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arXiv:1308.6258 · Physical Review A

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

Türker Topçu, Andrei Derevianko

Published Nov 6, 2013• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.053406

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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.
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.
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.
We examine single-frequency optical schemes for species-selective trapping of ultracold alkali-metal atoms. Independently addressing the elements of a binary mixture enables the creation of an optical lattice for one atomic species with little or no effect on the other. We analyze a ``tune-in'' scheme, using near-resonant detuning to create a strong potential for one specific element. A ``tune-out'' scheme is also developed, in which the trapping wavelength is chosen to lie between two strong transitions of an alkali-metal atom such that the induced dipole moment is zero for that species but is nonzero for any other. We compare these schemes by examining the trap depths and heating rates associated with both. We find that the tune-in scheme is preferable for $\mathrm{Li}\text{\ensuremath{-}}\mathrm{Na}$, $\mathrm{Li}\text{\ensuremath{-}}\mathrm{K}$, and $\mathrm{K}\text{\ensuremath{-}}\mathrm{Na}$ mixtures, while the tune-out scheme is preferable for $\mathrm{Li}\text{\ensuremath{-}}\mathrm{Cs}$, $\mathrm{K}\text{\ensuremath{-}}\mathrm{Rb}$, $\mathrm{Rb}\text{\ensuremath{-}}\mathrm{Cs}$, $\mathrm{K}\text{\ensuremath{-}}\mathrm{Cs}$, and $^{39}\mathrm{K}\text{\ensuremath{-}}^{40}\mathrm{K}$ mixtures. Several applications of species-selective optical lattices are explored, including the creation of a lattice for a single species in the presence of a phononlike background, the tuning of relative effective mass, and the isothermal increase of phase-space density.
Using first-principles calculations, we identify ``tune-out'' optical wavelengths, ${\ensuremath{\lambda}}_{\mathrm{zero}}$, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of tune-out wavelengths for sympathetic cooling in two-species mixtures of alkali metals with group II and other elements of interest. Special cases in which these wavelengths coincide with strong resonance transitions in a target system are identified.
The atomic polarizability represents the response characteristics of atoms to externally applied electro-magnetic fields. The wavelength (or frequency) at which the dynamic polarizability of an atom is equal to zero is referred to as the tune-out wavelength (or frequency). Spectroscopy technology based on the tune-out effect has potential applications in quantum precision measurement, quantum computation and quantum communication. Related research topics include the measurement of fundamental physical constants and strong interactions. The tune-out wavelengths of atoms in low-lying states primarily fall within the optical band, where the theoretical calculations and experimental measurements have significant progress. However, for Rydberg atoms in highly excited states, theoretical calculations are challenging due to their high density of atomic states. The difficulty of experimental measurement arises from small splitting of adjacent atomic energy levels. In this paper, we demonstrate the tune-out wavelengths measurement for Rydberg atoms in a cesium vapor cell at room temperature. We utilize a two-photon cascade excitation to prepare Rydberg states and employ amplitude-modulation electromagnetically-induced transparency (AM-EIT) spectroscopy to measure the tune-out wavelength. By continuously scanning the microwave frequencies, we obtain AM-EIT signals of Rydberg atoms. At near-resonant microwave transition wavelengths, strong AM-EIT signals are observed due to microwave-atom coupling. Conversely, at tune-out wavelengths, the dynamically polarization-induced destructive interference in neighboring energy states occurs which leads to the weak AM-EIT signals. The AM-EIT provides a spectral resolution of about 10 MHz. We have developed a simplified three-level model to calculate the tune-out wavelength. The results of our theoretical calculations are consistent with the experimental findings within a range of ±90 MHz.
We develop and study quantum and semiclassical models of Rydberg-atom spectroscopy in amplitude-modulated optical lattices. Both initial- and target-state Rydberg atoms are trapped in the lattice. Unlike in other spectroscopic schemes, the modulation-induced ponderomotive coupling between the Rydberg states is spatially periodic and perfectly phase-locked to the lattice trapping potentials. This leads to a type of sub-Doppler mechanism which we explain in detail. In our exact quantum model, we solve the time-dependent Schr\"odinger equation in the product space of center-of-mass (COM) momentum states and the internal-state space. We also develop a perturbative model based on the band structure in the lattice and Fermi's golden rule, as well as a semiclassical trajectory model in which the COM is treated classically and the internal-state dynamics quantum-mechanically. In all models we obtain the spectrum of the target Rydberg-state population versus the lattice modulation frequency, averaged over the initial thermal COM momentum distribution of the atoms. We investigate the quantum-classical correspondence of the problem in several parameter regimes and exhibit spectral features that arise from vibrational COM coherences and rotary-echo effects. Applications in Rydberg-atom spectroscopy are discussed.