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arXiv:1312.1738 · Physical Review A

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

Türker Topçu, Andrei Derevianko

Published Feb 10, 2014• 18 citations
arXivHTMLPDF

Abstract

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 $n$.

DOI
10.1103/physreva.89.023411

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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
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∼\ensuremath{\sim}\ensuremath∼1000 nm are ``universal'' as they do not depend on the principal quantum number nnn.
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.
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.
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.
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.
In this dissertation, I explore several aspects of Rydberg physics with laser spectroscopy. The experiments center around the use of a very deep, cavity-generated, one-dimensional optical lattice in a cold atom sample. The optical lattice produces elongated clouds of dense, cold atoms via dipole trapping and is able to generate extreme light shifts in the atoms due to its high intensity. I describe experiments which may be divided into two main classes. In the first, I use the dipole trap to prepare a dense sample of atoms for photoassociation of Rb atom pairs into diatomic Rydberg molecules. The Rydberg molecules are formed by low-energy scattering of the Rydberg electron of one atom from the other atom, which is a ground-state atom. This novel binding mechanism also has relevance for chemical physics. I present binding energy measurements for eight different cases of Rydberg molecules. The binding energies reveal information about electron-atom collisions, such as their scattering lengths, and about the spin couplings present within the molecular system. In the second class of experiments, I introduce two proposed measurements in which the optical lattice is ramped to very high intensity during the laser excitation, creating AC Stark shifts in the transition frequencies. In one measurement, low-lying atomic states are probed. Measurements of the light shifts are expected to yield data on the dynamic polarizability and the photoionization cross section of the 5D3/2D_{3/2}D3/2​-state in rubidium in a 1064-nm light field. I show corresponding preliminary experimental data. The polarizability and photo-ionization cross-section measurements will provide tests of atomic structure theory, which is important both at a fundamental level and for applications such as atomic clocks. In another proposed measurement, Rydberg atoms in the lattice experience ponderomotive shifts and strong mixing of their angular-momentum states, allowing direct optical excitation of the lattice-mixed high-angular-momentum states. I describe the theoretical basis and experimental preparation for spectroscopically characterizing the lattice-mixed states. The ability to optically excite selected high-angular-momentum states without the use of static or RF fields may be useful for quantum information processing and simulation.
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.