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arXiv:2511.02925

Motional entanglement in low-energy collisions near shape resonances

Yimeng Wang, Christiane P. Koch

quant-phphysics.atom-phSubmitted Nov 4, 2025• Announced Nov 6, 2025• 0 citations
v1 · Nov 4, 2025v2 · Dec 22, 2025
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Abstract

Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These can become entangled upon scattering, but how much entanglement can be created in this process? Here we address this question with fully coherent calculations of bipartite scattering in three-dimensional space, quantifying entanglement by the inverse of the single particle purity. We show that the standard plane-wave description of scattering fails to capture the entanglement properties, due to the essential role of quantum uncertainty in the initial state. For a more realistic description of a scattering setup and narrow initial momentum dispersion, we find the entanglement to scale linearly with the scattering cross section, including strong enhancement close to shape resonances. We discuss how the generation of motional entanglement can be detected in experiments. Our results open the way to probing and eventually using entanglement in quantum collisions.

Comments
7 pages, 3 figures

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Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These can become entangled upon scattering, but how much entanglement can be created in this process? Here we address this question with fully coherent calculations of bipartite scattering in three-dimensional space, quantifying entanglement by the inverse of the single particle purity. We show that the standard plane-wave description of scattering fails to capture the entanglement properties, due to the essential role of quantum uncertainty in the initial state. For a more realistic description of a scattering setup and narrow initial momentum dispersion, we find the entanglement to scale linearly with the scattering cross section, including strong enhancement close to shape resonances. We discuss how the generation of motional entanglement can be detected in experiments. Our results open the way to probing and eventually using entanglement in quantum collisions.
We study the quantum entanglement produced by a head-on collision between two Gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by sss-wave scattering amplitudes, we obtain an approximate analytic expression of the purity of an individual particle. The loss of purity provides an indicator of the degree of entanglement. In the case the wave packets are narrow in momentum space, we show that the loss of purity is solely controlled by the ratio of the scattering cross section to the transverse area of the wave packets.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
Abstract The amazing quantum effect of ‘entanglement’ was discovered in the 1935 thought experiment by Albert Einstein, Boris Podolsky and Nathan Rosen (‘EPR’)1. The ensuing research opened up fundamental questions and led to experiments that proved that quantum theory cannot be completed by local hidden variables2–4. Remarkably, EPR did not discuss how to create the entanglement in their thought experiment. Here I add this part. What is required in the original EPR thought experiment is a simple elastic particle collision, an unbalanced mass ratio of e.g. 1:3 and initial states that are position and momentum squeezed, respectively. In the limiting case of infinite squeeze factors, the measurement of the position or momentum of one particle allows an absolutely precise conclusion to be drawn about the value of the same quantity of the other particle. The EPR idea has never been tested in this way. I outline a way to do this.
Quantifying entanglement in a quantum system generally requires a complete quantum tomography followed by the NP-hard computation of an entanglement monotone---requirements that rapidly become intractable at higher dimensions. Observing entanglement in large quantum systems has consequently been relegated to witnesses that only verify its existence. In this article, we show that the violation of recent entropic witnesses of the Einstein-Podolsky-Rosen paradox also provides tight lower bounds to multiple entanglement measures, such as the entanglement of formation and the distillable entanglement, among others. Our approach only requires the measurement of correlations between two pairs of complementary observables---not a tomography---so it scales efficiently at high dimension. Despite this, our technique captures almost all the entanglement in common high-dimensional quantum systems, such as spatially or temporally entangled photons from parametric down-conversion.
We review recent progress in understanding quantum entanglement generated by 2→22\to 22→2 scattering processes in quantum field theory. Starting from the final-state density matrix, we discuss two complementary approaches to quantifying entanglement: projection onto fixed final-state momenta and tracing out the momentum degrees of freedom. We present analytic results for the concurrence of a mixed two-qubit final state and identify the role of quantum coherences, showing that the real part of the inelastic forward scattering amplitude constitutes a subleading correction to the linearized entropy connected to the relative entropy of coherence. Our framework is illustrated through two phenomenologically relevant examples: high-energy scattering of two flavored scalars in the two-Higgs doublet model and high-energy electron-positron annihilation in QED.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.