Condensate Splitting in an Asymmetric Double Well for Atom Chip Based Sensors

We report on the adiabatic splitting of a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms by an asymmetric double-well potential located above the edge of a perpendicularly magnetized TbGdFeCo film atom chip. By controlling the barrier height and double-well asymmetry, the sensitivity of the axial splitting process is investigated through observation of the fractional atom distribution between the left and right wells. This process constitutes a novel sensor for which we infer a single shot sensitivity to gravity fields of $\delta g/g\approx 2\times {10}^{-4}$. From a simple analytic model, we propose improvements to chip-based gravity detectors using this demonstrated methodology.

Figure 1

Schematic showing the corrugated potential above the edge of the TbGdFeCo film. A double well can be used to axially split a BEC by increasing $B_{\mathrm{bias}}$. The corrugated potential is due to the presence of inhomogeneity in the magnetic film.

Figure 2

Characterization of the double well as a function of trap-surface separation is performed using two component clouds. The dashed lines in (a) and (b) are to guide the eye. The well separation $\lambda$, barrier height $\beta$, and trap asymmetry $\Delta$ are shown schematically in (c).

Figure 3

Results of pulsed radio-frequency spectroscopy performed on a condensate which has been split symmetrically and then exposed to a large asymmetry. The shift in the output coupled spectra yields a measure of $\Delta$.

Figure 4

Fractional number difference versus the double-well potential asymmetry. The asymmetry is varied by randomly changing the end wire current imbalance $\delta I$. The experimental data points (open circles) and the line of best fit (dashed line) compare well with the simple analytic result (solid line).

Figure 5

The asymmetric double well is represented by two identical harmonic traps offset by $\Delta$ with a ground state which obeys $\mu ={\mu }^{\prime }+\Delta$ (a). From this model, we can extract the dependence of the fractional number difference on $\Delta$ for increasing atom number (b). In the standard quantum limit, the sensitivity improves as $N^{-0.1}$ as shown for two trap conditions (c).