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Physical Review A

Magic wavelengths for optical clock transitions in Rb 85 , Cs 133 , and Fr 223 in visible-near-infrared spectrum

Jyoti, Mandeep Kaur, Tiantian Shi, Jingbiao Chen

Published Nov 10, 2025• 0 citations
Publisher

Abstract

Neutral atom manipulation along with the modern laser cooling and trapping techniques have revolutionized the field of atomic physics, enabling innovation among atomic clocks as well as in the study of parity violation and the search for electron electric-dipole moment and nuclear anapole moment. The realization of highly precise and accurate atomic clocks evidently requires high signal-to-noise ratio, which is inversely proportional to Allan deviation. Keeping this in mind, we have calculated magic wavelengths $({\ensuremath{\lambda}}_{\mathrm{magic}})$ for optical clock transitions in $^{85}\mathrm{Rb}$, $^{133}\mathrm{Cs}$, and $^{223}\mathrm{Fr}$ atoms, viz, $5{S}_{1/2}\text{\ensuremath{-}}6{P}_{1/2,3/2}$, $6{S}_{1/2}\text{\ensuremath{-}}7{P}_{1/2,3/2}$, and $7{S}_{1/2}\text{\ensuremath{-}}8{P}_{1/2,3/2}$, respectively, particularly in the visible-near-infrared spectrum, owing to the fact that Allan deviation rapidly decreases with higher wavelengths of the electromagnetic spectrum, making them more acceptable for newer navigation systems, quantum computation devices as well as tools for high-precision experiments. In this study, we also recommend investigating near-resonant ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for $^{85}\mathrm{Rb}$ [420.81(2), $418.21(4),421.390(4)$, and 417.67 nm] and $^{133}\mathrm{Cs}$ [458.84(4) nm], utilizing dual-purpose lasers of $\ensuremath{\approx}420$ nm and $\ensuremath{\approx}459$ nm for cooling and pumping of atoms for four-level active optical clock system based on Rb and Cs frequency standards, respectively. We believe that these findings will aid in overcoming trapping challenges for atomic clocks as well as support studies for physics beyond the standard model.

DOI
10.1103/9yy9-v6v1

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Active clocks could provide better stabilities during initial stages of measurements over passive clocks, in which stabilities become saturated only after long-term measurements. This unique feature of an active clock has led to search for suitable candidates to construct such clocks. The other challenging task of an atomic clock is to reduce its possible systematics. A major part of the optical lattice atomic clocks based on neutral atoms are reduced by trapping atoms at the magic wavelengths of the optical lattice lasers. Keeping this in mind, we find the magic wavelengths between all possible hyperfine levels of the transitions in Rb and Cs atoms that were earlier considered to be suitable for making optical active clocks. To validate the results, we give the static dipole polarizabilities of Rb and Cs atoms using the electric dipole transition amplitudes that are used to evaluate the dynamic dipole polarizabilities and compare them with the available literature values.
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.
Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 → 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 − 13 / τ ( s ) -level, with integration time τ in seconds, and a relative accuracy of ∼ 10 − 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states.
Optical dipole traps (ODT) with far-off-resonance laser are important tools in more and more present cold-atom experiments, which allow confinement of laser-cooled atoms with a long storage time. Particularly, the magic wavelength ODT can cancel the position-dependent spatially inhomogeneous light shift of desired atomic transition, which is introduced by the ODT laser beam. Now it plays an important role in the state-insensitive quantum engineering and the atomic optical clock. To verify the magic wavelength or the magic wavelength combination for D2 line transition of cesium (Cs) and rubidium (Rb) atoms, we calculated and analyzed the light shift of the 133Cs 6S1/2 - 6P3/2 transition for a monochromatic ODT, and also the 87Rb 5S1/2 - 5P3/2 transition for a dichromatic ODT with a laser frequency ratio of 2:1. Also a dichromatic magic-wavelength ODT laser system for 87Rb atoms is proposed and experimentally realized by employing the quasi-phase-matched frequency doubling technique with telecom laser and fiber amplifier.
State-of-the-art optical clocks based on neutral atoms have already surpassed the world's best microwave atomic clocks in both accuracy and stability, paving the way to high-precision measurements of elementary aspects of nature, like the search for the drift of fundamental constants or the application of relativistic geodesy.These clocks operate with ensembles trapped in an optical lattice.Normally, high-power trapping laser fields induce a large AC Stark shift on the clock's transition frequency, as the clock states have different polarizabilities.A key feature of lattice clocks is the magic wavelength, for which the atomic polarizabilities of the clock states are equal, therefore compensating a differential frequency shift on the clock transition.In the periodic potential of the optical lattice, the energy spectrum of motional states features a band structure, analogous to electrons in a crystalline structure well-known from solid state physics.Within this band structure, atoms can tunnel between adjacent lattice sites.As a consequence from tunneling motion, the clock transition experiences a frequency shift and a broadening, which becomes pronounced in the shallow lattice regime.This work presents the first demonstration of a 24 Mg optical lattice clock including the precise determination of the frequency of the clock transition, its magic wavelength and its second-order Zeeman shift.Furthermore, the effect of tunneling in an optical lattice for magnesium has been extensively studied via optical spectroscopy of Bloch bands and substantiated with theoretical models, that were initially developed for a strontium optical lattice clock.Measuring lattice light induced frequency shifts of the clock transition for various lattice wavelengths and intensities, yielded a value of the magic wavelength of the 1 S 0 → 3 P 0 clock transition in 24 Mg of 468.463(207) nm.This value is in well agreement with a recent theoretical calculation of 468.45(23) nm, using a refined atomic structure model.The experimental value for the magic wavelength was independently verified with optical spectroscopy of Bloch bands carried out on the clock transition.Here, the AC Stark modified band structure is directly probed by a single frequency scan of the carrier resonance, featuring an asymmetric line shape, that is strongly dependent on the lattice wavelength.This technique demonstrates a novel method for the determination of the magic wavelength and could also be applied to other atomic species.In bosonic isotopes of alkaline earth(-like) elements, like 24 Mg, optical dipole excitation of the spin-forbidden 1 S 0 → 3 P 0 clock transition can be enhanced, e.g. by applying an external magnetic field.While these bosons are insensitive to first-order Zeeman shifts, the second-order Zeeman effect displays a dominant contribution to the clock's error budget.In this thesis, the magnetic polarizability β is measured to be -206.6(2.0)MHz/T 2 , consistent with a theoretical calculation, and the clock transition frequency was found to be 655 058 646 691(101) kHz.
We demonstrate the state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in an optical lattice. A magic wavelength of the proposed $|7{S}_{1/2};F=4,{M}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|6{P}_{3/2};F=3,{M}_{F}=0\ensuremath{\rangle}$ clock transition in Cs atoms is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about ${10}^{\ensuremath{-}15}$ in the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. The bad-cavity operational mode of the active clock is anticipated to improve remarkably its short-term stability by suppressing intrinsic thermal fluctuations. Thus, a composite clock system with better short-term and long-term stabilities can be built by combining the proposed active clock with another high-accuracy passive optical clock.