Quantum synchronization (QS) in open many-body systems offers a promising route for controlling collective quantum dynamics, yet existing manipulation schemes often rely on dissipation engineering, which distorts limit cycles, lacks scalability, and is strongly system-dependent. Here, we propose a universal and scalable method for continuously tuning QS from maximal synchronization under isotropic interactions to complete synchronization blockade (QSB) under fully anisotropic coupling in spin oscillator networks. Our approach preserves intrinsic limit cycles and applies to both few-body and macroscopic systems. We analytically show that QS arises solely from spin flip-flop processes and their higher-order correlations, while anisotropic interactions induce non-synchronizing coherence. A geometric QS measure reveals a macroscopic QSB effect in the thermodynamic limit. The proposed mechanism is experimentally feasible using XYZ interactions and optical pumping, and provides a general framework for programmable synchronization control in complex quantum networks and dynamical phases of matter.

The rapid development of metasurfaces - 2D ensembles of engineered nanostructures - is presently fostering a steady drive towards the miniaturization of many optical functionalities and devices to a subwavelength size. The material platforms for optical metasurfaces are rapidly expanding and for the past few years, we are seeing a surge in establishing meta-optical elements from high-index, highly transparent materials with strong nonlinear and electro-optic properties. Crystalline lithium niobate (LN), a prime material of choice in integrated photonics, has shown great promise for future meta-optical components, thanks to its large electro-optical coefficient, second-order nonlinear response and broad transparency window ranging from the visible to the mid-infrared. Recent advances in nanofabrication technology have indeed marked a new milestone in the miniaturization of LN platforms, hence enabling the first demonstrations of LN-based metasurfaces. These seminal works set the first steppingstone towards the realization of ultra-flat monolithic nonlinear light sources with emission ranging from the visible to the infrared, efficient sources of correlated photon pairs, as well as electro-optical devices. Here, we review these recent advances, discussing potential perspectives for applications in light conversion and modulation shaping as well as quantum optics, with a critical eye on the potential setbacks and limitations of this emerging field.

The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks.

Identifying and characterizing quantum phases of matter in the presence of long range correlations and/or spatial disorder is, generally, a challenging and relevant task. Here, we study a generalization of the Kiteav chain with variable-range pairing and different site-dependence of the chemical potential, addressing commensurable and incommensurable modulations as well as Anderson disorder. In particular, we analyze multipartite entanglement (ME) in the ground state of the dirty topological wires by studying the scaling of the quantum Fisher information (QFI) with the system's size. For nearest-neighbour pairing the Heisenberg scaling of the QFI is found in one-to-one correspondence with topological phases hosting Majorana modes. For finite-range pairing, we recognize long-range phases by the super-extensive scaling of the QFI and characterize complex lobe-structured phase diagrams. Overall, we observe that ME is robust against finite strengths of spatial inhomogeneity. This work contributes to establish ME as a central quantity to study intriguing aspects of topological systems.

"Strange" correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and non-translational invariant cases, and in presence of on-site disorder and long-range couplings, extend the validity of the strange correlators approach for the diagnosis of topological phases of matter, and indicate a general procedure for their optimal choice.

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramér-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.

Advancements in physics are often motivated/accompanied by advancements in our precision measurements abilities. The current generation of atomic and optical interferometers is limited by shot noise, a fundamental limit when estimating a phase shift with classical light or uncorrelated atoms. In the last years, it has been clarified that the creation of special quantum correlations among particles, which will be called here useful entanglement, can strongly enhance the interferometric sensitivity. Pioneer experiments have already demonstrated the basic principles. We are probably at the verge of a second quantum revolution where quantum mechanics of many-body systems is exploited to overcome the limitations of classical technologies. This review illustrates the deep connection between entanglement and sub shot noise sensitivity.

We perform saturated absorption spectroscopy on the D$\_2$ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05-0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a V configuration and on four-level systems in a N or double-N configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-N crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.

We extend the $t-z$ mapping formalism of time-dependent paraxial optics by identifying configurations displaying a synthetic magnetic vector potential, leading to a non-trivial band topology in propagating geometries. We consider an inhomogeneous 1D array of coupled optical waveguides beyond the standard monochromatic approximation, and show that the wave equation describing paraxial propagation of optical pulses can be recast in the form of a Schrödinger equation, including a synthetic magnetic field whose strength can be controlled via the transverse spatial gradient of the waveguide properties across the array. We use an experimentally-motivated model of a laser-written waveguide array to demonstrate that this synthetic magnetic field can be engineered in realistic setups and can produce interesting observable effects such as cyclotron motion, a controllable Hall drift of the wavepacket displacement in space or time, and unidirectional propagation in chiral edge states. These results significantly extend the variety of physics that can be explored within propagating geometries and pave the way for exploiting this platform for higher-dimensional topological physics and strongly correlated fluids of light.

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramér-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.

The prospect of developing more efficient classical or quantum photonic devices through the suppression of backscattering is a major driving force for the field of topological photonics. However, genuine protection against backscattering in photonics requires implementing architectures with broken time-reversal which is technically challenging. Here, we make use of a frequency-encoded synthetic dimension scheme in an optical fibre loop platform to experimentally realise a photonic Chern insulator inspired from the Haldane model where time-reversal is explicitly broken through temporal modulation. The bands' topology is assessed by reconstructing the Bloch states' geometry across the Brillouin zone. We further highlight its consequences by measuring a driven-dissipative analogue of the quantized transverse Hall conductivity. Our results thus open the door to harnessing topologically protected unidirectional transport of light in frequency-multiplexed photonic systems.

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this letter we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the maximal theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this letter we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the maximal theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

The rapid development of metasurfaces - 2D ensembles of engineered nanostructures - is presently fostering a steady drive towards the miniaturization of many optical functionalities and devices to a subwavelength size. The material platforms for optical metasurfaces are rapidly expanding and for the past few years, we are seeing a surge in establishing meta-optical elements from high-index, highly transparent materials with strong nonlinear and electro-optic properties. Crystalline lithium niobate (LN), a prime material of choice in integrated photonics, has shown great promise for future meta-optical components, thanks to its large electro-optical coefficient, second-order nonlinear response and broad transparency window ranging from the visible to the mid-infrared. Recent advances in nanofabrication technology have indeed marked a new milestone in the miniaturization of LN platforms, hence enabling the first demonstrations of LN-based metasurfaces. These seminal works set the first steppingstone towards the realization of ultra-flat monolithic nonlinear light sources with emission ranging from the visible to the infrared, efficient sources of correlated photon pairs, as well as electro-optical devices. Here, we review these recent advances, discussing potential perspectives for applications in light conversion and modulation shaping as well as quantum optics, with a critical eye on the potential setbacks and limitations of this emerging field.

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to proof-of-principle experiments. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network's posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning based procedure outperforms standard calibration methods. Thus, our work paves the way for Bayesian quantum sensors which can benefit from efficient optimization methods, such as in adaptive schemes, and take advantage of complex non-classical states. These capabilities can significantly enhance the sensitivity of future devices.

Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large-deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrates that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.

We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.

We review the basic concepts of quantum fluids of light and the different techniques that have been developed to exploit driving and dissipation to stabilize and manipulate interesting many-body states. In the weakly interacting regime, this approach has allowed to study, among other, superfluid light, non-equilibrium Bose-Einstein condensation, photonic analogs of Hall effects, and is opening the way towards the realization of a new family of analog models of gravity. In the strongly interacting regime, the recent observations of Mott insulators and baby Laughlin fluids of light open promising avenues towards the study of novel strongly correlated many-body states.

We investigate the time evolution of a non-resonant dressed-atom qubit in an XZ original configuration. It is composed of two electromagnetic fields, one oscillating parallel and the other orthogonal to the quantisation magnetic static field. The experiments are performed in rubidium and caesium atomic magnetometers, confined in a magneto-optical trap and in a vapour cell, respectively. Static fields in the $\mu$T range and kHz oscillating fields with large Rabi frequencies are applied. This dual-dressing configuration is an extension of the Landau-Zener multipassage interferometry in the presence of an additional dressing field controlling the tunneling process by its amplitude and phase. Our measurement of the qubit coherence introduces additional features to the transition probability readout of standard interferometry. The coherence time evolution is characterized by oscillations at several frequencies, each of them produced by a different quantum contribution. Such frequency description introduces a new picture of the qubit multipassage evolution. Because the present low-frequency dressing operation does not fall within the standard Floquet engineering paradigm based on the high-frequency expansion, we develop an ad-hoc dressing perturbation treatment. Numerical simulations support the adiabatic and non-adiabatic qubit evolution.

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions, the so-called Fermi polaron problem. On one side, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides quantitatively reliable insight into the phase diagram of strongly interacting population imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to study itinerant ferromagnetism, a long standing problem in quantum mechanics.