Simulating Meson Scattering on Trapped-Ions and Spin Quantum Simulators

Studying collisions of composite particles in nuclear and high-energy physics is an outstanding long-term goal for quantum simulators. Observations of confinement in quantum spin systems [1,2] have opened up the possibility to explore scattering dynamics in simple toy models using analog quantum simulators. Due to their complex nature, the preparation of hadronic wave packets has been a significant challenge limiting demonstrations of hadron scattering on analog simulators. In this paper, we develop methods to create meson-like wave packets in analog simulators. We then numerically study the elastic and inelastic scattering of these meson-like particles in the confined and deconfined regimes of a quantum Ising model. Our proposal outlines two broadly applicable wave-packet state-preparation schemes. One scheme uses beyond nearest-neighbor Ising spin interactions to create a blockade transition. The other scheme utilizes a quantum-bus--mediated exchange such as the native spin-phonon coupling in trapped-ion arrays. We benchmark both state-preparation protocols for model parameters that are experimentally feasible in current trapped-ion systems, and show convergence to high-fidelity wave packets. Additionally, we observe and quantify the prominence of various scattering outcomes, including the production of free kinks from meson bound states in the deconfined regime, which we show is detectable in experiments. We perform numerical simulations of the full collision protocol in a quantum Ising chain with a variable interaction range, and demonstrate the potential of current quantum simulators to resolve elastic and inelastic scattering channels.

[1] Marton Kormos, Mario Collura, Gabor Tak ́acs, and Pasquale Calabrese. Real-time confinement following a quantum quench to a non-integrable model. Nature Physics, 13(3):246–249, March 2017. Number: 3 Publisher: Nature Publishing Group.

[2] Fangli Liu, Rex Lundgren, Paraj Titum, Guido Pagano, Jiehang Zhang, Christopher Monroe, and Alexey V. Gorshkov. Confined quasiparticle dynamics in long-range interacting quantum spin chains. Physical review letters, 122(15):150601, 2019. Publisher: APS