Pair scattering from time-modulated impurity in the Bose-Hubbard model

TL;DR

Addresses transport through a time-periodically driven impurity in a 1D attractive Bose-Hubbard chain. Combines exact real-time wave-packet dynamics with Floquet theory to study both single-particle and doublon transport through the driven impurity. In the high-frequency limit the single-particle transmission matches the Floquet prediction that renormalizes the hopping by the Bessel factor $\mathcal{J}_0(\lambda)$, and the doublon sector is described by a Floquet-Schrieffer-Wolff effective Hamiltonian with pair hopping $J_p=\frac{2J^2}{|U|}$, frequency-dependent couplings $\gamma_p$ and a triangular impurity potential $\mu_p$. Numerically, for large $|U|$ the doublon transport agrees with the effective theory, while for intermediate/weak $|U|$ pair breaking and dynamical localization near the impurity emerge, indicating breakdown of perturbation theory and the potential for engineered quantum transport. The work points to experimentally accessible regimes in ultracold atoms where impurity driving can filter or trap bosonic pairs and realize Floquet-bound-state-like phenomena.

Abstract

We investigate scattering phenomena in a one-dimensional attractive Bose-Hubbard model with a time-periodically modulated impurity. We analyze both single-particle and pair (doublon) transmission, exploring a range of interaction strengths and drive amplitudes. Our exact numerical results reveal excellent quantitative agreement with analytical predictions in the high-frequency limit. At intermediate and weak attractive interactions, we observe significant pair dissociation and the emergence of dynamically localized single-particle modes. These features are reminiscent of Floquet Bound States in the Continuum (BICs). These findings provide new avenues for engineering controllable quantum transport and localized states in ultracold atom experiments.

Figures (6)

• Figure 1: Single particle transmission as a function of the driving amplitude $\lambda$. The numerical results $T_s^n$ (red dots) are compared with the analytic results $T_{s,\hbar\omega\gg J}^n(k_0)$ in the high frequency limit Eq. \ref{['Eq:singleTransmission']} (solid black line) and the averaged analytic results Eq. \ref{['Eq:integralOverT']} (green dots). In the simulation we use $L=128$, $\hbar \omega = 50J$, $k_0 d=1.7$, $j_0=-30$ and $\sigma=12d$.
• Figure 2: Transmission $T^{\alpha}_p(k_0)$ as a function of the driving amplitude $\lambda$ for different interaction strengths when an on site pair has been created. Solid black line: results obtained using the Floquet-Schrieffer Wolff transformation ($\alpha=$FSW) given in Eq. (\ref{['Eq:pairexacttrans']}), blue circles: numerical result for the total transmission $\alpha=n$ (Eq. \ref{['Eq:transport']}), red circles: numerical result for pair transmission $\alpha=n(n-1)$ (Eq. \ref{['Eq:transport']}), solid green line: the analytic results of single particle transmission in the high frequency limit (Eq. \ref{['Eq:singleTransmission']}) for comparison. In our simulation we used $\left| U\right| /\hbar\omega =2.62$, $L= 100$, $\sigma=12d$ and $k_0 d=1.7$, $j_0=-25$, $\Delta t= 0.01\hbar/J$ and the maximum bond dimension is considered is 60.
• Figure 3: Evolution of the total density $\langle n_j \rangle$ of a pair wave packet as a function of site index $j$ and time $t$ for $U/J = -40$, $\lambda = 0.4$, $\left| U\right| /\hbar\omega =2.62$ , $L= 100$, $\sigma=12d$, $k_0 d=1.7$, $j_0=-25$, $\Delta t= 0.01\hbar/J$. The pair propagation is hardly affected by the impurity, and all particles are transmitted.
• Figure 4: Evolution of the total density $\langle n_j \rangle$ of a pair wave packet as a function of site index $j$ and time $t$ for $U/J = -40$, $\lambda = 6$, $\left| U\right| /\hbar\omega =2.62$ , $L= 100$, $\sigma=12d$, $k_0 d=1.7$, $j_0=-25$, $\Delta t= 0.01\hbar/J$. The incoming pair is almost completely reflected at the driven impurity.
• Figure 5: Site-resolved single-particle density $\langle n_j \rangle$ (blue) and pair density $\langle n_j(n_j - 1) \rangle$ (green) of propagating pair wave packet at various times for (a) $\lambda = 0.0$, (b) $\lambda = 0.4$, (c) $\lambda = 2.6$, (d) $\lambda = 6$. The parameters chosen are $U/J = -10$, $\left| U\right| /\hbar\omega =2.62$ , $L= 100$, $\sigma=12d$, $k_0 d=1.7$, $\Delta t= 0.01\hbar/J$.