Few-boson tunneling dynamics of strongly correlated binary mixtures in a double well

We explore the tunneling dynamics of strongly correlated bosonic mixtures in a one-dimensional double well. The roles of the inter- and intraspecies interactions and their interplay are investigated using the numerically exact multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is studied for three initial configurations: complete and partial population imbalance and a species-separated state. Increasing the interspecies interaction leads to a strong increase of the tunneling time period analogous to the quantum self-trapping for condensates. The intraspecies repulsion can suppress or enhance the tunneling period depending on the strength of the interspecies correlations as well as the initial configuration. Completely correlated tunneling between the two species and within the same species as well as mechanisms of species separation and counterflow are revealed. These effects are explained by studying the few-body energy spectra as well as the properties of the contributing stationary states.

Figure 1

Energy spectrum for $g_A=0.0$ and small interaction strengths $g_{AB}$.

Figure 2

Population of the right well (a) $n_A$ of species $A$ and (b) $n_B$ of species $B$ at $g_{AB}=0.2$ for different $g_A$ values.

Figure 3

Population in the right well (a) $n_A$ of species $A$ and (b) $n_B$ of species $B$ at $g_{AB}=5.0$ for different $g_A$ values.

Figure 4

One-particle density as obtained by taking into account the most important eigenstates contributing to the initial state for (a) species $A$ and (b) species $B$ for $g_{AB}=5.0$.

Figure 5

(a) Population in the right well of the total $n_R$ and the individual species $n_A$, $n_B$ for $g_{AB}=25.0$ $g_A=20.0$. (b) Pair and triple probability. $P_{AA}$, $P_{AB}$, and $P_{AAB}$ correspond to the probabilities of finding $AA$, $AB,$ and $AAB$ bosons in the same well, respectively.

Figure 6

Population of the right well (a) $n_A$ of species $A$ and (b) $n_B$ of species $B$ at $g_{AB}=0.2$ for different values of $g_A$ for a species-separated initial state. (c) Energy spectrum for $g_{AB}=0.2$.

Figure 7

Population of the right well $n_R$, $n_A$, and $n_B$ for $g_{AB}=25.0$, (a) $g_A=0.0$, (b) $g_A=5.0$, and (c) $g_A=20.0$ for the species-separated initial state.

Figure 8

Population in the right well $n_R$, $n_A$, and $n_B$ for $g_{AB}=0.2$ and for (a) $g_A=0.0$, (b) $g_A=0.2$, (c) $g_A=0.3$, and (d) $g_A=5.0$.

Figure 9

Population in the right well $n_R$, $n_A$, and $n_B$ for (a) $g_{AB}=5.0$ and $g_A=0.0$, (b) $g_{AB}=5.0$ and $g_A=4.0$, (c) $g_{AB}=25.0$ and $g_A=5.0$, and (d) $g_{AB}=25.0$ and $g_A=20.0$.