The Pairing+Quadrupole Hamiltonian In A Coherent State Representation

Joseph N. Ginocchio

Takaharu Otsuka

K. P. Drumev, J. Cseh, A. I. Georgieva

J. Dobaczewski

Lachezar S. Simeonov, Nikolay V. Vitanov, Peter A. Ivanov

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.

U. Kaup

The Schwinger representation of the SO(8) fermion-pair algebra in terms of d and quasispin vector s bosons is used in derivation of a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the Hartree-Fock-Bogolyubov variational solution. One can go beyond the mean field and introduce an intrinsic Hamiltonian having the boson condensate as an eigenstate.