Interferences in the Density of Two Bose-Einstein Condensates Consisting of Identical or Different Atoms

The density of two initially independent condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and (2) each condensate consists of a different kind of atoms. Illustrative examples are presented.

Figure 1

The density $\rho (x,t)$ of two BECs of 500 atoms each for $\lambda =0.1$ as a function of time computed with TDMF(2) (black) compared to the density ${\rho }_{LL}+{\rho }_{RR}$ of two BECs which do not interact with each other, each computed with the Gross-Pitaevskii equation (red). The quantities shown are dimensionless. For more details see text.

Figure 2

The density of two BECs each made of 500 atoms of a different kind computed with TDCGP(2) for ${\lambda }_L={\lambda }_R=0.1$ and ${\lambda }_{LR}=0.2$ at $t=8$ (black). For comparison also the analogous result for identical particles computed with TDMF(2) (for details see Fig. 1) is shown (red). The lower panel shows the respective subdensities $N_L|{\psi }_L{|}^2$ for distinguishable atoms (black) and $N_R|{\psi }_R{|}^2$ for identical particles (red).

Figure 3

The density of two BECs each made of 500 atoms of a different kind. Upper panel: repulsive interaction of the two BECs, ${\lambda }_L={\lambda }_R=0$, ${\lambda }_{LR}=+0.2$. Middle panel: attractive interaction of the two BECs, ${\lambda }_L={\lambda }_R=0$, ${\lambda }_{LR}=-0.2$. Lower panel: ${\lambda }_L={\lambda }_R={\lambda }_{LR}=0.1$.