Double-slit interferometry with a Bose-Einstein condensate

A Bose-Einstein “double-slit” interferometer has been recently realized experimentally by Y. Shin et al., Phys. Rev. Lett. 92 050405 (2004). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevskii equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong degradation of the interference pattern observed experimentally. The role of quantum fluctuations is discussed.

Figure 1

Double-well potential in the $x$ direction. (a) The initial condensate with a distance between the two wells of $x_0=3\mu \mathrm{m}$ and the chemical potential higher than the barrier height. (b) Displaced wells in a time $t=t_{\mathit{ramp}}$ with $x_0\left(t_{\mathit{ramp}}\right)=6.5\mu \mathrm{m}$. In this configuration we have two independent condensates.

Figure 2

Contour plots of the probability density integrated over the $y$ coordinate $P_y(x,z,t)$ from 3D simulations for $t_{\mathit{hold}}=10.6\mathrm{ms}$ and $t_{\mathit{\text{free}}}=5.3\mathrm{ms}$, as a function of the ramping time $t_{\mathit{ramp}}$: (a) 2.7 ms, (b) 5.3 ms, (c) 10.6 ms, and (d) 21.2 ms.

Figure 3

Contour plots of the probability density integrated over the $y$ coordinate $P_y(x,z,t)$ for $t_{\mathit{ramp}}=5.3\mathrm{ms}$ and $t_{\mathit{\text{free}}}=5.3\mathrm{ms}$ as a function of the hold time $t_{\mathit{hold}}$: (a) 0, (b) 5.3 ms, (c) 10.6 ms, and (d) 21.2 ms.

Figure 4

Contour plot of the interference fringes calculated in TF approximation. The density is averaged over several experiments, according to Eq. (6). The quantum dynamics determines a phase uncertainty $\sigma$: (A) $\sigma =0$, (B) $\sigma =1$, (C) $\sigma =2$, (D) $\sigma =3$.