,Experimental measurement of the quantum geometric tensor using coupled qubits in diamond

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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 oscigations 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.
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