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Significance The BCS-BEC (Bardeen–Cooper–Schrieffer––Bose–Einstein-condensate) cross-over bridges the two important theories of bound particles in a unified picture with the ratio of the attractive interaction to the Fermi energy as a tuning parameter. A key issue is to understand the intermediate regime, where new states of matter may emerge. Here, we show that the Fermi energy of FeSe is extremely small, resulting in that this system can be regarded as an extraordinary “high-temperature” superconductor located at the verge of a BCS-BEC cross-over. Most importantly, we discover the emergence of an unexpected superconducting phase in strong magnetic fields, demonstrating that the Zeeman splitting comparable to the Fermi energy leads to a strong modification of the properties of fermionic systems in such a regime. Fermi systems in the cross-over regime between weakly coupled Bardeen–Cooper–Schrieffer (BCS) and strongly coupled Bose–Einstein-condensate (BEC) limits are among the most fascinating objects to study the behavior of an assembly of strongly interacting particles. The physics of this cross-over has been of considerable interest both in the fields of condensed matter and ultracold atoms. One of the most challenging issues in this regime is the effect of large spin imbalance on a Fermi system under magnetic fields. Although several exotic physical properties have been predicted theoretically, the experimental realization of such an unusual superconducting state has not been achieved so far. Here we show that pure single crystals of superconducting FeSe offer the possibility to enter the previously unexplored realm where the three energies, Fermi energy [Formula], superconducting gap Δ, and Zeeman energy, become comparable. Through the superfluid response, transport, thermoelectric response, and spectroscopic-imaging scanning tunneling microscopy, we demonstrate that [Formula] of FeSe is extremely small, with the ratio [Formula] in the electron (hole) band. Moreover, thermal-conductivity measurements give evidence of a distinct phase line below the upper critical field, where the Zeeman energy becomes comparable to [Formula] and Δ. The observation of this field-induced phase provides insights into previously poorly understood aspects of the highly spin-polarized Fermi liquid in the BCS-BEC cross-over regime.

The fine control afforded by trapped atomic ions is used to explore experimentally how the range of interactions between the ions influences the spreading of information in quantum many-body systems. Quantum speedometry The speed at which information propagates in quantum many-body systems determines the overall behaviour of these systems. If the interactions between the system components are short-ranged, the dynamics are well understood and relatively straightforward to compute. Less clear is what happens when long-range interactions are present. Now two groups have used the exquisite control afforded by trapped atomic ions to explore experimentally how the interaction range influences the time evolution of quantum many-body systems. The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles 1 . These elementary excitations are predicted to distribute quantum information in a fashion determined by the system’s interactions 2 . Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions 3 , 4 . First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts 5 , 6 , 7 , 8 , 9 , 10 , 11 . Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply 7 , 12 . Our results will enable experimental studies of a range of quantum phenomena, including transport 13 , 14 , thermalization 15 , localization 16 and entanglement growth 17 , and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.

The discovery of materials has often introduced new physical paradigms and enabled the development of novel devices. Two-dimensional magnetism, which is associated with strong intrinsic spin fluctuations, has long been the focus of fundamental questions in condensed matter physics regarding our understanding and control of new phases. Here we discuss magnetic van der Waals materials: two-dimensional atomic crystals that contain magnetic elements and thus exhibit intrinsic magnetic properties. These cleavable materials provide the ideal platform for exploring magnetism in the two-dimensional limit, where new physical phenomena are expected, and represent a substantial shift in our ability to control and investigate nanoscale phases. We present the theoretical background and motivation for investigating this class of crystals, describe the material landscape and the current experimental status of measurement techniques as well as devices, and discuss promising future directions for the study of magnetic van der Waals materials. Recent advances and future directions for the research of magnetic two-dimensional van der Waals materials are reviewed.

Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.

Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.

We study the dynamics of a two-level impurity embedded in a two-dimensional Bose–Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method (2020 Phys. Rev. Res. 2 033276) – closely related to slave boson approaches – that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.

The fine control afforded by trapped atomic ions is used to explore experimentally how the range of interactions between the ions influences the spreading of information in quantum many-body systems.

Nature retraction is a setback for Microsoft’s approach to quantum computing, as researchers continue to search for the exotic quantum states. Nature retraction is a setback for Microsoft’s approach to quantum computing, as researchers continue to search for the exotic quantum states.

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E₈ Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb₂O₆ (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E₈ spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

The fundamental parameters of majority and minority charge carriers—including their type, density and mobility—govern the performance of semiconductor devices yet can be difficult to measure. Although the Hall measurement technique is currently the standard for extracting the properties of majority carriers, those of minority carriers have typically only been accessible through the application of separate techniques. Here we demonstrate an extension to the classic Hall measurement—a carrier-resolved photo-Hall technique—that enables us to simultaneously obtain the mobility and concentration of both majority and minority carriers, as well as the recombination lifetime, diffusion length and recombination coefficient. This is enabled by advances in a.c.-field Hall measurement using a rotating parallel dipole line system and an equation, Δ μ H  = d( σ 2 H )/d σ , which relates the hole–electron Hall mobility difference (Δ μ H ), the conductivity ( σ ) and the Hall coefficient ( H ). We apply this technique to various solar absorbers—including high-performance lead-iodide-based perovskites—and demonstrate simultaneous access to majority and minority carrier parameters and map the results against varying light intensities. This information, which is buried within the photo-Hall measurement 1 , 2 , had remained inaccessible since the original discovery of the Hall effect in 1879 3 . The simultaneous measurement of majority and minority carriers should have broad applications, including in photovoltaics and other optoelectronic devices. A carrier-resolved photo-Hall technique is developed to extract properties of both majority and minority carriers simultaneously and determine the critical parameters of semiconductor materials under light illumination.