Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1305.6570 · Physical Review A

Intensity landscape and the possibility of magic trapping of alkali-metal Rydberg atoms in infrared optical lattices

Türker Topçu, Andrei Derevianko

Published Oct 7, 2013• 18 citations
arXivHTMLPDF

Abstract

Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ with exact values that depend on Ry-state quantum numbers.

DOI
10.1103/physreva.88.043407

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 $n$.

arXiv:1312.1738•Physical Review A•Feb 10, 2014•18 citations

Tune-out wavelengths and landscape-modulated polarizabilities of alkali-metal Rydberg atoms in infrared optical lattices

Türker Topçu, Andrei Derevianko

Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO${}_{2}$ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the $ns$, $np$, and $nd$ Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the ${m}_{z}=0$ Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted $l=0$ states.

arXiv:1308.6258•Physical Review A•Nov 6, 2013•12 citations

Magic running- and standing-wave optical traps for Rydberg atoms

Lukas Ahlheit, Chris Nill, Daniil Svirskiy +6 more

The authors present an experimental and theoretical study of how the geometry of an optical trap influences the magic wavelength for a collective Rydberg excitation, and find the magic trap wavelength where the coherence time in photon storage experiments is maximized. This magic wavelength depends not only on the Rydberg state, but also on the trap geometry due to the wave function of the almost-free Rydberg electron exploring the potential landscape surrounding the core. Hence, it is necessary to take the size of both Rydberg atom and trapping beams into account when trapping Rydberg atoms.

arXiv:2410.20901•Physical Review A•Jan 24, 2025•4 citations

Magic wavelengths for trapping the alkali-metal atoms with circularly polarized light

B. K. Sahoo, Bindiya Arora

Magic wavelengths for the Li, Na, and K alkali-metal atoms are determined using the circularly polarized light for the $ns$-$n{p}_{1/2,3/2}$ transitions, with $n$ denoting their ground-state principal quantum numbers, by studying their differential ac dynamic polarizabilities. These wavelengths for all possible sublevels are given linearly as well as circularly polarized lights and are further compared with the available results for the linearly polarized light. The present study suggests that it is possible to carry out state-insensitive trapping of different alkali-metal atoms using the circularly polarized light.

arXiv:1212.1814•Physical Review A•Feb 5, 2013•25 citations

Trapping Rydberg Atoms in Ponderomotive Optical Lattices.

Sarah Elizabeth Anderson

I examine the trapping of Rydberg atoms in an optical standing wave. This trap, called an optical lattice, offers a platform for utilizing Rydberg atoms and their unique properties in applications such as atomic spectroscopy and quantum computing. Toward this end, I demonstrate the capability to trap rubidium 85 Rydberg atoms in a one-dimensional 1064 nm wavelength optical lattice with high efficiency. I have achieved a 90% trapping efficiency by inverting the lattice immediately after Rydberg-atom excitation, using an electro-optic technique. In addition, I investigate the dependence of optical-lattice trapping potentials for Rydberg atoms on the angular portion of the atomic wavefunction. While ground-state atoms are point-like in relation to an optical-lattice field, Rydberg-atom wavefunctions extend over a substantial fraction of the lattice period, leading to an angular dependence of the lattice trapping potentials. I measure the potentials using various angular sublevels of Rydberg nD states prepared in the optical lattice with a superimposed transverse DC electric field. This unique angular dependence of Rydberg-atom optical lattices may be exploited to tailor the trapping potentials as needed for spectroscopy or quantum computing. Further, atom loss due to lattice-induced photoionization of Rydberg atoms must be characterized for applications. I investigate the photoionization process as a function of position within the volume of a Rydberg atom. Since Rydberg-atom sizes approximately equal the lattice period, the lattice intensity varies maximally within the atomic volume. I find that photoionization rates are higher for lattice intensity maxima located near the nucleus than within the lobes of the electronic probability distribution. Photoionization therefore occurs near the Rydberg-atom nucleus. Finally, I calculate photoionization rates for Rydberg atoms in optical fields and investigate how these rates relate to the validity of the electric dipole approximation. This approximation is usually central to matter-field interactions, and Rydberg atoms in optical fields present a system for studying the approximation in a limiting case. I further apply the photoionization calculations to experimentally-relevant conditions. With these advances, this thesis lays essential groundwork for the employment of Rydberg-atom optical lattices in applications.

•Jan 1, 2014•0 citations

Theory of magic optical traps for Zeeman-insensitive clock transitions in alkali-metal atoms

Andrei Derevianko

Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias $B$ field along a circularly polarized trapping laser field. We map out these $B$ fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.

arXiv:0912.3233•Physical Review A•May 20, 2010•45 citations
Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around 10\ensuremathμm10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}10\ensuremathμm with exact values that depend on Ry-state quantum numbers.
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=0J=0J=0 Rydberg states of Sr and evaluate the dynamic polarizabilities of the 5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​) 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 [5s25{s}^{2}5s2(1S0{}^{1}{S}_{0}1S0​) and 5s5p5s5p5s5p(3P0{}^{3}{P}_{0}3P0​)] and the J=0J=0J=0 Rydberg states [5sns5sns5sns(1S0{}^{1}{S}_{0}1S0​) and 5snp5snp5snp(3P0{}^{3}{P}_{0}3P0​)] vanishes. We tabulate these wavelengths as a function of the principal quantum number nnn 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 nnn.
Intensity-modulated optical lattice potentials can change sign for an alkali-metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO2{}_{2}2​ laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential experienced by the Rydberg atom can be made to vanish for atoms in ``targeted'' Rydberg states. Such state-selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the nsnsns, npnpnp, and ndndnd Rydberg states of Na and Rb atoms and discuss advantages of using such optical lattices for state-selective trapping of Rydberg atoms. We also develop exact analytical expressions for the lattice-induced polarizability for the mz=0{m}_{z}=0mz​=0 Rydberg states and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted l=0l=0l=0 states.
The authors present an experimental and theoretical study of how the geometry of an optical trap influences the magic wavelength for a collective Rydberg excitation, and find the magic trap wavelength where the coherence time in photon storage experiments is maximized. This magic wavelength depends not only on the Rydberg state, but also on the trap geometry due to the wave function of the almost-free Rydberg electron exploring the potential landscape surrounding the core. Hence, it is necessary to take the size of both Rydberg atom and trapping beams into account when trapping Rydberg atoms.
Magic wavelengths for the Li, Na, and K alkali-metal atoms are determined using the circularly polarized light for the nsnsns-np1/2,3/2n{p}_{1/2,3/2}np1/2,3/2​ transitions, with nnn denoting their ground-state principal quantum numbers, by studying their differential ac dynamic polarizabilities. These wavelengths for all possible sublevels are given linearly as well as circularly polarized lights and are further compared with the available results for the linearly polarized light. The present study suggests that it is possible to carry out state-insensitive trapping of different alkali-metal atoms using the circularly polarized light.
I examine the trapping of Rydberg atoms in an optical standing wave. This trap, called an optical lattice, offers a platform for utilizing Rydberg atoms and their unique properties in applications such as atomic spectroscopy and quantum computing. Toward this end, I demonstrate the capability to trap rubidium 85 Rydberg atoms in a one-dimensional 1064 nm wavelength optical lattice with high efficiency. I have achieved a 90% trapping efficiency by inverting the lattice immediately after Rydberg-atom excitation, using an electro-optic technique. In addition, I investigate the dependence of optical-lattice trapping potentials for Rydberg atoms on the angular portion of the atomic wavefunction. While ground-state atoms are point-like in relation to an optical-lattice field, Rydberg-atom wavefunctions extend over a substantial fraction of the lattice period, leading to an angular dependence of the lattice trapping potentials. I measure the potentials using various angular sublevels of Rydberg nD states prepared in the optical lattice with a superimposed transverse DC electric field. This unique angular dependence of Rydberg-atom optical lattices may be exploited to tailor the trapping potentials as needed for spectroscopy or quantum computing. Further, atom loss due to lattice-induced photoionization of Rydberg atoms must be characterized for applications. I investigate the photoionization process as a function of position within the volume of a Rydberg atom. Since Rydberg-atom sizes approximately equal the lattice period, the lattice intensity varies maximally within the atomic volume. I find that photoionization rates are higher for lattice intensity maxima located near the nucleus than within the lobes of the electronic probability distribution. Photoionization therefore occurs near the Rydberg-atom nucleus. Finally, I calculate photoionization rates for Rydberg atoms in optical fields and investigate how these rates relate to the validity of the electric dipole approximation. This approximation is usually central to matter-field interactions, and Rydberg atoms in optical fields present a system for studying the approximation in a limiting case. I further apply the photoionization calculations to experimentally-relevant conditions. With these advances, this thesis lays essential groundwork for the employment of Rydberg-atom optical lattices in applications.
Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias BBB field along a circularly polarized trapping laser field. We map out these BBB fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.