Composite Pulses in N-level Systems with SU(2) Symmetry and their Geometrical Representation on the Majorana Sphere

Abstract

High fidelity and robustness in population inversion is very desirable for many quantum control applications. We expand composite pulse schemes developed for two-level dynamics, and present an analytic solution for the coherent evolution of an N-level quantum system with SU(2) symmetry, for achieving high fidelity and robust population inversion, which outperforms common solutions in N-level dynamics. Our approach offers a platform for accurate steering of the population transfer in physical multi-level systems, which is crucial for fidelity in quantum computation and achieving fundamental excitations in nuclear magnetic resonances and atomic physics. We also introduce and discuss the geometrical trajectories of these dynamics on the Majorana sphere as an interpretation, allowing to gain physical insight on the dynamics of many-body or high-dimensional quantum systems.

9 pages, 6 figures

References in corpus (5)

• Stimulated Raman adiabatic passage in physics, chemistry and beyond
• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase
• Searching for Non-Abelian Phases in the Bose-Einstein Condensate of Dysprosium

Cited by in corpus (4)

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• Highly Efficient Creation and Detection of Deeply-bound Molecules via Invariant-based Inverse Engineering with Feasible Modified Drivings
• Quantum state engineering in a five-state chainwise system by coincident pulse technique