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Critical quantum systems are a promising resource for quantum metrology applications, due to the diverging susceptibility developed in proximity of phase transitions. Here, we assess the metrological power of parametric Kerr resonators undergoing driven-dissipative phase transitions. We fully characterize the quantum Fisher information for frequency estimation, and the Helstrom bound for frequency discrimination. By going beyond the asymptotic regime, we show that the Heisenberg precision can be achieved with experimentally reachable parameters. We design protocols that exploit the critical behavior of nonlinear resonators to enhance the precision of quantum magnetometers and the fidelity of superconducting qubit readout., Comment: 13 pages + Supplemental Material

In this article we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. The first one is a global one and says that if the difference between the covariance kernels of two Gaussian fields, taking values in some Sobolev space, has suitable Sobolev regularity, then these fields differ by a H\"older continuous Gaussian process. Our second decomposition theorem is more specialized and is in the setting of Gaussian fields whose covariance kernel has a logarithmic singularity on the diagonal -- or log-correlated Gaussian fields. The theorem states that any log-correlated Gaussian field $X$ can be decomposed locally into a sum of a H\"older continuous function and an independent almost $\star$-scale invariant field (a special class of stationary log-correlated fields with 'cone-like' white noise representations). This decomposition holds whenever the term $g$ in the covariance kernel $C_X(x,y)=\log(1/|x-y|)+g(x,y)$ has locally $H^{d+\varepsilon}$ Sobolev smoothness. We use these decompositions to extend several results that have been known basically only for $\star$-scale invariant fields to general log-correlated fields. These include the existence of critical multiplicative chaos, analytic continuation of the subcritical chaos in the so-called inverse temperature parameter $\beta$, as well as generalised Onsager-type covariance inequalities which play a role in the study of imaginary multiplicative chaos., Comment: Version 2: added also a global decomposition result and modified some proofs due to this. Version 3: minor changes

Establishing the physical mechanism governing exchange interactions is fundamental for exploring exotic phases such as the quantum spin liquids (QSLs) in real materials. In this work, we address exchange interactions in Sr2CuTe$_{1-x}$W$_{x}$O, a series of double perovskites that realize the spin-1/2 square lattice and were suggested to harbor a QSL ground state arising from random distribution of non-magnetic ions. Our {\it ab initio} multi-reference configuration interaction calculations show that replacing Te atoms with W atoms changes the dominant couplings from nearest to next-nearest neighbor explained by the crucial role of unoccupied states of non-magnetic ions in the super-superexchange mechanism. Combined with spin-wave theory simulations, our calculated exchange couplings provide an excellent description of the inelastic neutron scattering spectra of the end compounds, as well as explain the magnetic excitations in Sr2CuTe$_{0.5}$W$_{0.5}$O as emerging from the bond-disordered exchange couplings. Our results provide crucial understanding of the role of non-magnetic cations in exchange interactions paving the way to further exploration of QSL phases in bond-disordered materials., Version accepted in Phys. Rev. Lett

Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed., Comment: 15 pages, 15 figures, 4 tables, ApJ