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Atoms

Magic Wavelengths for Optical-Lattice Based Cs and Rb Active Clocks

Sukhjit Singh Sehra, Jyoti, Bindiya Arora, B. K. Sahoo, Yanmei Yu

Published Nov 10, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.3390/atoms8040079

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particular 'magic' wavelengths. This Review covers the experimental realizations of such clocks, the optimal design of optical lattices and recent demonstrations of improved stability for large numbers of atoms. Possible impacts and future applications of optical lattice clocks are also discussed, such as testing the fundamental laws of physics and developing relativistic geodesy.

Louis Essen

8half a century ago and have provided the definition of the second since 1967. The international atomic time (TAI) is currently kept by an ensemble of Cs clocks with a fractional uncertainty of Δν/ν0 ≈ 10 –15 , and some Cs fountain clocks 9,10 operate at even smaller uncertainties. Although Cs atomic clocks operate at the microwave transition of ν0 ≈ 9.2 GHz, using optical transition frequencies of several hundred terahertz should improve the fractional uncertainty Δν/ν0 by 4–5 orders of magnitude, as most measurement uncertainties Δν are independent of ν0 (except the Doppler shift Δ νD = (v/c)ν0, where v is the atomic velocity and c is the speed of light). The invention of the laser and the subsequent improvement of laser frequency stabilities 11 has allowed the realization of optical clocks to become a reality 2,3,12

•Jan 1, 2011•0 citations
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.
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.
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 85Rb^{85}\mathrm{Rb}85Rb, 133Cs^{133}\mathrm{Cs}133Cs, and 223Fr^{223}\mathrm{Fr}223Fr 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 85Rb^{85}\mathrm{Rb}85Rb [420.81(2), 418.21(4),421.390(4)418.21(4),421.390(4)418.21(4),421.390(4), and 417.67 nm] and 133Cs^{133}\mathrm{Cs}133Cs [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.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than 2×10−172\times10^{-17}2×10−17 is feasible, which is of the same accuracy as the expected best optical atomic clock.
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.
A generic scheme to trap atoms at the magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ that are independent of vector and tensor components of the interactions of the atoms with the external electric field is presented. The ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the laser cooling D2{D}_{2}D2​ lines in the Rb and Cs atoms are demonstrated and their corresponding polarizability values without vector and tensor contributions are given. Consequently, these ${\ensuremath{\lambda}}_{\mathrm{magic}}$ are independent of magnetic sublevels and hyperfine levels of the atomic states involved in the transition, thus, they can offer unique approaches to carrying out many high-precision measurements with minimal systematics. Inevitably, the proposed technique can also be used for electronic or hyperfine transitions in other atomic systems.
8half a century ago and have provided the definition of the second since 1967. The international atomic time (TAI) is currently kept by an ensemble of Cs clocks with a fractional uncertainty of Δν/ν0 ≈ 10 –15 , and some Cs fountain clocks 9,10 operate at even smaller uncertainties. Although Cs atomic clocks operate at the microwave transition of ν0 ≈ 9.2 GHz, using optical transition frequencies of several hundred terahertz should improve the fractional uncertainty Δν/ν0 by 4–5 orders of magnitude, as most measurement uncertainties Δν are independent of ν0 (except the Doppler shift Δ νD = (v/c)ν0, where v is the atomic velocity and c is the speed of light). The invention of the laser and the subsequent improvement of laser frequency stabilities 11 has allowed the realization of optical clocks to become a reality 2,3,12