Phase Separated BEC for High-Sensitivity Force Measurement

A trapped, phase separated, two component Bose-Einstein condensate (BEC) can be configured to give a single BEC bubble that floats freely in the surrounding BEC. We point out that this system gives a unique template to carry out mesoscopic quantum studies and to detect weak forces. We demonstrate the detection capabilities by proposing and studying a “quantum level” for fundamental quantum fluctuation studies and for mapping the potential energy landscape near a surface with exquisite accuracy.

Figure 1

Schematic of the proposed BEC level device. The bubble of BEC-$B$ (represented by a sphere) is confined within the BEC-$A$ sea (shown by the ellipsoid). The arrow along the axis of the ellipsoid is the direction of the external force that causes the bubble to be displaced from the center of the ellipsoid. This displacement can be measured by a laser configuration as shown in the figure.

Figure 2

Comparison of an analytical calculation that neglects the surface tension and the numerical GP solution. In (a) the half axial length $L$ of the bubble is plotted as a function of $N_A$ for $N_B=2\times {10}^4$, $\alpha =0.9$, $\xi =0.01$, $\beta =0.9$, and $a_A=0.001$, (b) the density profile obtained numerically for $N_A={10}^5$ is shown, and (c) shows the magnified view of the interface region in (b). The green line indicates the boundary between BEC-$A$ and $B$ obtained in (a).

Figure 3

Density of BEC-$A$ is shown as a surface plot for $\overline{\gamma }=0.1$. The subplots top, middle, and bottom correspond to $\alpha \sqrt{{\lambda }_B/{\lambda }_A}=0.90$, 0.93, and 0.95, respectively. The BEC-$B$ bubble is located within BEC-$A$ where ${\rho }_A(\mathbf{r})=0$.

Figure 4

Density profile of the quasi-1D BEC-$B$ for different values of $N_A$. The topmost figure shows the trapping potential while the remaining four plots (from top to bottom) correspond to $N_A=0$, 1000, 1500, and 2000.