Abstract
Geometry and topology are fundamental concepts, which underlie a wide range of fascinating physical phenomena such as topological states of matter and topological defects. In quantum mechanics, the geometry of quantum states is fully captured by the quantum geometric tensor. Using a qubit formed by an NV center in diamond, we perform the first experimental measurement of the complete quantum geometric tensor. Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states. We then apply our method to a system of two interacting qubits, by exploiting the coupling between the NV center spin and a neighboring 13C nuclear spin. Our results establish coherent dynamical responses as a versatile probe for quantum geometry, and they pave the way for the detection of novel topological phenomena in solid state.
Highlights
Various manifestations of the quantum geometric tensor (QGT) have been observed in experiments, using very different physical platforms and probes
Our approach builds on a strong connection between coherent Rabi oscillations upon parametric modulations and the quantum geometry of the underlying states
We report on the first experimental measurement of the complete QGT, using a qubit formed by an NV center spin in diamond
Summary
Parametric modulation induced coherent transition for discrete quantum systems. We experimentally demonstrate the connection between parametric modulation induced coherent transition and quantum geometric tensor for discrete quantum systems. We can get the following relation between parametric modulation induced coherent transition and the Fubini-Study metric as m. For a two-level quantum system, the corresponding Rabi frequency of coherent transition Ωl (aμ , aν ) = 2|Ωn↔m(λ)| is related to the Fubini-Study metric as follows. For a two-level quantum system, we have the Rabi frequency of coherent transition Ωc (aμ , aν ) = 2|Ωn↔m(λ)| is related to the Fubini-Study metric and the local Berry curvature as follows. In the limit aμ , aν 1 where μ, ν ∈ {λ1, λ2, · · · , λN }, each resonant transition can be approximated as a two-level system and the transition element m(λ)|∂μ H (λ)|n(λ) [see Eq(3) in the main text] can be measured
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