Two-particle states and interactions

Sergej Flach A, Mikhail Ivanchenko, Рамаз Хомерики

Single-particle states in a chain with quasiperiodic potential show a metal-insulator transition upon the change of the potential strength. We consider two particles with local interaction in the single-particle insulating regime. The two-particle states change from being localized to delocalized upon an increase of the interaction strength to a nonperturbative finite value. At even larger interaction strength the states become localized again. This transition of two-particle bound states into correlated metallic ones is due to a resonant mixing of the noninteracting two-particle eigenstates. In the discovered correlated metal states two particles move coherently together through the whole chain.

Yu-Heng Li, Yanjun Liu, Jing Lu +1 more

Abstract We study both the two-particle and single-particle fringe visibility in the generalized version of the Nakazato–Pascazio model where two qubits interact with a finite length one-dimensional array. Both the two-particle and single-particle fringe visibilities are investigated with different initial states of the particles spin. For different initial states of the particles spin, the two-particle fringe visibility either decreases or increases over time, and may even decrease first and increase later. Due to the interaction between the particles and the one-dimensional array, the single-particle fringe visibility increases over time when the initial state of the two particles spin is independent. The single-particle fringe visibility is equal to 0 as the two-particle spin is initially in the completely entangled state or in the singlet state.

Benedikt B. Brandt, Constantine Yannouleas, Uzi Landman

Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the two-particle density matrix constructed via configuration-interaction (CI) exact diagonalization of the microscopic Hamiltonian, we explored here the systematic evolution of characteristic, damped, interference patterns in the two-particle momentum and spatial correlation maps of two ultracold fermionic atoms trapped in a double-well potential, over the entire range of variation of the contact repulsive interatomic interaction strength. For the singlet ground state the two-particle momentum maps were found to transform from a square-plaid pattern for non-interacting particles, to a system of striped interference fringes, with the most intense fringe lying along the main diagonal indicating bunching. Two-particle momentum correlation maps for low-lying excited states were also analyzed, with the triplet excited state found to exhibit antibunching. A modified Hubbard-type effective model is shown to reproduce well the microscopic CI results. This led to uncovering of analytic expressions capturing the full evolution of the two-particle momentum correlation maps over the entire range of interparticle interactions, from the independent particle limit with a substantial site-double-occupancy fraction, to the Mott insulating regime.