Spatial coherent transport of interacting dilute Bose gases

We investigate coherent atomic tunneling of a dilute gas Bose-Einstein condensate (BEC) in a three-well system. In particular, we generalize stimulated Raman adiabatic passage (STIRAP) to adiabatically transport a BEC of 2000 ${}^7\mathrm{Li}$ atoms between two wells with minimal occupation in the intervening well. This protocol paves the way for a robust method of control in atom-optical devices.

Figure 1

(Color online) Macroscopic matter-wave transport without transit of a BEC in a three-well system. (a) Schematic representation of our system at $t=0$ in the $\left(z\text{−}y\right)$ plane. Two parallel, repulsive Gaussian barriers embedded in an ambient harmonic trap divide the system into three wells, with the BEC initially occupying well 1. (b) Isosurface plots of atomic density ($n_{\mathrm{iso}}=0.1n_0$, where $n_0$ is the initial peak density of the BEC) showing the adiabatic transportation of a BEC of 2000 ${}^7\mathrm{Li}$ atoms over a distance of $20\mathrm{\mu }\mathrm{m}$ [simulated using the three-dimensional (3D) Gross-Pitaevskii equation].

Figure 2

(Color online) System dynamics according to three-mode analysis. (a) Energies of the eigenmodes $D_{+}$, $D_0$, and $D_{-}$ of the noninteracting $(g_m=0)$ system. (b) Evolution of $N_1\left(t\right)∕N_T$ and $N_3\left(t\right)∕N_T$ for $g_m=0$ and $t_{\mathrm{p}}\to \infty$. (c) $N_3\left(t_{\mathrm{p}}\right)∕N_T$ as a function of $g_m$ and $t_p$, with white and black representing $N_3\left(t_{\mathrm{p}}\right)∕N_T=1$ and $0$, respectively. (d) $\max \left[N_2\right(t)∕N_T]$ as a function of $g_m$ and $t_{\mathrm{p}}$, with white and black representing $N_2\left(t_{\mathrm{p}}\right)∕N_T=0$ and $1$, respectively. In (c) and (d) the solid black and blue/gray curves represent $N_3\left(t_{\mathrm{p}}\right)∕N_T=0.99$ and $\max \left[N_2\right(t)∕N_T]=0.01$, respectively, and the region bounded by both corresponds to high fidelities $ϵ\ge 0.99$. We have assumed $E_1^0=E_3^0=0$ and $E_2^0=0.1\hslash {\Omega }_{\max }$ throughout.

Figure 3

(Color online) Dynamics of the system according to the 1D GPE. (a) Carpet plot showing the evolution of condensate density (dark=high density, light=low density) for an effective 1D interaction parameter of $g_{1D}=0.31$ and a pulse time of $t_{\mathrm{p}}=1000∕{\omega }_z$. (b) As (a) but for a small pulse time of $t_{\mathrm{p}}=14∕{\omega }_z$. Note the breakdown of the adiabatic transfer. (c) Evolution of the radially integrated axial density for the counter-intuitive protocol for a realistic BEC of $2000$ ${}^7\mathrm{Li}$ atoms with attractive interactions $a=-0.2\mathrm{nm}$. The horizontal dashed lines correspond to the center of the Gaussian barriers $\pm z_0$. We assume $\omega =2\pi \times 40\mathrm{Hz}$, $\sigma =1\mathrm{\mu }\mathrm{m}$, $z_0=3\mathrm{\mu }\mathrm{m}$, $V_{\max }=100\hslash \omega$, and $V_{\min }=5\hslash \omega$.