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arXiv:physics/0508087 · Physical Review A

Frequency-dependent polarizabilities of alkali-metal atoms from ultraviolet through infrared spectral regions

Marianna S. Safronova, Bindiya Arora, Charles W. Clark

Published Feb 9, 2006• 67 citations
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Abstract

We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali-metal atoms for light in the wavelength range 300--1600 nm, with particular attention to wavelengths of common infrared lasers. We parametrize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. This work is motivated by recent experiments involving simultaneous optical trapping of two different alkali-metal species. Our data can be used to predict the oscillation frequencies of optically trapped atoms, and particularly the ratios of frequencies of different species held in the same trap. We identify wavelengths at which two different alkali-metal atoms have the same oscillation frequency.

DOI
10.1103/physreva.73.022505

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We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali-metal atoms for light in the wavelength range 300--1600 nm, with particular attention to wavelengths of common infrared lasers. We parametrize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. This work is motivated by recent experiments involving simultaneous optical trapping of two different alkali-metal species. Our data can be used to predict the oscillation frequencies of optically trapped atoms, and particularly the ratios of frequencies of different species held in the same trap. We identify wavelengths at which two different alkali-metal atoms have the same oscillation frequency.
We investigate oscillation frequencies for simultaneous trapping of more than one type of alkali atoms in a common optical lattice. For this purpose, we present numerical results for magic trapping conditions, where the oscillation frequencies for two different kind of alkali atoms using laser lights in the wavelength range 500-1200 nm are same. These wavelengths will be of immense interest for studying static and dynamic properties of boson-boson, boson-fermion, fermion-fermion, and boson-boson-boson mixtures involving different isotopes of Li, Na, K, Rb, Cs and Fr alkali atoms. In addition to this, we were also able to locate a magic wavelength around 808.1 nm where all the three Li, K, and Rb atoms are found to be suitable for oscillating at the same frequency in a common optical trap.
Using first-principles calculations, we identify ``tune-out'' optical wavelengths, ${\ensuremath{\lambda}}_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.
Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO2{}_{2}2​ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the nsnsns, npnpnp, and ndndnd Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the mz=0{m}_{z}=0mz​=0 Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted l=0l=0l=0 states.
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the 7s7s7s 2S1/2^{2}{S}_{1/2}2S1/2​, 7p7p7p 2P1/2,3/2^{2}{P}_{1/2,3/2}2P1/2,3/2​, and 8s8s8s 2S1/2^{2}{S}_{1/2}2S1/2​ levels of the 7s7s7s $^{2}{S}_{1/2}\ensuremath{-}7p$ 2P1/2,3/2^{2}{P}_{1/2,3/2}2P1/2,3/2​ and 7s7s7s $^{2}{S}_{1/2}\ensuremath{-}8s$ 2S1/2^{2}{S}_{1/2}2S1/2​ transitions, respectively. Wavelengths in the ultraviolet, visible, and near infrared region are identified that are suitable for cooling and trapping. Magic wavelengths between the 600--700 nm and 700--1000 nm regions, which are blue and red detuned with the $7s\ensuremath{-}7p$ and $7s\ensuremath{-}8s$ transitions, are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground 7s7s7s 2S1/2^{2}{S}_{1/2}2S1/2​ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity nonconservation.
Magic wavelengths for the Li, Na, and K alkali-metal atoms are determined using the circularly polarized light for the nsnsns-np1/2,3/2n{p}_{1/2,3/2}np1/2,3/2​ transitions, with nnn denoting their ground-state principal quantum numbers, by studying their differential ac dynamic polarizabilities. These wavelengths for all possible sublevels are given linearly as well as circularly polarized lights and are further compared with the available results for the linearly polarized light. The present study suggests that it is possible to carry out state-insensitive trapping of different alkali-metal atoms using the circularly polarized light.
Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ with exact values that depend on Ry-state quantum numbers.