Expansion dynamics of a spherical Bose–Einstein condensate*

Abstract

We experimentally and theoretically observe the expansion behaviors of a spherical Bose-Einstein condensate. A rubidium condensate is produced in an isotropic optical dipole trap with an asphericity of 0.037. We measure the variation of the condensate size during the expansion process. The free expansion of the condensate is isotropic, which is different from that of the condensate usually produced in the anisotropic trap. The expansion in the short time is speeding and then after a long time the expansion velocity asymptotically approaches a constant value. We derive an analytic solution of the expansion behavior based on the spherical symmetry, allowing a quantitative comparison with the experimental measurement. The interaction energy of the condensate is gradually converted into the kinetic energy at the beginning of the expansion and the kinetic energy dominates after a long-time expansion. We obtain the interaction energy of the condensate in the trap by probing the expansion velocity, which is consistent with the theoretical prediction.

Concept study and preliminary design of a cold atom interferometer for space gravity gradiometry

“…The created BEC is immediately magnetically displaced up to a distance of about 5 mm away from the chip surface (frame b in figure 1) using the external magnetic coils and shortcut-toadiabaticity protocols as proposed in [42] and implemented in [43], allowing to reduce the duration of this transport down to about 200 ms. The geometry of the displaced trap can be tailored, thanks for instance to several layers of Z-shaped wires on the chip, to be almost spherically symmetric [44], with a final trapping frequency of about 15 Hz. These fast transports have the feature of inducing very low residual dipole oscillations in the final trap, which is an essential ingredient for the next steps.…”

Effective self-similar expansion of a Bose-Einstein condensate: Free space versus confined geometries

“…Remarkably, the final value λ f (g) decreases by increasing the nonlinear coupling, and it has a slight minimum at the crossover region between the noninteracting and hydrodynamic regimes. The first behavior is directly connected to the power law in the scaling equation 17: In the TF limit the right-hand side behaves like ∝λ −4 [9], and this implies a slower growth of λ (>1) as compared to the ∝λ −3 behavior of the noninteracting limit. This reflects the fact that asg is increased, the density distribution gets wider and this narrows the momentum distribution, thus reducing the contribution of kinetic energy to the condensate expansion.…”

“…Self-similarity is a remarkable property that plays a key role for describing the dynamics of several ultracold atomic systems. It characterizes the free expansion and the collective excitations of Bose-Einstein condensates both in the noninteracting and the hydrodynamic regimes [1][2][3][4][5][6][7][8][9], the expansion of a one-dimensional Bose gas in the mean-field Thomas-Fermi regime and in the Tonks-Girardeau regime [10], of a superfluid Fermi gas [7,11,12], and of a thermal cloud [13]. Recently, motivated by the experiment reported in Ref.…”

“…In the present paper we extend this analysis to the case of a three-dimensional (3D) BEC [21] for which we consider the expansion in free space and in trapped geometries (namely in cylindrical and planar waveguides). The aim of this work to understand in a quantitative framework how nonlinearity affects self-similar dynamics, in the context of the GP equation, for which scaling approaches have been widely employed [1][2][3][4][5][6][7]9,20]. This is particularly relevant in 3D-where the interplay between spatial anisotropies and interactions may not be trivial-and where there are not actual proofs that justify the usage of an effective scaling approach.…”

Interacting quantum mixtures for precision atom interferometry

“…To simplify the description of the dual-species theoretical treatment of its dynamics, we choose the external trap to be harmonic and isotropic as it could be realised by crossed optical traps for example [89]. For the atom number in species i (i = 1 for Rb and i = 2…”