The non-Abelian geometric phase in the diamond nitrogen-vacancy center

Abstract

This paper introduces a theoretical framework for understanding the accumulation of non-Abelian geometric phases in rotating nitrogen-vacancy centers in diamond. Specifically, we consider how degenerate states can be achieved and demonstrate that the resulting geometric phase for multiple paths is non-Abelian. We find that the non-Abelian nature of the phase is robust to fluctuations in the path and magnetic field. In contrast to previous studies of the accumulation of Abelian geometric phases for nitrogen-vacancy centers under rotation we find that the limiting time-scale is $T_1$. As such a non-Abelian geometric phase accumulation in nitrogen-vacancy centers has potential advantages for applications as gyroscopes.

5 pages, including 4 figures

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• High-sensitivity diamond magnetometer with nanoscale resolution
• Scanning magnetic field microscope with a diamond single-spin sensor
• Observation of Berry's Phase in a Solid State Qubit
• Experimental Realization of Non-Abelian Geometric Gates
• Magnetic field imaging with NV ensembles
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Cited by in corpus (7)

• Hybrid opto-mechanical systems with nitrogen-vacancy centers
• Non-Abelian adiabatic geometric transformations in a cold Strontium gas
• Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin
• Quantum memory assisted precision rotation sensing
• Quantum beats and metrology in a rapidly rotating Nitrogen-Vacancy center
• Quantum measurement of a rapidly rotating spin qubit in diamond
• Geometric and holonomic quantum computation