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arXiv:1909.03484 · Physical Review A

Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

Anal Bhowmik, Narendra Nath Dutta, Sonjoy Majumder

Published Dec 21, 2020• 6 citations
arXivHTMLPDF

Abstract

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular-momentum conservation of the beam. The theory is employed on $^{87}\mathrm{Sr}^{+}$ to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using the relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes a fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and orbital angular momentum of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ atoms.

DOI
10.1103/physreva.102.063116

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Magic wavelengths for trapping of Sr+^++ with focused optical vortex
A theory of dynamic polarizability for trapping relevant states of Sr+^++ is presented here when the ions interact with a focused optical vortex. The coupling between the orbital and spin angular momentum of the optical vortex varies with focusing angle of the beam and is studied in the calculation of the magic wavelengths for 5s1/2→4d3/2,5/25s_{{1}/{2}}\rightarrow 4d_{{3}/{2}, {5}/{2}}5s1/2​→4d3/2,5/2​ transitions of Sr+^++. The initial state of our interest here is 5s1/25s_{{1}/{2}}5s1/2​ with mJ=−1/2m_J = -1/2mJ​=−1/2 of which is different possible trapping state compare to our recent work on Sr+^++ [Phys. Rev. A \textbf{97}, 022511 (2018)]. We find variation in magic wavelengths and the corresponding polarizabilities with different combinations of orbital and spin angular momentum of the vortex beam. The variation is very significant when the wavelengths of the beam are in the infrared region of electromagnetic spectrum. The calculated magic wavelengths will help the experimentalists to trap the ion for performing the high precision spectroscopic measurements.
We investigate the propagation of an optical vector vortex weakly interacting with a coherently prepared atomic medium (phaseonium) in a three-level ΛΛΛ configuration. The vector beam consists of vortex pulse pairs with right- and left-circular polarizations, corresponding to opposite spin angular momentum (SAM), and carrying opposite orbital angular momentum (OAM) charges ±l\pm l±l. We show that during the propagation of the vortex pairs, analytically obtained in the linear regime, the medium inherits the topology of the vortex pair, mapping the OAM onto a spatially structured atomic coherence. This mapping produces 2∣l∣−2|l|-2∣l∣−fold azimuthal transparency structures that reshape the beam intensity from a ring into a petal-like pattern. The OAM-structured atomic coherence induces a corresponding optical anisotropy within the medium, which feeds back into the propagating vector beam, resulting in optical spin-orbit coupling manifested as SAM exchange, rotation, and evolution of polarization textures. Depending on the initial ground-state population of the phaseonium, the polarization state evolves between left-circular, linear, and right-circular polarizations.
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.
We investigate the propagation of optical vector vortices of slow light in a coherently prepared four-level tripod atomic system. The vector vortex consists of superposed pulse pairs with opposite circular polarizations and orbital angular momentum (OAM) charges ±l\pm l±l, weakly interacting with an atomic medium initially prepared in a coherent superposition of two ground states. A third unoccupied state is coupled to a stronger control laser without OAM, creating a phase-dependent configuration. In the linear regime, the vortex OAM is mapped onto the medium, producing symmetrical azimuthally structured absorption patterns, with losses significantly reduced by the control field. For small detunings, complementary spatially dependent amplification and absorption occur for the two circular polarization components. This OAM-structured coherence induces a dynamical anisotropy, affecting both the intensity and polarization of the slow-light vortex. Polarization states evolve periodically between left-circular, linear, and right-circular polarizations during propagation. Once the beam reaches a stationary regime, the ring-shaped intensity transforms into a petal-like structure, and the final polarization states stabilize according to the initial superposition. The rate of polarization transitions is tunable via the control field strength, demonstrating flexible control over slow-light vector vortex dynamics.
Two-photon polarizability of Ba+^++ ion: Control of spin-mixing process in an ultracold 137^{137}137Ba+^++--87^{87}87Rb mixture
Ionic clocks exhibit as the most promising candidates for the frequency standards. Recent investigations show the profound advantages of interrogating two laser beams with different frequencies in developing the frequency standards. Here we present a scheme of a two-photon mechanism to calculate the dynamic polarizabilities for the clock states, 62^22S12_{\frac{1}{2}}21​​ and 52^22D32,52_{\frac{3}{2}, \frac{5}{2}}23​,25​​, of Ba+^++ by employing relativistic coupled-cluster method. We illustrate the Stark-shift cancellation between these clock states at the two-photon magic wavelengths. These magic wavelengths can be essential inputs to achieve better accuracy in the ionic clock experiments. We also calculate the magic wavelengths under the single-photon interaction to serve as the reference and for a comparative study. The calculated single- and two-photon magic wavelengths lie in the optical region and thus are significant for future state-of-the-art experiments. Moreover, as an application of the two-photon polarizabilities, we investigate the impact of these polarizabilities on the spin-mixing processes, ∣0,0⟩|0,0\rangle∣0,0⟩ ↔\leftrightarrow↔ ∣+1,−1⟩|+1,-1\rangle∣+1,−1⟩ and ∣0,0⟩|0,0\rangle∣0,0⟩ ↔\leftrightarrow↔ ∣−1,+1⟩|-1,+1\rangle∣−1,+1⟩, of an ultra-cold spin-1 mixture of the 137^{137}137Ba+^++ and 87^{87}87Rb atoms. We determine the protocols of selecting these spin-mixing oscillations by changing the strength of an externally applied magnetic field and the frequencies of the interrogating laser beams.
In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 62S12 − 52D32,52 clock transitions of Ba+ ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, |0,0⟩↔|+1,−1⟩ and |0,0⟩↔|−1,+1⟩, of an ultra-cold spin-1 mixture of 137Ba+ ions and 87Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively.