Coherent single atom shuttle between two Bose-Einstein condensates

We study an atomic quantum dot representing a single hyperfine “impurity” atom which is coherently coupled to two well-separated Bose-Einstein condensates, in the limit when the coupling between the dot and the condensates dominates the intercondensate tunneling coupling. It is demonstrated that the quantum dot by itself can induce large-amplitude Josephson-like oscillations of the particle imbalance between the condensates, which display a two-frequency behavior. For noninteracting condensates, we provide an approximate solution to the coupled nonlinear equations of motion which allows us to obtain these two frequencies analytically.

Figure 1

(Color online) Large amplitude Josephson-like oscillations around zero particle imbalance, $n=0$, for $N_0=1000$, $\beta =10$, initial $n\left(0\right)=0.6$ and initial phase difference $\varphi \left(0\right)=\pi$ for (a) $\alpha =0.01$ and (b) $\alpha =0.1$ [where crossover to a self-trapped state has occured for $\Gamma =0$]. Black solid curve: $\Gamma =0$, red (thin gray) curve: $\Gamma =0.05$. In (a), we display in addition the noninteracting case $(\alpha =0)$ with $\Gamma =0$ in green (thick gray). We assume throughout our calculations that there is initially one particle in the dot, $s_z\left(0\right)=1$ and that the initial particle imbalance $n\left(0\right)=0.6$; time is in units of $T^{-1}$.

Figure 2

(Color online) The critical value of the scaled interaction $\alpha ={\alpha }_c$ for self-trapping of the effective Josephson oscillations, as a function of the scaled detuning $\beta$, for a $\varphi \left(0\right)=0$ junction (black dots) and $\varphi \left(0\right)=\pi$ junction (red squares), with $N_0=1000$, $\Gamma =0$, and $n\left(0\right)=0.6$. Within the shaded areas, the system shows Josephson-like oscillations, while inside the white area, it is self-trapped.

Figure 3

(Color online) Particle number dependence of induced oscillations for vanishing conventional tunneling rate, $\Gamma =0$, for $N_0=100$ (black, I), $N_0=300$ (red, II), and $N_0=1000$ (green, III). Parameters are $\beta =10$ and $\alpha =1$. The initial phase difference is (a) $\varphi \left(0\right)=0$ and (b) $\varphi \left(0\right)=\pi$; time is again in units of $T^{-1}$.

Figure 4

(Color online) Possible experimental setup for an atomic quantum dot coupled to BECs on a microchip (light blue). A standing laser wave (green) creates deep potential wells perpendicular to the chip surface, equivalent to an optical potential for all hyperfine states of the atoms. Two crossed conductors on the chip (yellow) create a tight magnetic potential for one hyperfine species (red) causing a large gap $U_{dd}$ for double occupation of the dot. An additional laser (not shown) couples the impurity atom (red) and the condensates (dark blue), resulting in the transfer coupling $T$.