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.

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.

The quest for quantum degenerate Fermi gases interacting through the anisotropic and long-range dipole-dipole interaction is an exciting and fast developing branch within the cold-atoms research program. Recent experimental progress in trapping, cooling, and controlling polar molecules with large electric dipole moments has, therefore, motivated much theoretical effort. In a recent letter, we have briefly discussed the application of a variational time-dependent Hartree-Fock approach to study theoretically both the static and the dynamic properties of such a system in a cylindersymmetric harmonic trap. We focused on the hydrodynamic regime, where collisions assure the equilibrium locally. Here, we present a detailed theory, extended to encompass the general case of a harmonic trap geometry without any symmetry. After deriving the equations of motion for the gas, we explore their static solutions to investigate key properties like the aspect ratios in both real and momentum space as well as the stability diagram. We find that, despite the lack of symmetry of the trap, the momentum distribution remains cylinder symmetric. The equations of motion are then used to study the low-lying hydrodynamic excitations, where, apart from the quadrupole and monopole modes, also the radial quadrupole mode is investigated. Furthermore, we study the timeof-flight dynamics as it represents an important diagnostic tool for quantum gases. We find that the real-space aspect ratios are inverted during the expansion, while the one in momentum space becomes asymptotically unity. In addition, anisotropic features of the dipole-dipole interaction are discussed in detail. These results could be particularly useful for future investigations of strongly dipolar heteronuclear polar molecules deep in the quantum degenerate regime.

We present new results on the localization of gauge fields in thick brane models. The fourdimensional observable universe is considered to be a topological defect which is generated by two scalar fields coupled with gravity embedded in a five-dimensional space-time. Like other thick brane models, the Bloch brane setup is not capable of supporting gauge field localization. In order to circumvent this problem we include the dilaton field and, as a result, obtain normalizable solutions. In addition, by writing the equations of motion as Schroedinger-like equations, we have found new kinds of resonances in the massive spectrum which appear also for heavy modes. This is in sharp contrast to what is commonly found in previous analog studies, where only light modes become resonant. At specific energies, the wave solutions exhibit very high amplitudes within the membrane. The influence of the dilaton coupling and of the internal structure on the resonant modes are also discussed.

Recently, a seminal STIRAP experiment allowed the creation of 40 K 87 Rb molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. In order to describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system as, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release from the trap, the momentum distribution becomes asymptotically isotropic, while the particle density becomes anisotropic.PACS numbers: 21.60. Jz,67.85.Lm Even before the realization of Bose-Einstein condensation (BEC) with 52 Cr [1], much experimental and theoretical interest has been dedicated to ultracold quantum gases interacting through the long-range and anisotropic dipole-dipole interaction (DDI) [2]. For bosonic dipolar particles, the starting point of the theoretical investigations was the construction of a corresponding pseudopotential by Yi and You [3]. After that, an exact solution of the Gross-Pitaevskii equation in the ThomasFermi regime was found for cylinder-symmetric traps [4]. Moreover, the DDI has been shown to shift the BEC critical temperature in a characteristic way in polarized systems [5] and to give rise to the Einstein-deHaas effect, when spinorial degrees of freedom are considered [6]. From the experimental point of view, timeof-flight (TOF) techniques demonstrated both the first DDI-signature through small mechanical effects [7] as well as strong dipolar effects in quantum ferrofluids [8]. Furthermore, the shape of the trap was manipulated to stabilize a purely dipolar BEC against collapse [9] [19][20][21][22]. Due to the resulting strong DDI a considerable deformation of the momentum distribution is expected [17,18]. Once these systems would have been further cooled into the quantum degenerate regime, the main task will be to identify unambiguously the presence of the DDI. In this respect, TOF experiments and oscillation frequency measurements represent the most fundamental diagnostic tools in the field of ultracold quantum gases. Their outcomes reveal important information on the nature of the system under investigation. They differ drastically depending on whether the system is in the collisionless (CL) regime, where collision rates are small, or in the hydrodynamic (HD) regime, where collisions take place so often that they lead to local equilibrium. To date, investigations of dynamical properties of trapped dipolar Fermi gases have either been restricted to the CL regime [23] or excluded a deformation of the momentum distribution in the HD regime [24]. Since the experiments with ultracold polar molecules are performed under strong dipolar interactions, one should expect them to lead the system into the HD regime, and thus an analysis allowing for an anisotropy in the momentum distribution ...

By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.

Many-body dipolar effects in Fermi gases are quite subtle as they energetically compete with the large kinetic energy at and below the Fermi surface (FS). Recently it was experimentally observed in a sample of erbium atoms that its FS is deformed from a sphere to an ellipsoid due to the presence of the anisotropic and long-range dipole-dipole interaction Aikawa et al (2014 Science 345 1484). Moreover, it was suggested that, when the dipoles are rotated by means of an external field, the FS follows their rotation, thereby keeping the major axis of the momentum-space ellipsoid parallel to the dipoles. Here we generalise a previous Hartree-Fock mean-field theory to systems confined in an elongated triaxial trap with an arbitrary orientation of the dipoles relative to the trap. With this we study for the first time the effects of the dipoles' arbitrary orientation on the ground-state properties of the system. Furthermore, taking into account the geometry of the system, we show how the ellipsoidal FS deformation can be reconstructed, assuming ballistic expansion, from the experimentally measurable real-space aspect ratio after a free expansion. We compare our theoretical results with new experimental data measured with erbium Fermi gas for various trap parameters and dipole orientations. The observed remarkable agreement demonstrates the ability of our model to capture the full angular dependence of the FS deformation. Moreover, for systems with even higher dipole moment, our theory predicts an additional unexpected effect: the FS does not simply follow rigidly the orientation of the dipoles, but softens showing a change in the aspect ratio depending on the dipoles' orientation relative to the trap geometry, as well as on the trap anisotropy itself. Our theory provides the basis for understanding and interpreting phenomena in which the investigated physics depends on the underlying structure of the FS, such as fermionic pairing and superfluidity.

No abstract