Stability and dynamical property for two-species ultracold atoms in double wells

We study undistinguishable two-species Bose-Einstein condensates (BECs) trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling strength in the adiabatic Rosen-Zener type effectively. Starting from two typical initial states, we study the evolution of the system and find that the interspecies interaction can produce totally distinct results, which is expected to provide a route to manipulate the BEC distribution.

Figure 1

(Color online) Equations (5) plotted for different values of $U$, $U_{ab}$, and $J$ in the $(z_a,z_b)$ plane for $({\varphi }_a,{\varphi }_b)=(\pi ,\pi )$. The black curve and the gray curve correspond to the first and the second equation of Eq. (5), respectively. The intersections of the two curves stand for the fixed points solutions. The conditions for the existence of each panel are (a) $0<2J<(U-U_{ab})\sqrt{(U-U_{ab})∕(U+U_{ab})}$, (b) $(U-U_{ab})\sqrt{(U-U_{ab})∕(U+U_{ab})}<2J<(U-U_{ab})$, (c) $(U-U_{ab})<2J<(U+U_{ab})$, and (d) $2J>(U+U_{ab})$.

Figure 2

(Color online) The stability diagrams of fixed points in the $(U_{ab},J)$ space for $({\varphi }_a,{\varphi }_b)=(\pi ,\pi )$. Here $U_{ab}$ and $J$ are in units of $U$. Panels (a)–(d) correspond to fixed points S, An, I, and As, respectively. The lined areas refer to the parameter space for the existence of each kind of fixed points, and the grayed areas to the stable region for those fixed points accordingly.

Figure 3

Schematic plot of $J_{\mathit{eff}}$ as a function of $t$.

Figure 4

Multiple stability diagram of the fixed points in the $(U_{ab},J)$ space for $({\varphi }_a,{\varphi }_b)=(\pi ,\pi )$ which is formed by projecting all four panels of Fig. 2 into one. The $(U_{ab},J)$ space is divided into four regions I–IV which correspond to Figs. 1a, 1b, 1c, 1d, respectively; and for given $U_{ab}$, there exist three critical values of $J$: $J_{c1}$, $J_{c2}$, and $J_{c3}$, accordingly.

Figure 5

Time dependence of the particle distribution difference (PDD) for each species between the two wells for the symmetrical initial state $(z_a,z_b)=(1,1)$. The parameters are $U=2$, $U_{ab}=0.4U$, ${\omega }_{\mathit{hf}}=25U$, and $T=6000∕U$. In this case $J_{c3}=0.7U$. (a) $J=0.4U$, (b) $J=0.6U$, (c) $J=0.75U$, and (d) $J=0.8U$.

Figure 6

Time dependence of the particle distribution difference (PDD) for each species between the two wells for the antisymmetrical initial state $(z_a,z_b)=(1,-1)$. The parameters are $U=2$, ${\omega }_{\mathit{hf}}=25U$, and $T=6000∕U$. (a) $U_{ab}=0.6U$ and $J=0.35U$, (b) $U_{ab}=0.005U$ and $J=0.49U$, (c) $U_{ab}=0.005U$ and $J=0.4965U$, (d) $U_{ab}=0.005U$ and $J=0.5U$, (e) $U_{ab}=0.005U$ and $J=0.565U$, (f) $U_{ab}=0.005U$ and $J=0.57U$, (g) $U_{ab}=0.005U$ and $J=0.575U$, and (h) $U_{ab}=0.005U$ and $J=0.85U$.