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.
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.
Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light-matter interaction and pave the way for its application and observation in other systems.
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.
Abstract We study high-resolution atomic localization in a multilevel atomic system driven simultaneously by a Gaussian and a Laguerre–Gaussian (LG) beam. The coexistence of the two fields creates a hybrid coupling landscape in which the Gaussian beam supplies radial confinement, while the LG beam contributes an orbital angular momentum (OAM)-dependent azimuthal modulation. By solving the steady-state density-matrix equations, we show that the resulting localization patterns contain mixed spatial harmonics whose structure is set by the topological charge, beam waist, and probe detuning. The OAM index determines the angular symmetry of the localized absorption features, whereas the beam waist controls their radial extent. Probe detuning provides an additional tuning mechanism that alters the contrast and geometry of the localization regions. These results highlight how structured light fields can be used to engineer controllable spatial localization in atomic media, with relevance to precision metrology, spatially resolved quantum control, and structured-light sensing.
Structured light, when strongly focused, generates highly confined vectorial electromagnetic field distributions which may feature a polarization component along the optical axis. Manipulating and detecting such 3D light fields is challenging, as conventional optical elements and detectors do not interact with the axial polarization component. Vector light can, however, be mapped onto atomic polarizations, making electric dipole transitions an ideal candidate to sense such 3D light configurations. Working in the hyperfine Paschen-Back regime, where the electric dipole transitions are spectrally resolved, we demonstrate direct evidence of the axial polarization component of strongly focused radial light. We investigate the influence of various input polarization states, including radial, azimuthal, and higher-order optical vortices, on atomic absorption profiles. Our results confirm a clear mapping between the 3D vector light and the atomic transition strength. This work provides new insights into vectorial light-matter interaction, and opens avenues for novel quantum sensing applications.
Structured light, when strongly focused, generates highly confined vectorial electromagnetic field distributions, which may feature a polarization component along the optical axis. Manipulating and detecting such 3D light fields is challenging, as conventional optical elements and detectors do not interact with the axial polarization component. Vector light can, however, be mapped onto atomic polarizations, making electric dipole transitions an ideal candidate to sense such 3D light configurations. Working in the hyperfine Paschen–Back regime, where the electric dipole transitions are spectrally resolved, we demonstrate direct evidence of the axial polarization component of strongly focused radial light. We investigate the influence of various input polarization states, including radial, azimuthal, and higher-order optical vortices, on atomic absorption profiles. Our results confirm a clear mapping between the 3D vector light and the atomic transition strength. This work provides insights into vectorial light–matter interaction and opens avenues for quantum sensing applications.