Erratum: Bright Solitonic Matter-Wave Interferometer [Phys. Rev. Lett. 113, 013002 (2014)]

Figure 1

Fringe visibility as a function of the $s$-wave scattering length $a$ for a $T=2\mathrm{ms}$ Mach-Zehnder atom interferometer in an optical waveguide.

Figure 2

Figure from original manuscript. (a) Longitudinal width of a matter wave as a function of the scattering length, measured after 90 ms of free expansion in the guide. The green dashed lines are to guide the eye. The soliton parameter $a_s=-2.3a_0$ is seen to minimize this expansion. (b) Comparison of the longitudinal expansion along the guide for three different scattering lengths: the repulsive self-interaction of $a=300a_0$, the low interaction case of $a=30a_0$, and the soliton parameter $a_s=-2.3a_0$. The dashed lines are parabolic fits to extract the acceleration of the cloud width. For $a=a_s$ this acceleration is consistent with zero. The error bars shown in both (a) and (b) are statistical.

Figure 3

Figure from original manuscript. (a) Each interferometric fringe is fitted to a function $N_{\text{rel}}=(\mathcal{V}/2)\cos (\varphi +\mathrm{\Phi })+c$ to extract the fringe visibility $\mathcal{V}$ and interferometric phase $\mathrm{\Phi }$. The data shown here are the interference fringe for a soliton, with $a=a_s$. (b) Fringe visibility (open circles) as a function of the $s$-wave scattering length $a$ for a $T=1\mathrm{ms}$ Mach-Zehnder atom interferometer. The red dashed lines are to guide the eye. A dramatic increase in the fringe visibility is seen at the soliton parameter $a_s\approx -2.3a_0$ for our system. Inset: the interferometric phase $\mathrm{\Phi }$ for various $a$. (c) Fringe visibility as a function of the interferometer time $T$. The results for a weakly interacting interferometer with $a=30a_0$ (filled green squares), and the soliton interferometer with $a=a_s=-2.3a_0$ (open circles) are shown. The Gaussian fits provide half-maximum decay times of 0.9 ms (green dashed line) and 2.3 ms (solid purple line), respectively. The solitonic matter-wave optimizes the fringe visibility at all times we have tested. Inset: measured interferometric phase $\mathrm{\Phi }$ for the soliton interferometer as a function of $T$, along with a quadratic fit. All uncertainties in (b) and (c) are $1\sigma$ confidence intervals of the fit to each interferometric fringe.