We theoretically investigate the interplay of interactions and non-Hermiticity in the dynamics of two bosons on the one-dimensional Hatano-Nelson lattice with nonreciprocal tunneling. We find that the nonreciprocity in the tunneling leads to the formation of an asymmetric density cone during the time-evolution of the system; the degree of asymmetry can be controlled by tuning the nonreciprocity parameter $\delta$. Next, we analyze the dynamics of this system in the presence of a static external force, $F$ and demonstrate that non-Hermiticity leads to asymmetric two-particle Bloch oscillations. Interestingly, when $F=0$ ($F\ne 0$), strong interactions lead to the formation of an inner density-cone (density-hourglass) structure; this inner structure also becomes asymmetric in the presence of non-Hermiticity. We further analyze the spatial correlations that develop between the two bosons, and establish that the system exhibits nonreciprocal bunching (antibunching) in the presence of weak (strong) interactions. Finally, we examine the growth of the quantum Fisher information $F_Q$ with time, and demonstrate that $F_Q$ decreases with increasing $\delta$. Interestingly however, for both one- and two-particle walks, the rapid growth of $F_Q$ characteristic of the Hermitian case, with an effective power law $F_Q\propto t^{\alpha }, \alpha \simeq 3$, persists in the presence of nonreciprocal tunneling.

Close

PrevNext

View figure in article

• Quantum simulation
• Quantum walks
• Non-Hermitian systems
• Bose-Hubbard model