Beyond mean-field low-lying excitations of dipolar Bose gases

摘要

We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuringnthe anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contactninteraction. Within the realm of the Bogoliubov–de Gennes theory, we consider static properties and low-lyingnexcitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system,nthe condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed inndetail. Making use of the local density approximation, we extend these results in order to study the propertiesnof a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving thenequations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations onnimportant properties of the gas, such as the equilibrium configuration and the low-lying excitations in the casenof a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discussnthe radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipoledipoleninteraction. As a result, we identify the radial quadrupole as a reasonably accessible source for thensignature of dipolar many-body effects and stress the enhancing character that dipolar interactions have fornquantum fluctuations in the other oscillation modes.