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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 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.

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A series of novel pH-sensitive gene delivery vectors (POEI 1, 2, and 3) are synthesized through Michael addition from low molecular weight PEI (LMW PEI) via acid-labile ortho ester linkage with terminal acrylates (OEAc) by various feed molar ratios. The obtained POEI 1 and POEI 2 can efficiently condense plasmid DNA into nanoparticles with size range of 200-300 nm and zeta-potentials of about +15 mV while protecting DNA from enzymatic digestion compared with POEI 3. Significantly, ortho ester groups of POEI main-chains can make an instantaneous degradation-response to acidic endosomal pH (≈5.0), resulting in accelerated disruption of polyplexes and intracellular DNA release. MTT assay reveals that all POEIs exhibit much lower cytotoxicity in different cells than branched PEI (25 KDa). As expected, POEI 1 and POEI 2 perform improved gene transfection in vitro, suggesting that such polycations might be promising gene vectors based on overcoming toxicity-efficiency contradiction.

The heterogeneity of a cement-based material results in a random spatial distribution of carbonation depth. Currently, there is a lack of both experimental and numerical investigations aiming at a statistical understanding of this important phenomenon. This paper presents both experimental and numerical supercritical carbonation test results of cement mortar blocks. The carbonation depths are measured along the carbonation boundary by the proposed rapid image processing technique, which are then statistically studied by calculating, e.g., their probability density and power spectral density (PSD). The results indicate that the distribution of the carbonation depth can be approximately represented by a lognormal distribution function and the PSD has quantitative correlation with some of the statistic parameters used in the simulations. In particular, the effects of the autocorrelation lengths and the coefficient of variation of porosity, which are used to define the random porosity field, on the irregularity of carbonation depth are analyzed numerically in details and validated by experimental results. The study has shown that using a random field of porosity with due consideration of spatial correlation and variance, the irregularity of carbonation depth can be realistically captured by the numerical model. The numerical results confirm that lognormal distributions represent the random nature of carbonation depth well and the average and variance of the irregular carbonation depth increase with the increase of carbonation time, autocorrelation length and coefficient of variation of porosity. The study also offers a potential method to numerically calibrate some of the statistic parameters required by a numerical carbonation model through comparing the PSD with that from experimental tests. Overall the methodology adopted in the paper can provide a foundation for future investigations on probability analysis of carbonation depth and other similar work based on multi-scale and-physics modelling.