Preparation And Spectroscopy Of Ultracold Rydberg-ground Molecules

Ultra-cold Rydberg-ground molecules consisting of a Rydberg atom and one or more ground-state atoms are formed by low-energy scattering between the Rydberg electron and ground-state atoms located inside the Rydberg electron's wave function.The low-energy scattering interaction,initially investigated by Fermi and Omont,has been predicted to lead to molecular binding in a novel type of Rydberg molecules,including the trilobite and butterfly molecules.Their unconventional binding mechanism,which is unlike covalent,ionic,and van der Waals bonds,results in loosely bound molecules with bond lengths on the order of thousands of Bohr radii.This kind of molecule with large size and huge permanent electric dipole moment is good candidate for the realization of certain strongly correlated many-body gases and for low-energy collision dynamics,as well as for quantum information processing and spin systems with long-range interactions.Consequently,these molecules have attracted considerable attention in recent years.In this paper,we present the experimental observations and theoretical calculations of the diatomic Rydberg-ground molecules formed by a highly excited Rydberg atom and a ground state atom.The interaction between a low-energy Rydberg electron and ground-state atom can be described using a Fermi pseudopotential approach.In the Fermi model,the ground-state atom is treated as a perturber of the Rydberg-electron wave function,resulting in oscillatory potential curves with localized minima capable of sustaining bound molecular states.The Cs n D-type Rydberg-ground molecules are investigated by photo-association spectroscopy in a cold atomic gas.We establish scaling laws for the energies of the lowest vibrational states vs principal quantum number and obtain zero-energy singlet and triplet s-wave scattering lengths from experimental data and a Fermi model.The lifetimes and electric dipole moments of molecules were also be measured.Main contents are as follows:1.A semi-empirical model is developed relating the scattering phase shift functions to the binding energies.Fermi pseudopotential is used to describe the low-energy scattering interaction between Rydberg electrons and ground state atoms.Using a Fermi model,we calculate molecular potential-energy curves(PECs)and vibrational energies.For Cs n D-type Rydberg-ground molecules in Hund's case-(c),the binding-energy ratio between j=3/2 and j=5/2 is/(+1)=2/3.The hyperfine-mixed singlet-triplet potentials(shallow potentials)have shallower wells and vary significantly depending on whether the ground-state atom is in its F=3 or F=4 hyperfine state.The shallow potentials for F=3 are deeper than those for F=4.The triplet potentials(deep potentials)are virtually unaffected by hyperfine mixing.2.The experiment is performed in a crossed optical dipole trap(CODT)loaded from a magneto-optical trap(MOT).Two counterpropagated 852 and 510nm lasers are applied to photo-associate the atoms into Rydberg-ground molecules.Rydberg molecular(atomic)ions are produced by Hornbeck-Molnar autoionization(blackbody photoionization)and detected with a microchannel plate(MCP)detector.We have obtained the photo-association spectra for all combinations of j and F,for n=33 to 39.3.The measured binding-energy data are employed to determine s-wave scattering lengths via comparison with model calculations.The calculations yield best fitting s-wave scattering-length functions for both triplet and singlet scattering,and,with zero-energy scattering lengths and.The functions are used to fit the both measured and calculated data to obtain the scaling laws for the energies of the lowest vibrational states vs principal quantum number.4.We measured the lifetimes and electric dipole moment of molecules.The molecular lifetimes are about 5?s,which is less than Rydberg atomic lifetime(tens of microseconds),we further analyzed several decay channels that may reduce the molecular lifetimes.Analysis of the spectra for 0.18,0.27,and 0.37V/cm yields averaged dipole-moment magnitudes of d=(4.79±0.78)ea₀ for n=37,^T(50),which is in good agreement with the theoretical calculation result d _Theor.=-4.64ea₀.The innovations of this work:1.Using a Fermi model,we calculate molecular potential-energy curves(PECs)and vibrational energies.We prepared Cs n D_5/2+6S_1/2Rydberg-ground molecules experimentally for the first time and observed Cs n D-type molecules involving Rydberg-state fine structure and ground-state hyperfine structure.We establish scaling laws for the energies of the v=0 vibrational states vs n.2.The measured binding-energy data are employed to determine s-wave scattering lengths via comparison with model calculations.The calculations yield best fitting s-wave scattering-length functions for both triplet and singlet scattering,and,with zero-energy scattering lengths and.3.We measured Cs n D-type molecular permanent electric-dipole moments with magnitudes of a few ea₀ for the first time.Calculations show that the dipole moment is negative,which differs from reports on other types of Rydberg-ground molecules.A negative d_i,v corresponds with a deficiency of electron charge from the vicinity of the perturber atom.This situation can generally be described as destructive interference of the Rydberg electron wave function near the perturber or,equivalently,as a destructive case of electronic configuration mixing near the perturber(linear combination of atomic orbitals picture).