Interspecies tunneling in one-dimensional Bose mixtures

We study the ground-state properties and quantum dynamics of few-boson mixtures with strong interspecies repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter, and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intraspecies repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the back action of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: by varying the degree of localization of the “barrier” atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons), this leads to the tunneling of attractively bound pairs.

Figure 1

(Color online; dimensionless harmonic oscillator units $a_A$ throughout) Top: Influence of the mass ratio $\alpha$ on a system with $g_{\sigma }=0$, $g_{\mathit{AB}}=25$, $N_A=N_B=2$. One-particle densities of the $A$ bosons (left) and the $B$ bosons (right) for a varying mass ratio $\alpha$ (be aware of the different scales in the plots). Bottom: Two-body density ${\rho }_{\mathit{AB}}^{(2)}(x_1,x_2)$ for $\alpha =1,0.5,0.1$ (from left to right).

Figure 2

In the limit of a vanishing mass ratio $\alpha =0.001$, the lighter $N_A=4$ bosons develop from an uncorrelated profile (red, —), over a widened distribution (green, - - -) to a fermionized state (blue, $\dots$) for an increasing intraspecies interaction $g_A$ and strong interspecies repulsion $g_{\mathit{AB}}=25$, while the density of the $B$ bosons represents an effective barrier for the lighter species (magenta, short-dotted central peak) that barely changes for different $g_A$.

Figure 3

Two-body density ${\rho }_{\mathrm{AA}}^{(2)}(x_1,x_2)$ of the lighter $A$ species for $N_A=4$, $N_B=1$ bosons, and a mass ratio $\alpha =0.001$ with fixed $g_{\mathit{AB}}=25$ and increasing $g_A=0$, 0.5, 25 (from left to right).

Figure 4

Beyond the static barrier: Two-body density ${\rho }_{\mathrm{AA}}^{(2)}(x_1,x_2)$ for $N_A=4$ and $N_B=1$ bosons for (top) $g_A=0$, with increasing mass ratios $\alpha =0.001,0.002,0.02$ (from left to right), and for (bottom) $g_A=0.5$, $\alpha =0.001,0.12,0.2$.

Figure 5

Evolution of a system with $g_A=25$, $g_{\mathit{AB}}=25$, $N_A=4,N_B=1$. Top: One-particle densities for increasing $\alpha$ of the (left) $A$ bosons and (right) $B$ bosons (be aware of the different scales in the plots). Bottom: Two-body correlation function ${\rho }_{\mathrm{AA}}^{(2)}(x_1,x_2)$ for $\alpha =0.9,1.0,1.1$ (from left to right).

Figure 6

Interspecies tunneling dynamics of noninteracting ($g_A=0$) $N_A=2$ bosons through a strongly repulsive $B$ atom $(g_{\mathit{AB}}=8)$: Top: Evolution of the population of the $A$ bosons for increasing mass ratios $\alpha =0.001,0.01,0.122$ (from left to right). Middle: Same as above but for the $B$ boson. Bottom: (a) Relative population of the right-hand side over time, $p_{A,R}(t)$; (b) probability $p_{A,2}(t)$ of finding two $A$ atoms on the same side for $\alpha =0.001$ (red, —), $\alpha =0.01$ (green, - - -), and $\alpha =0.12$ (blue, $\dots$)

Figure 7

Spectrum for $N_A=2$ and $N_B=1$ bosons with varying $\alpha$. Top: $g_A=0$. Middle: $g_A=0.5.$ Bottom: $g_A=25$. $g_{\mathit{AB}}=25$ throughout.

Figure 8

Interspecies tunneling dynamics of $N_A=2$ bosons with intraspecies interaction $g_A~0.5$ through a strongly repulsive $B$ atom $(g_{\mathit{AB}}=8)$ and increasing mass ratios $\alpha =0.001$ (red, —), $\alpha =0.01$ (green, - - -), and $\alpha =0.12$ (blue, $\dots$). Top: Relative $A$ population $p_{A,R}(t).$ Bottom: Pair probability $p_{A,2}(t).$

Figure 9

Interspecies tunneling dynamics of $N_A=2$ fermionized bosons ($g_A=25$) through a strongly repulsive $B$ atom $(g_{\mathit{AB}}=8)$ and increasing mass ratios $\alpha =0.001$ (red, —), $\alpha =0.01$ (green, - - -), and $\alpha =0.12$ (blue, $\dots$). Top: Normalized $A$ population $p_{A,R}(t).$ Bottom: Pair probability $p_{A,2}(t).$

Figure 10

Interspecies tunneling dynamics of $N_A=2$ bosons through $N_B=2$ atoms for $(g_{\mathit{AB}}=8),g_{\sigma }=0$ and increasing mass ratios. Normalized $A$ population $p_{A,R}(t)$ for $\alpha =0.001$ (red, —), $\alpha =0.02$ (green, - - -), and $\alpha =0.12$ (blue, $\dots$).

Figure 11

Interspecies tunneling dynamics of $N_A=3$ bosons through a strongly repulsive $B$ atom $(g_{\mathit{AB}}=8)$ and increasing mass ratios. Relative $A$ population $p_{A,R}(t)$ for $\alpha =0.001$ (red, —), $\alpha =0.01$ (green, - - -), and $\alpha =0.12$ (blue, $\dots$).(a) $g_A=0$, inset shows the long-time behavior for $\alpha =0.12$, (b) $g_A=0.5$, (c) $g_A=25$, inset shows the long-time behavior for $\alpha =0.12$.