High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation

• URL: http://arxiv.org/abs/2206.01108v1
• Date: Thu, 2 Jun 2022 15:47:36 GMT
• Title: High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation
• Authors: Andreas Kruckenhauser, Rick van Bijnen, Torsten V. Zache, Marco Di Liberto and Peter Zoller
• Abstract summary: We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on arrays of Rydberg atoms. These arrays offer the opportunity to perform quantum information processing operations for qudit-based quantum computing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the well-structured manifolds of states with principal quantum number $n$. This enables us to construct generalized large-spin Heisenberg models for which we develop state-preparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sine-Gordon and massive Schwinger models. Moreover, these high-dimensional manifolds also offer the opportunity to perform quantum information processing operations for qudit-based quantum computing, which we exemplify with an entangling gate and a state-transfer protocol for the states in the neighborhood of the circular Rydberg level.

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