Few-Boson Dynamics in Double Wells: From Single-Atom to Correlated Pair Tunneling

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.

Figure 1

Two-atom dynamics. (a) Relative population of the right-hand well over time, $p_{\mathrm{R}}(t)$, for different interaction strengths $g=0$ (solid line), $g=0.2$ (dashed line), $g=4.7$ (dotted line), and $g=25$ (dash-dotted line). (b) Snapshots of the one-body density $\rho (x)$ for different times $t$ in the fermionized case $g=25$. (All quantities are in harmonic-oscillator units throughout; see the text.)

Figure 2

Low-lying spectrum of two bosons in a double well as a function of the interaction strength $g$. Inset: Doublet formation with increasing $g$.

Figure 3

Top: Probability $p_2(t)$ of finding two atoms in the same well for $g=0$, 0.2, and 25. Bottom: Snapshots of the two-body correlation function ${\rho }_2(x_1,x_2)$ at equilibrium points, $\delta (t)=0$, for $g=0$ ($t=44$), $g=0.2$ ($t=128$), and $g=25$ ($t=53$)—from left to right.

Figure 4

Many-body effects in the fermionization limit ($g=25$). (a) Population of the right-hand well, $p_{\mathrm{R}}(t)$, for $N=3,4$ atoms initially in one well. Bottom: Density evolution $\rho (x;t)$ for $N-1=2$ atoms (b) and $N-1=3$ atoms (c) initially in the right-hand well if exactly one atom is present on the left.