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arXiv:1906.08924 · Journal of Physics B Atomic Molecular and Optical Physics

Anisotropic interactions in electric field polarized ultracold Rydberg gases

Akbar Jahangiri, James P Shaffer, Luís Felipe Gonçalves, Luís Gustavo Marcassa

Published Oct 11, 2019• 2 citations
arXivHTMLPDF

Abstract

Abstract We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective C 3 dipole–dipole and C 6 van der Waals coefficients. We compare the C 3 and C 6 with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole–dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in 50 S 1 / 2 states in the blockade regime. For internuclear distances close to the blockade radius, R bl ≈ 4–6 μ m, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of C 3 and C 6 which were used to analyze the original experiment. We find that the calculated C 6 coefficient is within 8% of the experimental value while the C 3 coefficient is within 20% of the experimental value.

DOI
10.1088/1361-6455/ab4d31

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•Jan 1, 2011•1 citation
Abstract We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective C 3 dipole–dipole and C 6 van der Waals coefficients. We compare the C 3 and C 6 with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole–dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in 50 S 1 / 2 states in the blockade regime. For internuclear distances close to the blockade radius, R bl ≈ 4–6 μ m, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of C 3 and C 6 which were used to analyze the original experiment. We find that the calculated C 6 coefficient is within 8% of the experimental value while the C 3 coefficient is within 20% of the experimental value.
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.
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Charge-dipole interactions are very common interactions among atoms and molecules, especially materials that can emit light or contain free charges. The second-order charge-dipole interactions, proportional to 1R4\frac{1}{R^4}R41​, are stronger than the second-order dipole-dipole interactions or van der Waals interactions, proportional to 1R6\frac{1}{R^6}R61​, at longer distances. In reality, there is more than one atom or charge; therefore, we focus on few-body charge-dipole interactions, such as charge-dipole-dipole interactions. Laser cooling and trapping allow us to study such interactions with much higher precision. In this article, charge-dipole interactions will be investigated in ultracold gases. To increase the interaction strength, we excite the ultracold atoms to highly excited states, Rydberg states. Here, we treat one Rydberg atom as a dipole, the excited electron and the ion core are the two poles of an electric dipole. Specifically, we study charge-atom interactions in ultracold Rydberg gases.
Atoms in an ultracold highly excited sample are strongly coupled through the dipole-dipole interaction. In an effort to understand and manipulate the complicated interactions in this system we are investigating their dependence on the relative orientation of the dipoles. By focusing a 480 nm beam from a tunable dye laser into a magneto-optical trap, we produce a nearly one-dimensional sample of Rydberg atoms. The trap lies at the center of four conducting rods with which we can vary the magnitude and direction of the electric field at the trap, thus controlling the orientation of the dipoles with respect to the sample axis. We have measured the strength of the interaction for a variety of relative orientations.
The work presented in this dissertation represents a comprehensive study on long-range interactions between alkali Rydberg atoms. As a consequence of their size, Rydberg atoms possess very large dipole moments, making them highly sensitive to external fields and to other Rydberg atoms. The strong dipole-dipole interaction between two Rydberg atoms results in a mixing of their angular momentum characters, which is the cornerstone of the work presented here. We describe the ℓ-mixing between various local molecular asymptotes through a residual Coulomb potential, assuming no electron cloud overlap. We then directly diagonalize an interaction Hamiltonian consisting of these Rydberg-Rydberg interactions and spin-orbit (fine structure) coupling in the Hund's case (c). In this manner, we calculate potential energy curves for various molecular symmetries and find that some of these curves exhibit deep potential wells, capable of supporting very extended bound molecular states ( macrodimers). We analyze the specific structure of the ℓ-mixing for these potential wells and derive convenient n-scaling relations for both their equilibrium separations Re and well depths De. We also explore various properties of the macrodimers, including their response to small electric fields and stability with respect to predissociation. We note throughout the dissertation that the detection of such extended dimers could help progress studies in a variety of areas such as exotic, ultracold chemistry and quantum information and computing. To facilitate detection, we propose a scheme to form and study the macrodimers via photoassociation (PA). We present calculated PA lineshapes from two different electronic ground states based on a harmonic trapping model. We find that both PA signals vary significantly with the laser detunings, indicating that different ℓ-characters could be probed at different equilibrium lengths. Finally, we extend the two-body formalism to the case of three interacting Rydberg atoms and present preliminary results for triply excited 58p rubidium atoms along a common axis. We provide a few examples of surface plots corresponding to different local asymptotes, each with a unique three-dimensional "landscape" and discuss the relevance of the physical features. The highlight of our analysis is the appearance of a potential well, which indicates the formation of a linear trimer. ^