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Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of ${}^{87}$Sr

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 Added by Roger Ding
 Publication date 2019
  fields Physics
and research's language is English




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Photoexcitation rates for creation of ultralong-range Rydberg molecules (ULRM) with 31$lesssim n lesssim41$ in both ground and excited vibrational levels in cold ($Tsim900$~nK) gases of polarized and unpolarized $^{87}$Sr are presented. The measured production rates of the $ u=0, 1$ and 2 vibrational levels reveal rather different $n$ dependences which are analyzed by evaluating the Franck-Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wavefunctions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited $ u=1$ molecules can furnish a probe of pair correlations over intermediate length scales extending from $sim20$~nm to greater than 250~nm.



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Since their first experimental observation, ultralong-range Rydberg molecules consisting of a highly excited Rydberg atom and a ground state atom have attracted the interest in the field of ultracold chemistry. Especially the intriguing properties like size, polarizability and type of binding they inherit from the Rydberg atom are of interest. An open question in the field is the reduced lifetime of the molecules compared to the corresponding atomic Rydberg states. In this letter we present an experimental study on the lifetimes of the ^3Sigma (5s-35s) molecule in its vibrational ground state and in an excited state. We show that the lifetimes depends on the density of ground state atoms and that this can be described in the frame of a classical scattering between the molecules and ground state atoms. We also find that the excited molecular state has an even more reduced lifetime compared to the ground state which can be attributed to an inward penetration of the bound atomic pair due to imperfect quantum reflection that takes place in the special shape of the molecular potential.
We predict that ultralong-range Rydberg bi-molecules form in collisions between polar molecules in cold and ultracold settings. The collision of $Lambda$-doublet nitric oxide (NO) with long-lived Rydberg NO($nf$, $ng$) molecules forms ultralong-range Rydberg bi-molecules with GHz energies and kilo-Debye permanent electric dipole moments. The Hamiltonian includes both the anisotropic charge-molecular dipole interaction and the electron-NO scattering. The rotational constant for the Rydberg bi-molecules is in the MHz range, allowing for microwave spectroscopy of rotational transitions in Rydberg bi-molecules. Considerable orientation of NO dipole can be achieved. The Rydberg molecules described here hold promise for studies of a special class of long-range bi-molecular interactions.
The lifetimes and decay channels of ultralong-range Rydberg molecules created in a dense BEC are examined by monitoring the time evolution of the Rydberg population using field ionization. Studies of molecules with values of principal quantum number, $n$, in the range $n=49$ to $n=72$ that contain tens to hundreds of ground state atoms within the Rydberg electron orbit show that their presence leads to marked changes in the field ionization characteristics. The Rydberg molecules have lifetimes of $sim1-5,mu$s, their destruction being attributed to two main processes: formation of Sr$^+_2$ ions through associative ionization, and dissociation induced through $L$-changing collisions. The observed loss rates are consistent with a reaction model that emphasizes the interaction between the Rydberg core ion and its nearest neighbor ground-state atom. The measured lifetimes place strict limits on the time scales over which studies involving Rydberg species in cold, dense atomic gases can be undertaken and limit the coherence times for such measurements.
A detailed theoretical framework for highly excited Rydberg molecules is developed based on the generalized local frame transformation. Our approach avoids the use of pseudopotentials and yields analytical expressions for the body-frame reaction matrix. The latter is used to obtain the molecular potential energy curves, but equally it can be employed for photodissociation, photoionization, or other processes. To illustrate the reliability and accuracy of our treatment we consider the Rb$^*-$Rb Rydberg molecule and compare our treatment with state-of-the-art alternative approaches. As a second application, the present formalism is used to re-analyze the vibrational spectra of Sr$^*-$Sr molecules, providing additional physical insight into their properties and a comparison of our results with corresponding measurements.
A combined experimental and theoretical spectroscopic study of high-$n$, ${30 lesssim n lesssim 100}$, triplet $text{S}$ and $text{D}$ Rydberg states in $^{87}text{Sr}$ is presented. $^{87}text{Sr}$ has a large nuclear spin, ${I=9/2}$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n$ $text{S}$ states, the hyperfine shifts are evaluated non-perturbatively taking advantage of earlier spectroscopic data for the ${I=0}$ isotope $^{88}text{Sr}$, which results in good agreement with the present measurements. For the $text{D}$ states, this procedure is reversed by first extracting from the present $^{87}text{Sr}$ measurements the energies of the $^{3}text{D}_{1,2,3}$ states to be expected for isotopes without hyperfine structure ($^{88}text{Sr}$) which allows the determination of corrected quantum defects in the high-$n$ limit.
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