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arXiv:1712.06059 · Physical Review A

Tunable magic wavelengths for trapping with focused Laguerre-Gaussian beams

Anal Bhowmik, Narendra Nath Dutta, Sonjoy Majumder

Published Feb 21, 2018• 13 citations
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Abstract

We present in this paper a theory of dynamic polarizability for an atomic state due to an external field of nonparaxial Laguerre-Gaussian (LG) beam using the sum-over-states technique. A highly correlated relativistic coupled-cluster theory is used to evaluate the most important and correlation-sensitive parts of the sum. The theory is applied on ${\mathrm{Sr}}^{+}$ to determine the magic wavelengths for $5{s}_{1/2}\ensuremath{\rightarrow}4{d}_{3/2},4{d}_{5/2}$ transitions. Results show the variation of magic wavelengths with the choice of orbital and spin angular momenta of the incident LG beam. Also, the tunability of the magic wavelengths is studied by using the focusing angle of the LG beam and its efficiency in the near-infrared region is observed. Evaluations of the wide spectrum of magic wavelengths from infrared to ultraviolet have substantial importance to experimentalists for carrying out high-precision measurements in fundamental physics. These magic wavelengths can be used to confine the atom or ion at the dark central node or at the high-intensity ring of the LG beam.

DOI
10.1103/physreva.97.022511

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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 $5s_{{1}/{2}}\rightarrow 4d_{{3}/{2}, {5}/{2}}$ transitions of Sr$^+$. The initial state of our interest here is $5s_{{1}/{2}}$ with $m_J = -1/2$ 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.

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The present paper determines the precise values of magic wavelengths corresponding to the clock transitions ${5}^{2}S\text{--}{4}^{2}D$ of the ${\mathrm{Y}}^{2+}$ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.

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Theoretical analysis of polarization-angle-dependent magic-wavelength optical dipole trap of Cs atoms

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Laser cooling and trapping of neutral atoms is of great significance for studying the physical and chemical properties of atoms. To further realize the spatial localization of atoms, optical dipole trap (ODT) was proposed to manipulate individual atoms, ions or molecules and has become an increasingly important technique in the field of cold atomic physics and quantum optics. To eliminate the differential light shift of transitions between atomic states, ODT can be turned off during excitation/radiation. However, it will shorten the trap lifetime of the atom and reduce the repetition rate of the single photon. The AC stark shift can be eliminated experimentally by constructing blue-detuned dark ODT, but the micron-level dark ODT usually requires more complex experimental equipment and is not easy to operate. Therefore, magic-wavelength ODT was constructed to realize that the transition frequency of photons between atomic states is the same as in free space. When the trapping laser makes the differential light shift of the transition between the two atomic states zero, the laser wavelength is called the magic wavelength. The magic-wavelength ODT can eliminate the differential light shift of the transition between atoms, improve the repetition rate of the experimental sequence and weaken the atomic decoherence. In recent years, it has become a powerful tool for manipulating cold atoms, especially for coherently manipulating the atomic inner states. In the present work, with the theory of multi-level model, we calculate the dynamic electric polarizability of the 6S1/2 ground state and the 6P3/2 excited state connecting the D2 line of cesium atom in a range of 800–1000 nm, and obtain the magic wavelength of the optical trapping laser to trap the ground state and the excited state. Since the polarizability of atomic states with angular momentum greater than 0.5 is very sensitive to the polarization angle, the polarization-angle-dependent magic wavelength and the corresponding magic polarizability are analyzed by taking the linearly-polarized trapping laser for example. The magic polarization angle is 54.7° and the magic wavelength at this angle are 886.4315 and 934.0641 nm, respectively. The robustness of the magic conditions and the feasibility of the experimental operation are further analyzed.

Acta Physica Sinica•Jan 1, 2023•2 citations
We present in this paper a theory of dynamic polarizability for an atomic state due to an external field of nonparaxial Laguerre-Gaussian (LG) beam using the sum-over-states technique. A highly correlated relativistic coupled-cluster theory is used to evaluate the most important and correlation-sensitive parts of the sum. The theory is applied on Sr+{\mathrm{Sr}}^{+}Sr+ to determine the magic wavelengths for 5s1/2\ensuremath→4d3/2,4d5/25{s}_{1/2}\ensuremath{\rightarrow}4{d}_{3/2},4{d}_{5/2}5s1/2​\ensuremath→4d3/2​,4d5/2​ transitions. Results show the variation of magic wavelengths with the choice of orbital and spin angular momenta of the incident LG beam. Also, the tunability of the magic wavelengths is studied by using the focusing angle of the LG beam and its efficiency in the near-infrared region is observed. Evaluations of the wide spectrum of magic wavelengths from infrared to ultraviolet have substantial importance to experimentalists for carrying out high-precision measurements in fundamental physics. These magic wavelengths can be used to confine the atom or ion at the dark central node or at the high-intensity ring of the LG beam.
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.
The present paper determines the precise values of magic wavelengths corresponding to the clock transitions 52S–42D{5}^{2}S\text{--}{4}^{2}D52S–42D of the Y2+{\mathrm{Y}}^{2+}Y2+ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.
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 87Sr+^{87}\mathrm{Sr}^{+}87Sr+ 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 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na atoms.
We demonstrate magic wavelengths for the 6s 2S1/2−6p 2P3/2,1/26s ~ {^2}S_{1/2}-6p ~ {^2}P_{3/2,1/2}6s 2S1/2​−6p 2P3/2,1/2​ transitions in the Cs atom due to the circularly polarized light. In addition, we also obtain magic wavelengths using the linearly polarized light in order to verify the previously reported values and make a comparative study with the values obtained for the circularly polarized light. Most of these wavelengths are found to be in the optical region and could be of immense interest to the experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, 6p 2P1/26p ~{^2}P_{1/2}6p 2P1/2​ and 6p 2P3/26p ~{^2}P_{3/2}6p 2P3/2​ states. We use the available precise values of the electric dipole (E1) matrix elements for the most dominantly contributing transitions from the lifetime measurements of the above excited states and obtain other relevant important E1 matrix elements by employing a relativistic coupled-cluster method approximating at the singles and doubles level. Accuracies in these quantities are substantiated by comparing our evaluated scalar polarizability values with the corresponding experimental results.
We present magic wavelengths for the $n{S}_{1/2}\text{\ensuremath{-}}n{P}_{1/2,3/2},$ and $n{S}_{1/2}\text{\ensuremath{-}}m{D}_{3/2,5/2}$ transitions in Mg+,{\mathrm{Mg}}^{+},Mg+, Ca+,{\mathrm{Ca}}^{+},Ca+, Sr+,{\mathrm{Sr}}^{+},Sr+, and Ba+{\mathrm{Ba}}^{+}Ba+ alkaline-earth-metal ions, for the principal quantum numbers nnn and mmm for the ground and first excited DDD states, respectively. These wavelengths are presented for linearly polarized light by plotting the dynamic polarizabilities of the nS,nP1/2,3/2,nS,n{P}_{1/2,3/2},nS,nP1/2,3/2​, and mD3/2,5/2m{D}_{3/2,5/2}mD3/2,5/2​ states of the considered ions. Required dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with available high-precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca+{\mathrm{Ca}}^{+}Ca+ concur with the recent measurements reported by Liu et al. [Phys. Rev. Lett. 114, 223001 (2015)]. Knowledge of these magic wavelengths is propitious to carry out many proposed high-precision measurements trapping the above ions in electric fields with the corresponding frequencies.
Laser cooling and trapping of neutral atoms is of great significance for studying the physical and chemical properties of atoms. To further realize the spatial localization of atoms, optical dipole trap (ODT) was proposed to manipulate individual atoms, ions or molecules and has become an increasingly important technique in the field of cold atomic physics and quantum optics. To eliminate the differential light shift of transitions between atomic states, ODT can be turned off during excitation/radiation. However, it will shorten the trap lifetime of the atom and reduce the repetition rate of the single photon. The AC stark shift can be eliminated experimentally by constructing blue-detuned dark ODT, but the micron-level dark ODT usually requires more complex experimental equipment and is not easy to operate. Therefore, magic-wavelength ODT was constructed to realize that the transition frequency of photons between atomic states is the same as in free space. When the trapping laser makes the differential light shift of the transition between the two atomic states zero, the laser wavelength is called the magic wavelength. The magic-wavelength ODT can eliminate the differential light shift of the transition between atoms, improve the repetition rate of the experimental sequence and weaken the atomic decoherence. In recent years, it has become a powerful tool for manipulating cold atoms, especially for coherently manipulating the atomic inner states. In the present work, with the theory of multi-level model, we calculate the dynamic electric polarizability of the 6S1/2 ground state and the 6P3/2 excited state connecting the D2 line of cesium atom in a range of 800–1000 nm, and obtain the magic wavelength of the optical trapping laser to trap the ground state and the excited state. Since the polarizability of atomic states with angular momentum greater than 0.5 is very sensitive to the polarization angle, the polarization-angle-dependent magic wavelength and the corresponding magic polarizability are analyzed by taking the linearly-polarized trapping laser for example. The magic polarization angle is 54.7° and the magic wavelength at this angle are 886.4315 and 934.0641 nm, respectively. The robustness of the magic conditions and the feasibility of the experimental operation are further analyzed.