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arXiv:2602.20726 · Physical Review A

Tune-out wavelength for the thulium atom near 576 nm

Ivan Pyrkh, Arjuna Rudnev, Daniil Pershin, Davlet Kumpilov, Ivan Cojocaru, Vladimir Khlebnikov, Pavel Aksentsev, Ayrat Ibrahimov, Sergey Kuzmin, Alexander Raskatov, German Subbotin, Kirill Dyadkin, Anna Zykova, Vladislav Tsyganok, Alexey Akimov

physics.atom-phquant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026• 0 citations
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Abstract

We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of $575.646_{-0.014}^{+0.016}$ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to $575.646_{-0.004}^{+0.004}$. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.

DOI
10.1103/2cbw-v4t4

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Acta Physica Sinica•Jan 1, 2024•0 citations
We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of 575.646−0.014+0.016575.646_{-0.014}^{+0.016}575.646−0.014+0.016​ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to 575.646−0.004+0.004575.646_{-0.004}^{+0.004}575.646−0.004+0.004​. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.
Recently, thulium has been condensed to Bose-Einstein condensate. Machine learning was used to avoid a detailed study of all obstacles, making cooling difficult. This paper analyzes the atomic loss mechanism for the 532-nm optical trap, used in the Bose-condensation experiment, and compares it with the alternative and more traditional micrometer-range optical dipole trap. We also measured the scalar and tensor polarizability of thulium at 1064 nm, which were found to be $167\ifmmode\pm\else\textpm\fi{}25$ a.u. ($275\ifmmode\pm\else\textpm\fi{}41\phantom{\rule{0.55542pt}{0ex}}\phantom{\rule{0.55542pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}\mathrm{F}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}$) and $\ensuremath{-}4\ifmmode\pm\else\textpm\fi{}1$ a.u. ($7\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.55542pt}{0ex}}\phantom{\rule{0.55542pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}\phantom{\rule{0.28em}{0ex}}\mathrm{F}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}$), respectively.
Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper the real part of tensor and vector dynamic polarizability was experimentally measured and compared to a theoretical simulation. For an optical dipole trap operating around 532.07 nm, tensor polarizability was found to be $\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}53\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and vector polarizability was $680\ifmmode\pm\else\textpm\fi{}240\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ The measurements were compared with simulations, which were done based on the known set of levels from a thulium atom. The simulations are in good agreement with experimental results. In addition, losses of atoms from the dipole trap were measured for different trap configurations and compared to the calculated imaginary part of vector and tensor polarizabilities.
We report a precision measurement of a tune-out wavelength for 87Rb^{87}\mathrm{Rb}87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.
We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the D1{D}_{1}D1​, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and D2{D}_{2}D2​, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for 133Cs^{133}\mathrm{Cs}133Cs in the ground hyperfine state (F=3,mF=+3)(F=3,{m}_{F}=+3)(F=3,mF​=+3). At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a 133Cs^{133}\mathrm{Cs}133Cs Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.
Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the 6p6p6p, 7s7s7s, 7p7p7p, 8s8s8s, 8p8p8p, and 6d6d6d states and the dynamic dipole polarizabilities of the 6p6p6p and 7s7s7s states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the 7s1/27{s}_{1/2}7s1/2​, 7p1/27{p}_{1/2}7p1/2​, 8p1/28{p}_{1/2}8p1/2​, and 8p3/28{p}_{3/2}8p3/2​ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the 6p1/26{p}_{1/2}6p1/2​--7s7s7s and 6p3/26{p}_{3/2}6p3/2​--7s7s7s transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the 7s1/27{s}_{1/2}7s1/2​--7p1/27{p}_{1/2}7p1/2​ and 7s1/27{s}_{1/2}7s1/2​--7p3/27{p}_{3/2}7p3/2​ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the 6p1/26{p}_{1/2}6p1/2​--7p1/27{p}_{1/2}7p1/2​ transition, are also evaluated and compared with available theoretical and experimental values.
The atomic polarizability represents the response characteristics of atoms to externally applied electro-magnetic fields. The wavelength (or frequency) at which the dynamic polarizability of an atom is equal to zero is referred to as the tune-out wavelength (or frequency). Spectroscopy technology based on the tune-out effect has potential applications in quantum precision measurement, quantum computation and quantum communication. Related research topics include the measurement of fundamental physical constants and strong interactions. The tune-out wavelengths of atoms in low-lying states primarily fall within the optical band, where the theoretical calculations and experimental measurements have significant progress. However, for Rydberg atoms in highly excited states, theoretical calculations are challenging due to their high density of atomic states. The difficulty of experimental measurement arises from small splitting of adjacent atomic energy levels. In this paper, we demonstrate the tune-out wavelengths measurement for Rydberg atoms in a cesium vapor cell at room temperature. We utilize a two-photon cascade excitation to prepare Rydberg states and employ amplitude-modulation electromagnetically-induced transparency (AM-EIT) spectroscopy to measure the tune-out wavelength. By continuously scanning the microwave frequencies, we obtain AM-EIT signals of Rydberg atoms. At near-resonant microwave transition wavelengths, strong AM-EIT signals are observed due to microwave-atom coupling. Conversely, at tune-out wavelengths, the dynamically polarization-induced destructive interference in neighboring energy states occurs which leads to the weak AM-EIT signals. The AM-EIT provides a spectral resolution of about 10 MHz. We have developed a simplified three-level model to calculate the tune-out wavelength. The results of our theoretical calculations are consistent with the experimental findings within a range of ±90 MHz.