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Entanglement generation in QED scattering processes

Marco Rigobello, Simone Notarnicola, Giuseppe Magnifico, Simone Montangero

Published May 7, 2021• 2 citations
OpenAlex

Abstract

We study real-time meson-meson scattering processes in $(1+1)$-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.

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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 real-time meson-meson scattering processes in (1+11+11+1)-dimensional QED by means of tensor networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. 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 consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.
With the aim of studying nonperturbative out-of-equilibrium dynamics of high-energy particle collisions on quantum simulators, we investigate the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions. Working in the bosonized formulation of the model and in the thermodynamic limit, we use uniform-matrix-product-state tensor networks to construct multiparticle wave-packet states, evolve them in time, and detect outgoing particles post collision. This facilitates the numerical simulation of scattering experiments in both confined and deconfined regimes of the model at different energies, giving rise to rich phenomenology, including inelastic production of quark and meson states, meson disintegration, and dynamical string formation and breaking. We obtain elastic and inelastic scattering cross sections, together with time-resolved momentum and position distributions of the outgoing particles. Furthermore, we propose an analog circuit-QED implementation of the scattering process that is native to the platform, requires minimal ingredients and approximations, and enables practical schemes for particle wave-packet preparation and evolution. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.
Scattering processes are a crucial ingredient for the investigation of fundamental interactions. The ever-increasing amount of data produced at particle colliders has fuelled recent progresses in the field of scattering amplitudes computation. To date, on the numerical side, the results achieved are mainly based on Monte-Carlo simulations. In this Thesis the problem is attacked with a different approach: a real-time simulation of the dynamics of a 1+1 dimensional quantum field theory is performed, exploiting the powerful tensor network methods from many-body theory. A matrix product state representation of the asymptotic input states is identified, allowing for the preparation of the initial momentum wave packets. This initial state is then evolved and we aim to compute the S-matrix elements from the knowledge of the final state. We focus on a specific fermionic U(1)-gauge model, developing a set of tools which are relevant for a broader class of 1+1 dimensional quantum field theories with global or local symmetries.
We present a first real-time study of hadronic scattering in a (1+1)(1+1)(1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation, we investigate scattering processes across sectors of fixed global baryon number B=0,1,2B = 0, 1, 2B=0,1,2, corresponding respectively to meson--meson, meson--baryon, and baryon--baryon collisions. At strong coupling, the B=0B = 0B=0 and B=2B = 2B=2 channels exhibit predominantly elastic dynamics closely resembling the U(1) Schwinger model. The mixed B=1B = 1B=1 sector displays qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, with the slower state becoming spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information lattice.
A bstract We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation — where the gauge field is exactly integrated out and no truncation of the electric flux is required — we investigate scattering processes across sectors of fixed global baryon number B = 0, 1, 2. These correspond respectively to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling, the B = 0 and B = 2 channels exhibit predominantly elastic dynamics closely resembling those of the U(1) Schwinger model. In contrast, the mixed B = 1 sector shows qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.
Tensor network methods have demonstrated their suitability for the study of equilibrium properties of lattice gauge theories, even close to the continuum limit. We use them in an out-of-equilibrium scenario, much less explored so far, by simulating the real-time collisions of composite mesons in the lattice Schwinger model. Constructing wave-packets of vector mesons at different incoming momenta, we observe the opening of the inelastic channel in which two heavier mesons are produced and identify the momentum threshold. To detect the products of the collision in the strong coupling regime we propose local quantitites that could be measured in current quantum simulation platforms.