arXiv:1602.00046 · Journal of Physics B Atomic Molecular and Optical Physics

Possibility of triple magic trapping of clock and Rydberg states of divalent atoms in optical lattices

Türker Topçu, Andrei Derevianko

Published Jun 28, 2016• 12 citations

Abstract

Abstract We predict the possibility of ‘triply magic’ optical lattice trapping of neutral divalent atoms. In such a lattice, the 1 ⁢ S 0 and 3 P 0 clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation out of the motional ground state as a result of the excitations between the clock and the Rydberg states. We also calculate trapping laser-induced photoionization rates of divalent Rydberg atoms at magic frequencies. We find that such rates are below the radiative spontaneous-emission rates, due to the presence of Cooper minima in photoionization cross-sections.

DOI: 10.1088/0953-4075/49/14/144004

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arXiv:1602.00046 · Journal of Physics B Atomic Molecular and Optical Physics

Possibility of triple magic trapping of clock and Rydberg states of divalent atoms in optical lattices

Türker Topçu, Andrei Derevianko

Published Jun 28, 2016• 12 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0953-4075/49/14/144004

Related papers

Divalent Rydberg atoms in optical lattices: Intensity landscape and magic trapping

Türker Topçu, Andrei Derevianko

We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the $5sns$ ( ${}^{1}{S}_{0}$ ) and $5snp$ ( ${}^{3}{P}_{0}$ ) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [ $5{s}^{2}$ ( ${}^{1}{S}_{0}$ ) and $5s5p$ ( ${}^{3}{P}_{0}$ )] and the $J=0$ Rydberg states [ $5sns$ ( ${}^{1}{S}_{0}$ ) and $5snp$ ( ${}^{3}{P}_{0}$ )] vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number $n$ .We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the $5sns$(${}^{1}{S}_{0}$) and $5snp$(${}^{3}{P}_{0}$) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [$5{s}^{2}$(${}^{1}{S}_{0}$) and $5s5p$(${}^{3}{P}_{0}$)] and the $J=0$ Rydberg states [$5sns$(${}^{1}{S}_{0}$) and $5snp$(${}^{3}{P}_{0}$)] vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number $n$.

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J=0

Rydberg states of Sr and evaluate the dynamic polarizabilities of the

5sns

(

{}^{1}{S}_{0}

) and

5snp

(

{}^{3}{P}_{0}

) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [

5{s}^{2}

(

{}^{1}{S}_{0}

) and

5s5p

(

{}^{3}{P}_{0}

)] and the

J=0

Rydberg states [

5sns

(

{}^{1}{S}_{0}

) and

5snp

(

{}^{3}{P}_{0}

)] vanishes. We tabulate these wavelengths as a function of the principal quantum number

n

of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\ensuremath{\sim}$1000 nm are ``universal'' as they do not depend on the principal quantum number

n

125s

Rydberg states for 10 $\ensuremath{\mu}\mathrm{K}$ Cs atoms are presented. Consideration of the trapping potential and photoionization rates suggests that these traps will be useful for quantum-information experiments with atomic qubits.

J=1/2

ground state. Our numerical results show that, while such a magic trap for alkali metals would require prohibitively large magnetic fields, the group IIIB metals such as Al are suitable candidates.