Alkaline-earth atoms in their lowest triplet P_2 state are exceptionally long-lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. We develop a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. The consequences are illustrated by application to metastable strontium. The coupling among molecular rotational states is demonstrated to induce the formation of a long-range molecular potential well. Its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable strontium displays a resonance at a field of 339 Gauss.
The static and dynamic properties of the alkaline-earth atoms in their metastable state are computed in a configuration interaction approach with a semi-empirical model potential for the core. Among the properties determined are the scalar and tensor polarizabilities, the quadrupole moment, some of the oscillator strengths and the dispersion coefficients of the van der Waals interaction. A simple method for including the effect of the core on the dispersion parameters is described.
The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J (J=0,1,2) fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique--based on a physically motivated potential that models the presence of the ionic core--is employed to solve the Schroedinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are cal…
Metastability and long-range interactions of Mg, Ca, and Sr in the lowest-energy metastable $^3P_2$ state are investigated. The calculated lifetimes are 38 minutes for Mg*, 118 minutes for Ca*, and 17 minutes for Sr*, supporting feasibility of cooling and trapping experiments. The quadrupole-quadrupole long-range interactions of two metastable atoms are evaluated for various molecular symmetries. Hund's case (c) 4_g potential possesses a large 100-1000 K potential barrier. Therefore magnetic trap losses can possibly be reduced using cold metastable atoms in a stretched M=2 state. Calculations …
Ultra-cold collisions of spin-polarized 24Mg,40Ca, and 88Sr in the metastable 3P2 excited state are investigated. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The estimates are based on molecular potentials between 3P2 alkaline-earth atoms obtained from ab initio atomic and molecular structure calculations. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 …
We present a method for creating a quantum degenerate gas of metastable alkaline-earth atoms. This has yet to be achieved due to inelastic collisions that limit evaporative cooling in the metastable states. Quantum degenerate samples prepared in the $^{1}S_{0}$ ground state can be rapidly transferred to either the $^{3}P_{2}$ or $^{3}P_{0}$ state via a coherent 3-photon process. Numerical integration of the density matrix evolution for the fine structure of bosonic alkaline-earth atoms shows that transfer efficiencies of $\simeq90\%$ can be achieved with experimentally feasible laser parameter…
Derivations for the higher tensor components of the quadrupole polarizabilities are given and their values for the metastable states of the Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions are estimated. We also give the scalar quadrupole polarizabilities of the ground and metastable states of these ions to compare our results with the previously available theoretical and experimental results. Reasonably good agreement between our calculations with the previous values of scalar quadrupole polarizabilities demonstrate their correctness. The reported scalar and tensor quadrupole polarizabilit…
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the $^3P_1$ state into the long-living metastable state $^3P_0$, thus enabling the strictly forbidden $^1S_0$$-$$^3P_0$ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on ato…
Measuring the hyperfine structure (HFS) of long-lived $^3P_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}$Sr needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. Results of similar analyses for $^{9}$Be, $^{25}…
In continuation to our earlier reported data on the electric dipole (E1) matrix elements and lifetimes of the metastable states of the alkaline earth ions in [Atomic Data and Nuc. Data Tables {\bf 137} (2021) 101381], we present here the tune-out and magic wavelengths of the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions by determining dynamic E1 polarizabilities. Furthermore, we have evaluated the electric quadrupole (E2) matrix elements of a large number of forbidden transitions using an all-order relativistic many-body method and compare them with the previously reported values…
Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
We present a complete scheme for quantum information processing using the unique features of alkaline earth atoms. We show how two completely independent lattices can be formed for the $^1$S$_0$ and $^3$P$_0$ states, with one used as a storage lattice for qubits encoded on the nuclear spin, and the other as a transport lattice to move qubits and perform gate operations. We discuss how the $^3$P$_2$ level can be used for addressing of individual qubits, and how collisional losses from metastable states can be used to perform gates via a lossy blockade mechanism.
Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for ${}^{171}$Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable el…
The theoretical description of the external degrees of freedom of atoms trapped inside a magneto-optical trap (MOT) often relies on the decoupling of the evolution of the internal and external degrees of freedom. That is possible thanks to much shorter timescales typically associated with the first ones. The electronic structure of alkaline-earth atoms, on the other hand, presents ultra-narrow transitions and metastable states that makes such an approximation invalid in the general case. In this article, we report on a model based on open Bloch equations for the evolution of the number of atom…
Ultracold gases of fermionic alkaline-earth (like) atoms are hopeful candidates for the quantum simulation of many-body physics induced by magnetic impurities (e.g., the Kondo physics), because there are spin-exchange interactions (SEIs) between two atoms in the electronic ground ($^1$S$_0$) and metastable ($^3$P) state, respectively. Nevertheless, this SEI cannot be tuned via magnetic Feshbach resonance. In this work we propose three methods to control the SEI between one atom in the $^1$S$_0$ state and another atom in the $^3$P$_2$ states or $^3$P$_2$-$^3$P$_0$ dressed states, with one or tw…
Degenerate quantum gases of alkaline-earth-like elements open new opportunities in research areas ranging from molecular physics to the study of strongly correlated systems. These experiments exploit the rich electronic structure of these elements, which is markedly different from the one of other species for which quantum degeneracy has been attained. Specifically, alkaline-earth-like atoms, such as strontium, feature metastable triplet states, narrow intercombination lines, and a non-magnetic, closed-shell ground state. This review covers the creation of quantum degenerate gases of strontium…
Magnetic Feshbach resonances have allowed great success in the production of ultracold diatomic molecules from bi-alkali mixtures, but have so far eluded observation in mixtures of alkali and alkaline-earth-like atoms. Inelastic collisional properties of ultracold atomic systems exhibit resonant behavior in the vicinity of such resonances, providing a detection signature. We study magnetic field dependent inelastic effects via atom loss spectroscopy in an ultracold heteronuclear mixture of alkali $^6$Li in the ground state and alkaline-earth-like $^{174}$Yb in an excited electronic metastable …
A STIRAP-like scheme is proposed to exploit a three-photon resonance taking place in alkaline-earth-metal ions. This scheme is designed for state transfer between the two fine structure components of the metastable D-state which are two excited states that can serve as optical or THz qu-bit. The advantage of a coherent three-photon process compared to two-photon STIRAP lies in the possibility of exact cancellation of the first order Doppler shift which opens the way for an application to a sample composed of many ions. The transfer efficiency and its dependence with experimental parameters are…
Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a $4D$ metastable level are impervious to autoionization over more than a few millisecond t…
Alkaline-earth (AE) atoms have metastable clock states with minute-long optical lifetimes, high-spin nuclei, and SU($N$)-symmetric interactions that uniquely position them for advancing atomic clocks, quantum information processing, and quantum simulation. The interplay of precision measurement and quantum many-body physics is beginning to foster an exciting scientific frontier with many opportunities. Few particle systems provide a window to view the emergence of complex many-body phenomena arising from pairwise interactions. Here, we create arrays of isolated few-body systems in a fermionic …
