Compensation of the trap-induced quadrupole interaction in trapped Rydberg ions

Lachezar S Simeonov,Peter A Ivanov,Nikolay V Vitanov

doi:10.1038/s41598-019-43865-5

Abstract

The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.

Highlights

Ion trap system is one of the leading platforms in quantum information technologies[1,2,3]
Such an effect arises due to the huge electric dipole moment of the Rydberg ion and causes undesired excitation of electronic transitions driven by the radio-frequency electric field of the Paul trap, see Fig. 1
We show that the effect of the quadrupole coupling is merely to rescale the Rabi frequencies Ωi which drive the transition between the Rydberg levels

Summary

Rydberg ions

The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. This detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Though the 88Sr+ ions are excited more to Rydberg levels, the nD3/2 Rydberg states are coupled by the quadrupole field of the trap. TdhitesreinfoterernthalesRtryudcbteurrgeimonusctabnentoakloenngienrtobeaccoconusindte.rIenddaeseda,paosisnht-olwikne in refs[14,24,26], the electric field of the Paul trap may excite internal electronic transitions which are no longer negligible contrary to the ordinary trapped ions

The Paul trap electric field can be written as

Including the quadrupole interaction the total Hamiltonian becomes

We find that the effective Hamiltonian becomes

Conclusion

Additional Information