Quantum fluctuations in dipolar Bose gases

Abstract

We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the condensate and the excited particles. This allows to obtain the Bogoliubov spectrum analytically in the limit of large particle numbers. After discussing the condensate depletion and the ground-state energy correction, we derive quantum corrected equations of motion for harmonically trapped dipolar Bose gases by using superfluid hydrodynamics. These equations are subsequently applied to analyze the equilibrium configuration, the low-lying oscillation frequencies, and the time-of-flight dynamics. We find that both atomic magnetic and molecular electric dipolar systems offer promising scenarios for detecting beyond mean-field effects. . This investigation pioneered a series of experiments which led to a robust understanding of the DDI on a mean-field level. Experimental successes include the direct observation of the DDI in the time-of-flight (TOF) dynamics [2,3], the stabilization of a purely dipolar gas [4], and the observation of a dwave Bose-nova explosion [5]. In the meantime, the DDI has also been observed even in 87 Rb [6] and evidences of it have been found in 7 Li [7]. Recently, an important experiment has been realized, in which the influence of the DDI upon the oscillation frequencies of 52 Cr has been studied [8]. Parallel to these experiments, much theoretical work has been pursued [9]. For instance, building on the previous construction of the dipolar pseudo-potential [10], a solution of the mean-field Gross-Pitaevskii (GP) equation was obtained [11,12], which accounts quantitatively for the static as well as the dynamic properties of trapped dilute 52 Cr gases [2,3,8]. Nowadays, dipolar interactions in magnetic systems are, therefore, considered to be relatively well understood in terms of the GP mean-field theory. Nonetheless, highly magnetic atoms, such as dysprosium [13], or strongly polar heteronuclear molecules, exemplified by 40 K 87 Rb [14][15][16], are expected to push the understanding of dipolar systems beyond the edge of mean-field theory's domain of validity.

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.…”

“…Note that there is no superfluid depletion in (42) which is due to quantum fluctuations, in contrast to the condensate depletion which has a quantum fluctuations component determined by Eq. (20).…”

“…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…”

Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates

“…(1) correspond to the NLNLSE thoroughly employed for the study of dipolar condensates [1], the last line stems from the LHY correction to the equation of state, which is obtained using the local density approximation (LDA) from the knowledge of the LHY correction in homogeneous 3D space [23,24]. The strength of the LHY correction is given by g LHY =…”

An Arrested Implosion

“…Using the results of Refs. [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.…”