Stabilization of a purely dipolar quantum gas against collapse

Abstract

We report on the experimental observation of the dipolar collapse of a quantum gas which sets in when we reduce the contact interaction below some critical value using a Feshbach resonance. Due to the anisotropy of the dipole-dipole interaction, the stability of a dipolar Bose-Einstein condensate depends not only on the strength of the contact interaction, but also on the trapping geometry. We investigate the stability diagram and find good agreement with a universal stability threshold arising from a simple theoretical model. Using a pancake-shaped trap with the dipoles oriented along the short axis of the trap, we are able to tune the scattering length to zero, stabilizing a purely dipolar quantum gas.Interactions between atoms dominate most of the properties of quantum degenerate gases [1]. In the ultracold regime these interactions are usually well described by an effective isotropic zero-range potential. The strength and sign of this contact interaction is determined by a single parameter, the scattering length a. The contact interaction is responsible for a variety of striking properties of quantum gases. Strongly influencing the excitation spectrum of the condensate it gives rise to e.g. the superfluidity of Bose-Einstein condensates (BEC) or the existence of vortex lattices. The contact interaction also plays a crucial role in the physics of strongly correlated systems like in the BEC-BCS crossover [2] or in quantum phase transitions like the Mott insulator transition [3].Another fundamental topic is the question of the existence of a stable ground state depending on the modulus and sign of the contact interaction. In the homogeneous case repulsive contact interaction (a > 0) is necessary for the stability of the BEC. In contrast, if the contact interaction is attractive (a < 0), the BEC is unstable. This instability can be prevented by an external trapping potential. The tendency to shrink towards the center of the trap is in that case counteracted by the repulsive quantum pressure arising from the Heisenberg uncertainty relation. Detailed analysis [4] yields that a condensate is stable as long as the number of atoms N in the condensate stays below a critical value N crit given bywhere a ho is the harmonic oscillator length and k is a constant on the order of 1/2. This scaling, as well as the collapse dynamics for N > N crit , have been studied experimentally with condensates of 7 Li [5, 6] and 85 Rb [7,8]. In [9, 10] the atom number dependance of the collapse of mixtures of bosonic 87 Rb and fermionic 40 K quantum gases has been investigated. Being anisotropic and long-range, the dipole-dipole interaction (DDI) differs fundamentally from the contact interaction. Besides many other properties, the stability condition therefore changes in a system with a DDI present. Considering the case of a purely dipolar condensate with homogeneous density polarized by an external field, one finds that due to the anisotropy of the DDI, the BEC is unstable, independent of how small the dipole moment is [11]. As in the ...

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“…We solve the 3D GP equation (3) numerically by the split-step Crank-Nicolson method [28] for a dipolar BEC [27,30] using both real-and imaginary-time propagation in Cartesian coordinates employing a space step of 0.025 and a time step upto as small as 0.00001. In numerical calculation, we use the parameters of 52 Cr atoms [26], e.g., a dd = 15.3a 0 and m = 52 amu with a 0 the Bohr radius. We take the unit of length l = 1 µm, unit of time τ ≡ ml 2 /h = 0.82 ms and the unit of energyh 2 /(ml 2 ) = 1.29 × 10 −31 J.…”

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