Quantum dynamics of two composite particles on a one-dimensional lattice

Xizhou Qin, Yongguan Ke, Xi-Wen Guan +3 more

We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent- and/or co-walking dependent on both quantum statistics and interaction strength. We find that two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent propagation speed. Such an effective single-particle picture of co-walking is analytically derived in the context of degenerate perturbation and the analytical results are well consistent with direct numerical simulation. In addition to implementing universal quantum computation and observing bound states, two-particle quantum walks offer a novel route to detecting quantum statistics. Our theoretical results can be examined in experiments of light propagations in two-dimensional waveguide arrays or spin-impurity dynamics of ultracold atoms in one-dimensional optical lattices.

Fumika Suzuki

Mama Kabir Njoya Mforifoum, Andreas Buchleitner, Gabriel Dufour

We study the Hong-Ou-Mandel interference of two identical, composite particles, each formed of two bosonic or fermionic constituents, as they scatter against a potential barrier in a one-dimensional lattice. For tightly bound composites, we show that the combination of their constituents' mutual interactions and exchange symmetry gives rise to an effective nearest-neighbour interaction between composites, which induces a reduction of the interference contrast.

Elisheva Elbaz

Manuel Gessner

Fumika Suzuki, Marina Litinskaya, William George Unruh

We study scattering of a composite quasiparticle, which possesses a degree of freedom corresponding to relative separation between two bound excitations, by a $\ensuremath{\delta}$-like impurity potential on a one-dimensional discrete lattice. First, we show that, due to specific properties of their dispersion, lattice excitations bind to impurities with both negative and positive potentials. We demonstrate that the finite size of the composite excitation leads to formation of multiple excitation-impurity bound states. The number and the degree of localization of these bound states depend on the signs and relative magnitudes of the impurity potential and the binding strength of two quasiparticles. We also report the existence of excitation-impurity bound states whose energies are located in the continuum band. Secondly, we study a change in the entanglement between the center of mass and relative coordinate degrees of freedom of a biexciton wave packet during single impurity scattering and decoherence caused by it. For a composite quasiparticle on a lattice, the entanglement between its relative and center of mass coordinate degrees of freedom arises naturally due to inseparability of the two-particle Hamiltonian. One of the main focuses of our study is to investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics.