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Physical Review A

Entanglement between two interacting atoms in a one-dimensional harmonic trap

Baoqing Sun, Dong Zhou, Li You

Published Jan 24, 2006• 31 citations
Publisher

Abstract

We investigate quantum entanglement properties between two interacting atoms in a one-dimensional harmonic trap. We provide detailed results for the dependencies of atom-atom entanglement on the statistical nature of atoms being bosonic or fermionic, the interaction strength as parameterized by a contact pseudo-potential, and temperature.

DOI
10.1103/physreva.73.012336

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We investigate quantum entanglement properties between two interacting atoms in a one-dimensional harmonic trap. We provide detailed results for the dependencies of atom-atom entanglement on the statistical nature of atoms being bosonic or fermionic, the interaction strength as parameterized by a contact pseudo-potential, and temperature.
We have investigated quantum entanglement for two interacting ultracold bosonic atoms in one-dimensional harmonic traps. The effective potential is modeled by delta interaction. For this two-atom system, we have investigated quantum entanglement properties, such as von Neumann entropy and linear entropy for its ground state and excited states. Using a computational scheme that is different from previously employed, a total of the lowest 16 states are studied. Here we show the dependencies of entanglement properties under various interacting strengths. Comparisons for the ground state entanglement are made with earlier results in the literature. New results for the other 15 excited states are reported here.
We investigate quantum entanglement between two (spin-1∕21∕21∕2) fermions inside a cylindrical harmonic trap, making use of the von Neumann entropy for the reduced single-particle density matrix as the pure-state entanglement measure. We explore the dependence of pair entanglement on the geometry and strength of the trap and on the strength of the pairing interaction over the complete range of the effective BCS to BEC crossover. Our result elucidates an interesting connection between our model system of two fermions and that of two interacting bosons.
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The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.