Self-trapping of excitations: Two-dimensional quasiparticle solitons in an extended Bose-Hubbard dimer array

Considering a two-dimensional (2D) Bose-Hubbard spinor lattice with weak nearest-neighbor interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer to the rest of the lattice. Beyond a critical interaction strength, low-energy on-site excitations are quickly dispersed throughout the array, while stronger excitations are self-trapped, resulting in localized energy breathers and solitons. These structures are quasiparticle analogs to the discrete 2D solitons in photonic lattices. Full many-body simulations additionally demonstrate the localization of one-particle entropy.

Figure 1

Energy of the initially excited dimer site as a function of the rescaled time $\tau$ for various initial conditions. Mean-field results are plotted in the left panel, whereas full many-body calculations are shown on the right. Simulations were carried out with $n=100$ particles in each site of a $20\times 20$ array, with $u=1.0$ and $v=0.05$. The quantum initial preparations were coherent spin states $|\theta ,\phi \rangle$ corresponding to the same $\{\theta ,\phi \}$ as the classical preparations. Both calculations show self-trapping of excitations at high initial excitation energy vs dispersion at low excitation energy.

Figure 2

Snapshots of the dimer excitation energy distribution in the array at different times during the classical evolution, for (a) $E/K=0.05$, (b) $E/K=0.267$, and (c) $E/K=0.4$. When the initial excitation energy is small, energy disperses throughout the array, while larger initial excitation results in breathing and self-trapping. Parameters are as in Fig. 1. For clarity, only the central $13\times 13$ sites in the array are shown. Energies are normalized to the initial excited dimer's energy in each case.

Figure 3

Classical phase-space trajectories for the initially excited dimer (top) and the quantum Husimi phase-space distribution at $\tau =400$ (bottom) for the same parameters as in Fig. 2.

Figure 4

Energy distribution $E_i\left(\tau \right)$ and one-particle entropy distribution ${\mathcal{S}}_i\left(\tau \right)$ at the end of the quantum simulation ($\tau =3000$), for the same initial excitation energies and parameters as in Fig. 2. Note that the color map is scaled logarithmically. In order to clearly present the formed heat soliton, we focus only on the central $11\times 11$ sites of the array.

Figure 5

Energy of the initially excited four dimer sites as a function of the rescaled time $\tau$ for various initial conditions. Mean-field results are plotted in the left panel, whereas full many-body calculations are shown on the right. Parameter values are chosen the same as in Fig. 1.

Figure 6

Snapshots of the dimer excitation energy distribution in the array at different times during the classical evolution, for (a) $E/K=0.262$ and (b) $E/K=0.5$. When the initial excitation energy is small, the energy of the four sites disperses throughout the array, while larger initial excitation results in self-trapping. Parameters are as in Fig. 1. For clarity, only the central $14\times 14$ sites in the array are shown. Energies are normalized to the initial excited dimer's energy in each case.