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Chinese Physics Letters

Observation of Cesium (nD 5/2 +6S 1/2 ) Ultralong-Range Rydberg-Ground Molecules

Suying Bai, Jingxu Bai, Xiaoxuan Han, Yuechun Jiao, Jianming Zhao, Suotang Jia

Published Dec 1, 2020• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/37/12/123201

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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.
We present an experimental observation of 37D5/2 + 6S1/2 Cs2 Rydberg-ground molecules by employing a two-photon photoassociation method. Two distinct Rydberg-ground molecular signals, deep and shallow bound molecules, are observed at the red detuning of atomic line. In theory, the model of scattering interaction between the Rydberg electron and ground-state atom is used to simulate the experiments. Two potential energy curves with energy minimum, deep pure triplet 3Σ and shallow hyperfine-mixed singlet–triplet 1,3Σ potentials, refer to the attained Rydberg-ground molecular signals, respectively. Calculations of the binding energy of triplet 3Σ and mixed 1,3Σv = 0 states are compared with the measurements. The agreement between the calculated and measured values of the binding energy yields zero-energy scattering lengths asT(0) = −19.2a0 and asS(0) = −1.3a0, respectively.
The ultralong-range Cs2 Rydberg molecules consisting of a Rydberg, nD5/2 ( principal quantum number n =35-38), and a ground state atom, 6S1/2 (F=4) are prepared by a two-photon photoassociation spectroscopy in an ultracold Cs gas. This kind of molecule is bound with the low energy scattering and has a permanent dipole moment. We observe two Rydberg-ground state molecular spectra, one is deep-bound molecule, TΣ state, bound by triplet s-wave scattering length and the other one is shallow-bound molecule, S,TΣ state, bound by mixed singlet-triplet s-wave scattering length. The binding energy of Rydberg-ground molecules are attained by analyzing the two photon photoassociation spectrum, corresponding permanent dipole moment is measured by applying an external electric field, which is compared to the calculation.
We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.
We report on the observation of long-range Cs 2 Rydberg molecules consisting of a p-state Rydberg atom and a ground-state atom. Two types of molecular states are visible in the photoassociation spectra: states bound purely by triplet s -wave scattering and states bound by mixed singlet-triplet s -wave scattering. An effective Hamiltonian including s -wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom reproduces the experimental observations. The detailed analysis reveals the important role of singlet scattering in long-range Rydberg molecules and yields an effective singlet s-wave scattering length for low-energy e − -Cs collisions.
In this work the existence of a novel type of molecule is shown whose binding is based solely on electron-atom scattering. These molecules are composed of a Rydberg atom and a ground state atom - here Rb(ns) and Rb(5s) - where the binding arises from scattering of the Rydberg electron from the ground state atom. The ground state atom is bound to the Rydberg wavefunction, which has radii on the order of 100nm, and thus these molecules are of long-range. Although the theoretical description of this interaction goes back to the famous work of Fermi in the year 1934 which was expanded in the following decades by Omont and Greene, the experimental proof of their existence was still missing. Up to now, experimental evidence for the ultralong-range Rydberg molecules was found only in spectral line broadenings. The present experiments have demonstrated the direct photoassociation of these ultralong-range Rydberg molecules for Rb(ns)-Rb(5s) triplet states from a cold and dense sample of rubidium 87 atoms for a range of principal quantum numbers, n, between 34 and 40. The high-resolution photoassociation spectra allowed for the observation of several vibrational states separated by only a few Megahertz. Based on the model by Greene the vibrational ground states v=0 are assigned and the dependence of their binding energy on the principal quantum number, n, is used to extract the triplet s-wave scattering length for electron-Rb(5s) collisions from the data. The remarkably good agreement between experiment and theory for the vibrational ground state v=0 over a range of principal quantum numbers attests to the accuracy of Fermi's original pseudopotential approach in describing interactions in excited multi-atom systems. Aside from this good agreement for the state v=0, the measurements also show that contributions from p-wave scattering cannot be neglected, as a number of excited vibrational states is observed in the experiment that are not predicted from the theory assuming only s-wave scattering. Calculations of Li, Pohl and coworkers have shown that a full solution of the electron-atom scattering is necessary for the assignment of all vibrational states. This work finds the molecular bound states to be very sensitive to both s-wave as well as p-wave electron-atom scattering and the Rydberg molecules turn out to be an accurate experimental platform to study electron-atom collisions in a previously inaccessible ultralow-energy regime. In general, the ultralong-range Rydberg molecules investigated here for rubidium are expected for all species with negative scattering length for electron-atom interaction, e. g. the other alkali atoms. Rydberg atom and ground state atom do not even have to be of the same chemical element, the only requirement is a negative scattering length of the ground state atom for electron scattering. Moreover, the binding force of the Rydberg electron is not restricted to a single ground state atom and molecules with more than one ground state atom can be created. The fact that these exotic molecules have huge bond lengths but nevertheless a vibrational spectrum with several states make a new type of ultracold Rydberg chemistry feasible. In the future, larger polymers or even heteronuclear molecules can be realized, where the number of atoms, the constituent atomic elements and the addressed Rydberg state allow to precisely select the properties of the long-range molecule.
We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the ground Cs perturber atoms by including the full set of spin-resolved 1,3SJ{}^{1,3}S_J1,3SJ​ and 1,3PJ{}^{1,3}P_J1,3PJ​ scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet (S=1) spin states through Rydberg electron spin-orbit and ground electron hyperfine interactions. Excellent agreement with observed data in Saßmannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and profiles is obtained. We also determine the spin-dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules in which all of the relativistic contributions are accounted for.