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The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit(1), which is proportional to 1/root N. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states(2). Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 10(11) rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states(3,4) to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments(5-10), with a corresponding angular variance of the squeezed collective spin of 4.6 x 10(-13) radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.

Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe alloys are all indirect-bandgap semiconductors that cannot emit light efficiently. The goal(1) of achieving efficient light emission from group-IV materials in silicon technology has been elusive for decades(2-6). Here we demonstrate efficient light emission from direct-bandgap hexagonal Ge and SiGe alloys. We measure a sub-nanosecond, temperature-insensitive radiative recombination lifetime and observe an emission yield similar to that of direct-bandgap group-III-V semiconductors. Moreover, we demonstrate that, by controlling the composition of the hexagonal SiGe alloy, the emission wavelength can be continuously tuned over a broad range, while preserving the direct bandgap. Our experimental findings are in excellent quantitative agreement with ab initio theory. Hexagonal SiGe embodies an ideal material system in which to combine electronic and optoelectronic functionalities on a single chip, opening the way towards integrated device concepts and information-processing technologies.

A hexagonal (rather than cubic) alloy of silicon and germanium that has a direct (rather than indirect) bandgap emits light efficiently across a range of wavelengths, enabling electronic and optoelectronic functionalities to be combined on a single chip.

Colonization, speciation and extinction are dynamic processes that influence global patterns of species richness(1-6). Island biogeography theory predicts that the contribution of these processes to the accumulation of species diversity depends on the area and isolation of the island(7,8). Notably, there has been no robust global test of this prediction for islands where speciation cannot be ignored(9), because neither the appropriate data nor the analytical tools have been available. Here we address both deficiencies to reveal, for island birds, the empirical shape of the general relationships that determine how colonization, extinction and speciation rates co-vary with the area and isolation of islands. We compiled a global molecular phylogenetic dataset of birds on islands, based on the terrestrial avifaunas of 41 oceanic archipelagos worldwide (including 596 avian taxa), and applied a new analysis method to estimate the sensitivity of island-specific rates of colonization, speciation and extinction to island features (area and isolation). Our model predicts-with high explanatory power-several global relationships. We found a decline in colonization with isolation, a decline in extinction with area and an increase in speciation with area and isolation. Combining the theoretical foundations of island biogeography(7,8) with the temporal information contained in molecular phylogenies(10) proves a powerful approach to reveal the fundamental relationships that govern variation in biodiversity across the planet.

Using a global molecular phylogenetic dataset of birds on islands, the sensitivity of island-specific rates of colonization, speciation and extinction to island features (area and isolation) is estimated.