Measurement of the Spin-Dipolar Part of the Tensor Polarizability ofRb87

Abstract

We report on the measurement of the contribution of the magnetic-dipole hyperfine interaction to the tensor polarizaility of the electronic ground-state in 87 Rb. This contribution was isolated by measuring the differential shift of the clock transition frequency in 87 Rb atoms that were optically trapped in the focus of an intense CO2 laser beam. By comparing to previous tensor polarizability measurements in 87 Rb, the contribution of the interaction with the nuclear electric-quadrupole moment was isolated as well. Our measurement will enable better estimation of black-body shifts in Rb atomic clocks. The methods reported here are applicable for future spectroscopic studies of atoms and molecules under strong quasi-static fields.Atomic systems are a good experimental platform for the test of quantum many-body theories with high precision. Atomic structure calculations for heavy atoms, with a large number of electrons, require sophisticated approximations and numerical methods. The predictions of such calculations can be readily tested using spectroscopy experiments. One such prediction entails atomic polarizabilities.Due to their symmetry under parity, atoms do not have permanent electric-dipole moments. When placed in a static electric field, however, their electronic wavefunction is polarized and a dipole moment which is proportional to the applied field is induced. The atomic polarizability is the proportionality tensor between the induced dipole moment and the field. This tensor can be further reduced to scalar and rank-two tensor parts. The latter, also known as the tensor polarizability, is determined by the hyperfine interaction of the electron with different magnetic and electric moments of the nucleus. The ab-initio calculation of the different polarizabilites is a difficult task and requires the use of advanced quantum many-body methods [1]. The measurement of the tensor atomic polarizability requires precision spectroscopy under strong applied electric fields.The precision of spectroscopic experiments benefits from long interrogation times. Optical dipole traps with their long storage times were therefore considered as a promising platform to this end. However, it was soon realized that the perturbation of atomic levels by the trapping optical fields introduces systematic line shifts and broadenings, and therefore compromises the precision of spectroscopy. Here, we rather take advantage of the large Stark shifts of atoms that are trapped in the focus of an intense CO 2 laser field in order to measure the tensor differential polarizability of the clock transition in 87 Rb. The slowly varying field of the CO 2 laser, as compared with the atomic resonance frequencies in Rb, allows for the measurement of the static polarizability to a good approximation. The interaction of atoms with laser light has been previously used to investigate atomic structure [2][3][4][5] This tensor shift of the clock transition depends only on the contribution of the spin-dipolar hyperfine interaction to the polarizability a...

Polarizabilities and tune-out wavelengths of the hyperfine ground states ofRb87,85

“…The difference of present tensor polarizabilities of the F = 2 and F = 1 ground states of 87 Rb is −1.0409 × 10 −4 a.u., which is more negative than the experimental value −0.8841 × 10 −4 a.u. [50]. The difference between experiment and the present calculation is 1.568 × 10 −5 a.u., which is larger than the experimental error bar 1.045 × 10 −5 a.u..…”

“…[49] 0.99 (24)[−2] Expt. [50] 0.9967(32)[−2] 85 Rb: α (1) (F = 3) − α (1) [(F = 2) Present RCICP 4.486[−3] Perturbation theory [30] 4.311[−3] Expet. [49] 4.389(96)[−3] 87 Rb: α…”

Measuring Magnetic Fields with Magnetic-Field-Insensitive Transitions

“…The population in the |2, 0 state was measured using absorption imaging of the |2, 0 state normalized by absorption imaging of all the atoms in both the F = 1 and F = 2 manifolds. Further information regarding the setup may be found in [21,22].…”

“…With this assumption we may safely expand Eq. (22) in largeB f and minimize the resulting sensitivity yielding,…”

“…( 21). The power broadening error, ε P.B , in (22) is squared in order to independently account for two pulses. Both corrections in Eq.…”