Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates

Abstract

We find that pancake dipolar condensates can exhibit a roton-maxon character of the excitation spectrum, so far only observed in superfluid helium. We also obtain a condition for the dynamical stability of these condensates. The spectrum and the border of instability are tunable by varying the particle density and/or the confining potential. This opens wide possibilities for manipulating the superfluid properties of dipolar condensates.Recent progress in cooling and trapping of polar molecules [1, 2] opens fascinating prospects for achieving quantum degeneracy in trapped gases of dipolar particles. Being electrically or magnetically polarized, polar molecules interact with each other via long-range anisotropic dipole-dipole forces. This makes the properties of such dipolar gases drastically different from the properties of commonly studied atomic cold gases, where the interparticle interaction is short-range. Other candidates to form a dipolar gas are atoms with large magnetic moments [3,4], and atoms with dc-field-[5] or lightinduced electric dipole moments [6,7,8].The dipole-dipole interaction is responsible for a variety of novel phenomena in ultracold dipolar systems. The energy independence of the dipole-dipole scattering amplitude for any orbital angular momenta provides realistic possibilities for achieving a superfluid BCS transition in single-component dipolar Fermi gases (see [9] and refs. therein). Dipolar bosons in optical lattices have been shown to provide a highly controllable environment for engineering various quantum phases [10]. In addition to superfluid and Mott-Insulator ones, recently observed in Munich experiments [11] with bosonic atoms, the long-range dipole-dipole potential provides supersolid and checker-board phases. Dipole-dipole interactions are also responsible for spontaneous polarization and spin waves in spinor condensates in optical lattices [12], and may lead to self-bound structures in the field of a traveling wave [13]. Recently, dipolar particles have been considered as promising candidates for the implementation of fast and robust quantum-computing schemes [8,14].The long-range and anisotropic (partially attractive) character of dipole-dipole forces ensures a strong dependence of the stability of trapped dipolar Bose-Einstein condensates on the trapping geometry [7]. For cylindrical traps with the aspect ratio l z /l ρ > l * = 0.43, a purely dipolar condensate is dynamically unstable if the number of particles N exceeds a critical value. A detailed study of the excitation modes for this geometry is contained in Ref. [15]. It has also been argued in Ref. [7] that in pancake traps with l z /l ρ < l * the ground state solution is expected for any N .In this Letter we analyze the nature of excitations and instability of pancake-shaped dipolar condensates. For this purpose, we consider the physically transparent case of an infinite pancake trap, with the dipoles perpendicular to the trap plane. For the maximum condensate density n 0 → ∞, the dynamical stability requires the pre...

Three-body interactions with cold polar molecules

“…Recently, systems of polar molecules in the rovibrational ground state have attracted a lot of interest recently due to their rich internal structure and the presence of large permanent dipole moments, which give rise to dipole-dipole interactions and offer the possibility to tune the interaction with static electric fields and microwave fields. 11,12,13,14,15,16 and cooling of polar molecules with the goal to create quantum degenerate ground state molecules are currently developed in several laboratories. 17,18,19,20,21,22,23 We show below that for an appropriate choice of static electric and microwave fields the effective interaction reduces to the form as in Eq.…”

“…Recently, systems of polar molecules in the rovibrational ground state have attracted a lot of interest recently due to their rich internal structure and the presence of large permanent dipole moments, which give rise to dipole-dipole interactions and offer the possibility to tune the interaction with static electric fields and microwave fields. 11,12,13,14,15,16 The techniques for trapping arXiv:cond-mat/0703688v1 [cond-mat.stat-mech] …”

Stabilization of a purely dipolar quantum gas against collapse

“…A clear subject for future studies is the dynamics of the dipolar collapse, which might show anisotropic features. Another remarkable property of a dipolar BEC in a pancake-shaped trap is the existence of a roton minimum in its Bogoliubov spectrum [18]. Furthermore, close to the collapse threshold, the existence of structured ground states is predicted [28,29], a precursor for the supersolid phase [30] that is expected to appear in dipolar BECs in three dimensional optical lattices.…”

“…The numerical prefactors in a dd are chosen such that a homogeneous condensate becomes unstable to local den- sity perturbations for a ≤ a dd [18]. As Chromium has a magnetic dipole moment of µ = 6µ B (µ B the Bohr magneton), a dd ≃ 15a 0 , where a 0 is the Bohr radius.…”

Erratum: Transverse Instability of Straight Vortex Lines in Dipolar Bose-Einstein Condensates [Phys. Rev. Lett.100, 240403 (2008)]

“…However, recent experiments on cold molecules [15], Rydberg atoms [16], and atoms with large magnetic moment [17], open a fascinating new research area, namely that of dipolar gases, for which the dipoledipole interaction (DDI) plays a significant or even dominant role. The DDI is long-range and anisotropic (partially attractive), and leads to fundamentally new physics in condensates [18,19,20], degenerated Fermi gases [21], and strongly-correlated atomic systems [22]. It leads to the Einstein-de Haas effect in spinor condensates [23], and may be employed for quantum computation [24], and ultra cold chemistry [25].…”