Observation of Geometric Phases for Three-Level Systems using NMR Interferometry

Abstract

Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the first experiment for producing and measuring an Abelian geometric phase shift in a three-level system by using NMR interferometry. In contrast to existing experiments, based on the geometry of $S^2$, our experiment concerns the geometric phase with the geometry of $SU(3)/U(2)$. Two interacting qubits have been used to provide such a three-dimensional Hilbert space.

arXiv comment4 pages, 4 figures

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• Spin coherent states in NMR quadrupolar system: experimental and theoretical applications
• Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits
• Preservation of quantum Fisher information and geometric phase of a single qubit system in a dissipative reservoir through the addition of qubits
• Nuclear Spins as Quantum Testbeds: Singlet States, Quantum Correlations, and Delayed-choice Experiments