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

Abstract

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

Bogoliubov theory of dipolar Bose gas in a weak random potential

“…Note that, in order to avoid any instability, we restricted ǫ dd in Fig. 1 to the maximum value one, so that the radicand in the Bogoliubov spectrum (23) remains positive when k → 0 [42,43]. We conclude that Eqs.…”

“…Thus, following Refs. [43,53], we can evaluate (25) by introducing an ultraviolet cutoff, where the interaction has to be renormalized by inserting the term m(nV k ) 2 2 k 2 , so that the divergent part is removed…”

“…Note that (5) is not continuous at q = 0, as the limit q → 0 is direction dependent. This is the origin for various anisotropic properties, which are characteristic for dipolar Bose gases [37,39,42,43]. The operatorsâ k and a † k are the annihilation and creation operators in Fourier space, respectively, which turn out to satisfy the bosonic commutation relations…”

An Arrested Implosion

“…In principle, pure liquid droplets in the absence of trapping should reach an equilibrium with an absence of growth [4,21]. On the other hand, time-of-flight expansion under a dipolar interaction is nontrivial but well studied [32,33], and it is modified by beyond mean-field effects [27]; these effects are isotropic and counteract magnetostriction. Mean-field hydrodynamic equations could not describe the expansion of our droplets.…”

“…[25][26][27] the beyond mean-field correction to the chemical potential μ ¼ ð∂e=∂nÞ for a dipolar gas is given by μ bmf ≃ ð32gn=3 ffiffiffi π p Þ ffiffiffiffiffiffiffi ffi na 3 p ð1 þ 3 2 ϵ 2 dd Þ, where we have taken the lowest order expansion of the Q 5 function of Ref. [27] since ϵ dd is close to 1. Doing this we effectively neglect the imaginary part, which is very small compared to the real part, such that a long lifetime is still ensured, though it is only in a metastable equilibrium.…”