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.

We experimentally observe Floquet Raman transitions in the weakly driven solid state spin system of nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model, and allows us to observe coherent spin state transfer arising from Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of analog photon-assisted Floquet Raman transition and dynamical localisation in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control of a quantum system with potential applications in various types of quantum technologies based on driven quantum dynamics. In particular, the Floquet-Raman system may be used as a quantum simulator for the physics of periodically driven systems.

Due to its superior coherent and optical properties at room temperature, the nitrogen-vacancy (NV) center in diamond has become a promising quantum probe for nanoscale quantum sensing. However, the application of NV containing nanodiamonds to quantum sensing suffers from their relatively poor spin coherence times. Here we demonstrate energy efficient protection of NV spin coherence in nanodiamonds using concatenated continuous dynamical decoupling, which exhibits excellent performance with less stringent microwave power requirement. When applied to nanodiamonds in living cells we are able to extend the spin coherence time by an order of magnitude to the T1-limit of up to 30µs. Further analysis demonstrates concomitant improvements of sensing performance which shows that our results provide an important step towards in vivo quantum sensing using NV centers in nanodiamond.Introduction.-Nitrogen-Vacancy (NV) centers in diamond exhibit stable fluorescence and have a spin triplet ground state, which can be coherently manipulated by microwave fields [1]. Observation of spin-dependent fluorescence provides an efficient way to readout the spin state of NVs. The energy splitting of the NV spin depends on physical parameters, such as magnetic field [2-4], electric field [5, 6], temperature [7-10] and pressure [11,12]. A variety of quantum sensing protocols for precise measurement of these physical parameters in different scenarios have been developed [13][14][15][16][17][18][19][20][21][22]. These protocols are all based on determining the NV spin energy splitting, which is why the measurement sensitivity is limited by the NV spin coherence time.Spin coherence in bulk diamond is mainly affected by surrounding electronic impurities (P1 centers) and nuclear spins (natural abundance of 13 C isotope). The spin reservoir can be eliminated by using isotopically engineered high-purity type IIa diamond [23]. In order to mitigate the influence of any residual impurities, pulsed dynamical decoupling has been widely exploited to prolong spin coherence time [24][25][26]. Its excellent performance when applied to NVs in bulk diamond is a result of the quasi-static characteristics of the spin reservoir in bulk diamond and the high available microwave power. Unfortunately, these two factors may not be satisfied for NV centers in nanodiamonds, which are required for sensing applications in vivo. NVs contained within nanodiamonds typically exhibit poor spin coherence time, which has been attributed to nanodiamond surface spin noise and electric charge noise that include prominent high frequency components. Preserving the coherence of NVs in nanodiamonds becomes even more problematic

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