Few-boson tunneling in a double well with spatially modulated interaction

We study few-boson tunneling in a one-dimensional double well with a spatially modulated interaction. The dynamics changes from Rabi oscillations in the noninteracting case to a highly suppressed tunneling for intermediate coupling strengths followed by a reappearance near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations, we observe tunneling between the higher bands. The dynamics is explained on the basis of the few-body spectrum and stationary eigenstates. For a higher number of particles $N⩾3$, it is shown that the inhomogeneity of the interaction can be tuned to generate tunneling resonances. Finally, a tilted double well and its interplay with the interaction asymmetry are discussed.

Figure 1

Population of the right-hand well over time $p_R(t)$ for different interaction strengths at $\alpha =0.2$ for two bosons. Inset: Long-time behavior for very low interaction strength $g_0=0.005$. Barrier height $h=8$ and width $\omega =0.5$ have been used for all calculations. (All quantities are in dimensionless harmonic oscillator units throughout.)

Figure 2

(a) Two-particle energy spectrum as a function of the interaction strength $g_0$ for $\alpha =0.2$. Inset: Lowest-energy levels for low interaction strength. Bottom: Few-body energy spectrum with $g_0$ for (b) $\alpha =0$ and (c) $\alpha =0.2$.

Figure 3

Population of the right well over time $P_R(t)$ at $g_0=0.2$ for different $\alpha$ values. Inset: Variation of maximum population of the right well $P_R^{max}$ with $\alpha$ for $g_0=0.2$.

Figure 4

(a) Population variation with time $P_R(t)$ at $g_0=25$ and $\alpha =1$ for $P_R(0)=1$ (i.e., initially populating the right well). (b) Energy spectrum for $\alpha =1$.

Figure 5

(a) Population of the right-hand well over time $P_R(t)$, for three bosons for different interaction strengths at $\alpha =0.2$. (b) Three-boson energy spectrum at $\alpha =0.2$.

Figure 6

Population of the right well over time $P_R(t)$ at $g_0=0.2$ for different $\alpha$ values for (a) three particles and (b) four particles. Inset: Variation of maximum population of the right well $P_R^{max}$ with $\alpha$ for $g_0=0.2$.

Figure 7

Three-particle energy levels for $0<g_0<0.3$ for (a) $\alpha =0$, (b) $\alpha =0.04$, and (c) $\alpha =0.5$.

Figure 8

Temporal evolution of (a) pair probability and (b) three-particle probability at $\alpha =0$ and $\alpha =0.5$ for $N=3$ and $g_0=0.2$.

Figure 9

Variation of (a) tunneling maximum $P_L^{max}$ with tilt $d$, (b) maximum single-particle probability ${\mathrm{p̄}}_1$ with tilt $d$ for $N=2$, $g_0=0.2$, and $\alpha =0.2$.

Figure 10

Two-particle energy spectrum with tilt $d$ for $\alpha =0.2$ and $g_0=0.2$.