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arXiv:quant-ph/0601177 · Physical Review A

Entanglement generation via scattering of two particles with hard-core repulsion

Frank Schmüser, Dominik Janzing

Published May 1, 2006• 20 citations
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Abstract

We analyze the entanglement generation in a one-dimensional scattering process. The two colliding particles have a Gaussian wave function and interact by hard-core repulsion. In our analysis, results on the entanglement of two-mode Gaussian states are used. The produced entanglement depends in a nonobvious way on the ratio of masses and initial widths for the two particles. The asymptotic wave function of the two particles and its associated ellipse yield additional geometric insight into these conditions. We discuss the difference from the quantitative analysis of the amount of entanglement generated by beam splitters with squeezed light.

DOI
10.1103/physreva.73.052313

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We analyze the entanglement generation in a one-dimensional scattering process. The two colliding particles have a Gaussian wave function and interact by hard-core repulsion. In our analysis, results on the entanglement of two-mode Gaussian states are used. The produced entanglement depends in a nonobvious way on the ratio of masses and initial widths for the two particles. The asymptotic wave function of the two particles and its associated ellipse yield additional geometric insight into these conditions. We discuss the difference from the quantitative analysis of the amount of entanglement generated by beam splitters with squeezed light.
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these constraints, three different mechanisms of entanglement can be identified: the superposition of reflected and transmitted modes, momentum correlations of the reflected mode due to inversion of the relative momentum, and momentum correlations in the transmitted and reflected modes due to dependence of the scattering amplitude on the relative momentum. We consider three standard potentials, the hard core, Dirac delta, and double Dirac delta, and show that the relative importance of these mechanisms depends on the interaction and on the properties of the incoming wavefunction. We find that even when the momenta distributions of the incoming articles are sharply peaked, entanglement due to the momentum correlations generated by reflection can be quite large for particles with unequal mass.
We address the interaction of two Gaussian states of light interfering at a balanced beam splitter and analyze the correlations exhibited by the resulting bipartite system. Nonlocal quantum correlations (entanglement) arise if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities. In particular, our result clarifies the role of squeezing as a prerequisite for entanglement and provide a tool to optimize the generation of entanglement by passive devices.
We study an experimental scheme to generate Gaussian two-mode entangled states via beam splitter. Specifically, we consider a nonclassical Gaussian state (squeezed state) and a thermal state as two input modes, and evaluate the degree of entanglement at the output. Experimental conditions to generate entangled outputs are completely identified and the critical thermal noise to destroy entanglement is analytically obtained. By doing so, we discuss the possibility to link the resistance to noise in entanglement generation with the degree of single-mode nonclassicality.
We show that when two quantum-mechanical particles of the same mass, interacting through a hard-core repulsive potential, collide in one dimension, they exchange their wavefunctions, making them look as if they had passed through each other. We give a simple explanation of this phenomenon, and compare to its classical analog, which can be demonstrated using the “Newton's cradle” toy. We also consider briefly what happens when the masses are unequal, showing how entanglement arises in this case.
We study real-time meson-meson scattering processes in (1+1)(1+1)(1+1)-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position, starting from the free fermions model and extending it to the interaction theory. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we measure the scattering amplitudes for the process in terms of the initial and final momenta and the entanglement produced by the collision. We remarkably find two different regimes for the asymptotic entanglement between the two mesons: it is perturbatively small for weak couplings, while, in the intermediate regime, it turns out to reach a non-zero value at long times after the scattering.
We study the entanglement creation in the low-energy scattering of two particles in three dimensions, for a general class of interaction potentials that are not required to be spherically symmetric. The incoming asymptotic state, before the collision, is a product of two normalized Gaussian states. After the scattering, the particles are entangled. We take as a measure of the entanglement the purity of one of them. We provide a rigorous explicit computation, with error bound, of the leading order of the purity at low energy. The entanglement depends strongly on the difference of the masses. It takes its minimum when the masses are equal, and it increases rapidly with the difference of the masses. It is quite remarkable that the anisotropy of the potential gives no contribution to the leading order of the purity, in spite of the fact that entanglement is a second-order effect.