Creation and Detection of a Mesoscopic Gas in a Nonlocal Quantum Superposition

We investigate the scattering of a quantum matter wave soliton on a barrier in a one-dimensional geometry, and we show that it can lead to mesoscopic quantum superposition states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition, and we discuss in detail the experimental feasibility.

Figure 1

Evolution of the center of mass wave function of a solitonic gas with $N=99$ atoms, by integration of (16) for the initial condition (15), with $\Delta K\simeq 0.093K_0$, $X_0=-15\xi$. Left panel: $|\Phi (X,t){|}^2$ (solid lines); effective potential $\overline{V}(X,t)$ (dashed lines). Right panel: modulus of the Fourier transform $s(Q,t)$ of $|\Phi (X,t){|}^2$; the vertical lines are in $Q=\pm 2K_0$. The time is in units of $ML/\hslash K_0$ (here $L=80\xi$). At $t=0.63$ the state is a nonlocal superposition. At $t=1.31$ the two reflected spatial components strongly interfere; two narrow peaks of height 0.315 emerge on $|s(Q)|$ in $Q=\pm 2K_0$. Maximal interference occurs at $t=1.36$. The last line is an average over a Poisson distribution for $N$, with a mean value $\overline{N}=99$; the peak height in $|s(Q)|$ is reduced to 0.062.