Structured light encompasses a vast variety of light fields. It has unique properties such as non-uniform transverse intensity and a polarization pattern across their beam cross-sections. In this contribution, we discuss the photoexcitation of a single ionic target system driven by different sets of structured light modes. Specifically, we provide a compilation of transition amplitudes for various structured light modes interacting with atomic systems based on the first-order perturbation theory. To illustrate this, we will choose an electric quadrupole transition (4sS1/22→3dD5/22) in the target Ca+ ion driven by a structured light field. For this particular interaction, we examine how the beam parameters affect the population of magnetic sub-levels in the atomic excited state.
Structured light encompasses a vast variety of light fields. It has unique properties such as non-uniform transverse intensity and a polarization pattern across their beam cross-sections. In this contribution, we discuss the photoexcitation of a single ionic target system driven by different sets of structured light modes. Specifically, we provide a compilation of transition amplitudes for various structured light modes interacting with atomic systems based on the first-order perturbation theory. To illustrate this, we will choose an electric quadrupole transition (4sS1/22→3dD5/22) in the target Ca+ ion driven by a structured light field. For this particular interaction, we examine how the beam parameters affect the population of magnetic sub-levels in the atomic excited state.
We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S1/2 to D5/2 transition using a 40Ca+ ion. Various applications and advantages are expected when using light carrying angular momentum: In quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.
ENGLISH ABSTRACT : Structured light has seen many applications in the fields of telecommunications, optical microscopy, and quantum information processing, however, few works exist that explore the interactions of structured light with atoms. In this thesis, we seek to explore these interactions further, both theoretically and experimentally. Of particular interest is the interaction between an atom and a Laguerre-Gauss beam of topological charge l = 1. Such a beam is easily constructed in a lab setting, and also carries an additional unit of orbital angular momentum that has been shown to couple with atomic transitions. Theoretically, we derive a framework upon which to describe atomic transitions due structured light. We find that tailoring light’s structure will have a direct influence on the strength of quadrupole transitions in atoms. A theoretical analysis of the effects of an atom situated in a magnetic field interacting with a Laguerre-Gauss beam of topological charge l = 1 was conducted. It was found that atoms placed in a region of zero intensity, such as the beam centre, can undergo quadrupole transitions – in contrast to dipole transitions that rely on the field intensity. We go on to show the differences between this beam and a gaussian beam, and find that the former can cause transitions between magnetic sub-levels that are typically considered forbidden in quadrupole spectroscopy under certain conditions. We explain this through the principle of conservation of angular momentum. Experimentally, we chose to use a potassium vapour cell as our medium, as the linewidth of its quadrupole transition was relatively large, and could be simply modelled as a three-level system to easily understand its dynamics. We performed an experiment where we indirectly measured a 4 2S1/2 → 3 2Dj quadrupole transition for j = 3/2, 5/2, induced by a custom-built external cavity diode laser operating at ∼ 464.3 nm. The 4 2S1/2 → 3 2Dj transition was measured by monitoring the fluorescence due to a dipole decay 4 2Pj 0 → 4 2S1/2 during the decay cascade from 3 2Dj → 4 2Pj 0 → 4 2S1/2 , where j 0 = 1/2, 3/2. We then used our theoretical framework to fit the sum of two gaussian peaks to our measured fluorescence spectrum, and find an excellent agreement with our data.
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.
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.
In this paper we analyze the novel quantum properties of atomic photo-excitations generated by Orbital Angular Momentum (OAM) photons. It was previously predicted for Bessel beams (BB), that transitionsin atomic systems driven by twisted laser beams obey a modified set of position-dependent angular-momentum selection rules. It was also shown, that in the case of perfect alignment of the atom on the beam axis, total angular momentum of the photon must be fully transferred to the internal degrees of freedom of the target, which causes dramatic enhancement of higher-multipole processes. As a result, weak atomic transitions, which are hardly observable in interactions with simple states of light, become accessible with OAM photons. In the current paper, we extend the earlier developed theory to describe atomic photoexcitations by Bessel-Gauss (BG) and Laguerre-Gauss (LG) modes. It allowed us to infer the information about the phase structure of the beam, such as mode content and topological charge. The formalism exhibits a high level of sensitivity to the polarization content of the laser beam, which is on the order of 0.005% of the polarization admixture. The theoretical predictions are confirmed experimentally for photo-excitation of Ca40+ ions, trapped in a micro-structured, segmented Paul trap. The full set of quadrupole transitions from the S-state were generated by 729nm OAM laser beam shaped with a holographic phase-plate with a fork-dislocation. The experiment was conducted by Ferdinand Schmidt-Kaler's group at the University of Mainz.
Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite-Gaussian, Laguerre-Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing. We provide open code to reproduce our results or to evaluate interaction matrix elements for different transition types, beam structures and interaction geometries.