantum control is proposed by applying twisted light, also known as optical vortex beams, to drive ultranarrow atomic transitions in neutral Ca, Mg, Yb, Sr, Hg, and Cd bosonic isotopes. This innovative all-optical spectroscopic method introduces spatially tailored electric and magnetic fields to fully rewrite atomic selection rules, reducing simultaneously probe-induced frequency shifts and additional action of external ac and dc field distortions. A twisted-light focused probe beam produces strong longitudinal electric and magnetic fields along the laser propagation axis, which opens the $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{0}$ doubly forbidden clock transition with a high E1M1E1M1E1M1 two-photon excitation rate. This long-lived clock transition is thus immune to nonscalar electromagnetic perturbations. Zeeman components of the M2M2M2 magnetic quadrupole $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{2}$ transition considered for quantum computation and simulation are now selectively driven by transverse or longitudinal field gradients with vanishing electric fields. These field gradients are manipulated by the mutual action of orbital and spin angular momentum of the light beam and are used in presence of tunable vector and tensor polarizabilities. A combination of these two different twisted-light induced clock transitions within a single quantum system, at the same magic wavelength and in presence of a common thermal environment, significantly reduces systematic uncertainties. Furthermore, it generates an optical synthetic frequency which efficiently limits the blackbody radiation shift and its variations at room temperature. Engineering light-matter interaction by optical vortices merged with composite pulses will ultimately benefit experimental atomic and molecular platforms targeting an optimal coherent control of quantum states, reliant quantum simulation, novel approaches to atomic interferometry, and precision tests of fundamental theories in physics and high-accuracy optical metrology.