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arXiv:1806.04043 · Journal of Physics B Atomic Molecular and Optical Physics

Adiabatic potentials of cesium ( nD J ) 2 Rydberg–Rydberg macrodimers

Xiaoxuan Han, Suying Bai, Yuechun Jiao, Georg A. Raithel, Jianming Zhao, Suotang Jia

Published Mar 26, 2019• 11 citations
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Abstract

Abstract Electrostatic multipole interactions generate long-range Rydberg–Rydberg macrodimers. We calculate the adiabatic potentials of cesium nD J 2 Rydberg macrodimers for principal quantum numbers n ranging from 56 to 62, for J = 3/2 and 5/2, and for the allowed values of the conserved sum of the atomic angular-momentum components along the internuclear axis, M . For most combinations ( n , M , J ) exactly one binding potential exists, which should give rise to Rydberg macrodimer states. We study the dependence of the adiabatic potentials on the size of the two-body basis sets used in the calculation, and on the maximal order, q max , of the multipole terms included in the calculation. We determine the binding energies and lengths of the binding adiabatic potentials, investigate their scaling behaviors as a function of the effective principal quantum number, and discuss vibrational-state wave functions. We consider the applicability of the calculated potentials and excitation rates to an experimental scheme for preparing nD J 2 Rydberg-atom macrodimers using two-color double-resonant photoassociation.

DOI
10.1088/1361-6455/ab1371

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Abstract Electrostatic multipole interactions generate long-range Rydberg–Rydberg macrodimers. We calculate the adiabatic potentials of cesium nD J 2 Rydberg macrodimers for principal quantum numbers n ranging from 56 to 62, for J = 3/2 and 5/2, and for the allowed values of the conserved sum of the atomic angular-momentum components along the internuclear axis, M . For most combinations ( n , M , J ) exactly one binding potential exists, which should give rise to Rydberg macrodimer states. We study the dependence of the adiabatic potentials on the size of the two-body basis sets used in the calculation, and on the maximal order, q max , of the multipole terms included in the calculation. We determine the binding energies and lengths of the binding adiabatic potentials, investigate their scaling behaviors as a function of the effective principal quantum number, and discuss vibrational-state wave functions. We consider the applicability of the calculated potentials and excitation rates to an experimental scheme for preparing nD J 2 Rydberg-atom macrodimers using two-color double-resonant photoassociation.
Long-range macrodimers formed by DDD-state cesium Rydberg atoms are studied in experiments and calculations. Cesium [62DJ]2{[62{D}_{J}]}_{2}[62DJ​]2​ Rydberg-atom macrodimers, bonded via long-range multipole interaction, are prepared by two-color photoassociation in a cesium atom trap. The first color (pulse A) resonantly excites seed Rydberg atoms, while the second (pulse B, detuned by the molecular binding energy) resonantly excites the Rydberg-atom macrodimers below the [62DJ]2{[62{D}_{J}]}_{2}[62DJ​]2​ asymptotes. The molecules are measured by extraction of autoionization products and Rydberg-atom electric-field ionization, and ion detection. Molecular spectra are compared with calculations of adiabatic molecular potentials. From the dependence of the molecular signal on the detection delay time, the lifetime of the molecules is estimated to be $3--6\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$.
The long-range multipole interactions between ultra-cold Rydberg atoms form adiabatic potentials, one of which shows a binding potential that can be used to bind Rydberg-Rydberg molecules. Rydberg-atom molecule, known as macrodimer due to its larger size (~μm), has the properties of the abundant vibrational energy levels and large electric dipole moment and so on. Compared with Rydberg atom, the Rydberg molecule, including Rydberg-ground molecule and Rydberg-Rydberg molecule, is susceptible to manipulate by an external field and possesses potential applications in the weak-signal detection, the quantum gas correlation measurement and the vacuum fluctuation and so on. In this paper, we investigate a (60D5/2)2 Rydberg macrodimer theoretically and experimentally. In the calculation, we take into account the multipole interaction of a Rydberg-atom pair, including dipole-dipole, dipole-quadrupole, dipole-octupole and quadrupole-quadrupole interaction and so on. The adiabatic potential of 60D5/2 Rydberg-atom pair is obtained by diagonalizing the interaction Hamiltonian on a grid of internuclear separations, R. The potential depth and binding length of the Rydberg molecular potential well are obtained. In experiment, we prepare the ultra-cold Cs (60D5/2)2 Rydberg molecules by a two-color photoassociation method in a cesium ultracold atom trap. The first-color (pulse-A) resonantly excites a seed Rydberg atom A, and the second color (pulse-B) is detuned and resonantly excites the second Rydberg atom B near to the atom A. Both pulse-A and pulse-B are two-photon excitations (852 nm + 510 nm), between which their 852-nm lasers have the same frequency, whereas the 510-nm laser frequency of the pulse-A is set to be resonant with the atomic transition and the frequency of the pulse-B is detuned by using a double-passed acousto-optic modulator. When the pulse-B is detuned to the molecular binding energy, atom-A and-B are bonded, forming an ultra-cold Cs (60D5/2)2 Rydberg molecule. The two-color photoassociation spectra of Rydberg-Rydberg molecules are detected by the field ionization of Rydberg atoms and molecules with a ramped electric field. Molecular spectra are compared with calculated adiabatic molecular potentials, which yields the binding energy and equilibrium internuclear distance. The two-color photoassociation method used in this work has a doubly resonant character that results in the enhanced excitation rate.
Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme is employed to form these molecules in states, which correlate to np(n+1)s dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair states. We show that a full model is required to accurately predict the occurrence of bound Rydberg macrodimers. The macrodimers are distinguished from repulsive molecular states by their behavior with respect to spontaneous ionization and possible decay channels are discussed.
We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy curves for various symmetries of doubly excited n s and n p rubidium atoms. We show that the potential curves for these symmetries exhibit deep (∼ GHz) potential wells, which can support very extended (∼ µm) bound vibrational states ( macrodimers ). We present n -scaling relations for both the depth D e of the wells and the equilibrium separations R e of these macrodimers, and explore their response to small electric fields and stability with respect to predissociation. Finally, we present a scheme to form and study these macrodimers via photoassociation, and show how one can probe the various ℓ-character of the potential wells.
Ultralong-range Cs 2 Rydberg-ground molecules ( nD 5/2 + 6 S 1/2 F ) (33 ≤ n ≤ 39, F = 3 or 4) are investigated by a two-photon photo-association spectroscopy of an ultracold Cs gas. Two vibrational ground molecular spectra of triplet 3 Σ and hyperfine mixed singlet-triplet 1,3 Σ molecular states and their corresponding binding energies are attained. The experimental observations are simulated by an effective Hamiltonian including low energy electron scattering pseudopotentials, the spin-orbit interaction of the Rydberg atom, and the hyperfine interaction of the ground-state atom. The zero-energy singlet and triplet s-wave scattering lengths are extracted by comparing the experimental observations and calculations. Dependences of the measured binding energies on the effective principal quantum number, n eff = n − δ D ( δ D is the quantum defect of Rydberg D state), yield the scaling of n eff − 5.60 ± 0.16 ( 3 ​ Σ , F = 3 ) , n eff − 5.62 ± 0.16 ( 3 ​ Σ , F = 4 ) for deep triplet potential and n eff − 5.65 ± 0.38 ( 1 , 3 ​ Σ , F = 3 ) , n eff − 6.19 ± 0.14 ( 1 , 3 ​ Σ , F = 4 ) for shallow mixed singlet-triplet potential well. The simulations of low-energy Rydberg electron scattering show agreement well with the experimental measurements.