Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential

The quantum self-trapping phenomenon of a Bose-Einstein condensate (BEC) represents a remarkable nonlinear effect of wide interest. By considering a purely dipolar BEC in a double-well potential, we study how the dipole orientation affects the ground-state structure and the transition between self-trapping and Josephson oscillations in dynamics. Three-dimensional numerical results and an effective two-mode model demonstrate that the onset of self-trapping of a dipolar BEC can be radically modified by the dipole orientation. We also analyze the failure of the two-mode model in predicting the rate of Josephson oscillations. We hope that our results can motivate experimental work as well as future studies of self-trapping of ultracold dipolar gases in optical lattices.

Figure 1

(Color online) Column density of the ground-state density profile $\int {\mid \Psi \left(\mathbf{r}\right)\mid }^{2}dx$ for two different angles $\phi$.

Figure 2

(Color online) The ground-state energy and chemical potential as well as the population difference between the two wells as functions of $\phi$.

Figure 3

(Color online) Column density of the condensate. (a) For the dipole orientation angle $\phi =\pi ∕4$, the population is mainly trapped in the left well instead of tunneling between the two wells. (b) Changing only the dipole orientation parameter to $\phi =5\pi ∕12$, the tunneling between the two wells, or the Josephson oscillation, is observed. See the text for other system parameters.

Figure 4

(a) Population imbalance $S\left(t\right)$ versus time for different values of the dipole orientation parameter $\phi$. As $\phi$ exceeds a critical value ${\phi }_c\approx 0.37\pi$, the population imbalance starts to oscillate around zero. (b) Time-averaged $S\left(t\right)$ as a function of the dipole orientation parameter $\phi$. When $\phi$ exceeds ${\phi }_c$, the time-averaged population imbalance suddenly decreases to zero. The transition between Josephson oscillations and quantum self-trapping can hence be manipulated by tuning the dipole orientation. Other system parameters are the same as those used in Fig. 1.

Figure 5

(Color online) (a) Values for the two-mode model parameters $A_{11}$, $A_{22}$, $B_{12}$, and $\kappa$ as functions of the dipolar orientation parameter $\phi$, calculated by first fitting the Gaussian ansatz in (16) with the time-averaged properties of the density profile in our three-dimensional simulations. (b) Value of $\Lambda$ calculated from Eq. (14b) and value of ${\Lambda }_c$ calculated from Eq. (15) with $\varphi \left(0\right)=0$ as a function of the dipolar orientation parameter $\phi$. Note that for $\phi <{\phi }_c\approx 0.39\pi$, $\Lambda >{\Lambda }_c$, and for $\phi >{\phi }_c$, $\Lambda <{\Lambda }_c$.