We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and $1700{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ and the neutron star–black hole merger rate to be between 7.8 and $140{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and $44{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ at a fiducial redshift ($z=0.2$). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to $(1+z{)}^{\kappa }$ with $\kappa =2.9_{-1.8}^{+1.7}$ for $z\lesssim 1$. Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from ${1.2}_{-0.2}^{+0.1}$ to ${2.0}_{-0.3}^{+0.3}{M}_{\odot }$. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of ${8.3}_{-0.5}^{+0.3}$ and ${27.9}_{-1.8}^{+1.9}{M}_{\odot }$. While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately $60M_{\odot }$, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below ${\chi }_i\approx 0.25$. While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum.

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times {10}^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions.

Vortices are topological defects of type-II superconductors in an external magnetic field. In a similar fashion to a quantum anomalous Hall insulator, quantum anomalous vortices (QAV) spontaneously nucleate due to orbital-and-spin exchange interaction between supercurrent and magnetic impurity moment without an external magnetic field. Here, we used scanning superconducting quantum interference device microscopy (sSQUID) to search for its signatures in iron-chalcogenide superconductor Fe(Se,Te). Under zero magnetic field, we found a stochastic distribution of isolated anomalous vortices and antivortices with flux quanta ${\mathrm{\Phi }}_0$. By applying a small local magnetic field under the coil of the nano-SQUID device, we observed hysteretic flipping of the vortices reminiscent of the switching of ferromagnetic domains, suggesting locally broken time-reversal symmetry. We further observed vectorial rotation of a flux line linking a vortex-antivortex pair by manipulating the local field. These unique properties of the anomalous vortices satisfy the defining criteria of QAV. Our observation suggests an emergent quantum phase with spontaneously nucleated vortex-antivortex matter in an iron-based superconductor with nontrivial topological band structure.

Quantum coherences characterize the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems, these coherences can fluctuate. A simple toy model to study such fluctuations in an out-of-equilibrium setting is the open quantum symmetric simple exclusion process (Q-SSEP), which describes spinless fermions in one dimension hopping to neighboring sites with random amplitudes coupled between two reservoirs. Here, we show that the dynamics of fluctuations of coherences in Q-SSEP have a natural interpretation as free cumulants, a concept from free probability theory. Based on this insight, we provide heuristic arguments as to why we expect free probability theory to be an appropriate framework to describe coherent fluctuations in generic mesoscopic systems where the noise emerges from a coarse-grained description. In the case of Q-SSEP, we show how the link to free probability theory can be used to derive the time evolution of connected fluctuations of coherences as well as a simple steady-state solution.

Chirality is widespread in nature, playing a fundamental role in biochemical processes and in the origin of life itself. The observation of dynamics in chiral molecules is crucial for the understanding and control of the chiral activity of photoexcited states. One of the most promising techniques for the study of photoexcited chiral systems is time-resolved photoelectron circular dichroism (TR-PECD), which offers an intense and sensitive probe for vibronic and geometric molecular structure as well as electronic structures, and their evolution on a femtosecond timescale. However, the nonlocal character of the PECD effect, which is imprinted during the electron scattering off the molecule, makes the interpretation of TR-PECD experiments challenging. In this respect, core photoionization is known to allow site and chemical sensitivity to photelectron spectroscopy. Here we demonstrate that TR-PECD utilizing core-level photoemission enables probing the chiral electronic structure and its relaxation dynamics with atomic site sensitivity. Following UV pumped excitation to a $3s$ Rydberg state, fenchone enantiomers (${\mathrm{C}}_{10}{\mathrm{H}}_{16}\mathrm{O}$) were probed on a femtosecond scale using circularly polarized soft x-ray light pulses provided by the free-electron laser FERMI. C $1s$ binding energy shifts caused by the redistribution of valence electron density in this $3s$-valence-Rydberg excitation allowed us to measure transient PECD chiral responses with an enhanced C atom site selectivity compared to that achievable in the ground state molecule. This chemical-specific, site-specific, and enantiosensitive observation of the electronic structure of a transiently photoexcited chiral molecule is expected to pave the way toward chiral femtochemistry probed by core-level photoemission.

We consider critical one-dimensional quantum systems initially prepared in their ground state and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any two-point chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast to the general expectation of heating, we demonstrate that, over the noise realizations, the system reaches a nontrivial and universal stationary distribution of states characterized by broad tails of physical quantities. As an example, we analyze the entanglement entropy production associated to a given interval of size $\ell$. The corresponding stationary distribution has a $3/2$ right tail for all $\ell$ and converges to a one-sided Levy stable for large $\ell$. We obtain a similar result for the local energy density: While its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with $3/2$ decay exponent. We show that this stationary distribution for the energy density emerges even if the initial state is prepared at finite temperature. Our results are benchmarked via analytical and numerical calculations for a chain of noninteracting spinless fermions with excellent agreement.

Optically active solid-state spin defects have the potential to become a versatile resource for quantum information processing applications. Nitrogen-vacancy defect centers (NV) in diamond act as quantum memories and can be interfaced with coherent photons as demonstrated in entanglement protocols. However, particularly in diamond nanostructures, the effect of spectral diffusion leads to optical decoherence hindering entanglement generation. In this work, we present strategies to significantly reduce the electric noise in diamond nanostructures. We demonstrate single NVs in nanopillars exhibiting a lifetime-limited linewidth on a timescale of one second and long-term spectral stability with an inhomogeneous linewidth as low as 150 MHz over three minutes. Excitation power and energy-dependent measurements in combination with nanoscopic Monte Carlo simulations contribute to a better understanding of the impact of bulk and surface defects on the NV’s spectral properties. Finally, we propose an entanglement protocol for nanostructure-coupled NVs providing entanglement generation rates up to hundreds of kHz.

We analyze a crossover between ergodic and nonergodic regimes in an interacting spin chain with a dilute density of impurities, defined as spins with a strong local field. The dilute limit allows us to unravel some finite size effects and propose a mechanism for the delocalization of these impurities in the thermodynamic limit. In particular, we show that impurities always relax by exchanging energy with the rest of the chain. The relaxation rate only weakly depends on the impurity density and decays exponentially, up to logarithmic corrections, with the field strength. We connect the relaxation to fast operator spreading and show that the same mechanism destabilizes the recursive construction of local integrals of motion at any impurity density. In the high field limit, impurities appear to be localized, and the system is nonergodic, over a wide range of system sizes. However, this is a transient effect, and the eventual delocalization can be understood in terms of a flowing localization length.

We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose spectrum encompasses an integrated dispersion that exceeds the cavity free-spectral range. We are able to access this regime in low-dispersion photonic chip-based microresonators by employing synchronous pulse driving, which increases the peak power over the continuous-wave-driving regime. Exploring this dispersion-folded regime, we demonstrate that the presence of periodically varying dispersion can excite higher-order comb structures, which we explore in both the normal and anomalous dispersion regimes. In the former, we observe the coexistence of switching wave fronts with Faraday instability-induced period-doubling patterns. They manifest as strong satellite microcombs highly separated either side of the core microcomb, at an offset close to half the repetition rate but while sharing the same repetition rate. In the latter, for dissipative Kerr solitons in anomalous dispersion, we observe the formation of higher-order phase-matched dispersive waves (“Kelly-like” sidebands), where the folded dispersion crosses the frequency comb grid. We observe up to the fifth higher-order dispersive wave in our experiments and show that these higher-order dispersive waves coherently extend the soliton frequency comb bandwidth significantly. For both cases, we show that our results can be understood by considering four-wave mixing in a two-dimensional Fourier transform representation. The results demonstrate the rich novel nonlinear dynamics of driven dissipative nonlinear cavities with periodically varying dispersion in the dispersion-folded pumping regime.

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature $T_c$ for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This $\mathrm{MPS}+\mathrm{MF}$ framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute $T_c$ for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The $\mathrm{MPS}+\mathrm{MF}$ framework thus enables the quantitative study of USC and high-$T_c$ superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., $T_c$ due to its mean-field component, is near constant in microscopic parameters. These features of the $\mathrm{MPS}+\mathrm{MF}$ approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ${\eta }_c=0.25$ in our fiducial analysis compared to ${\eta }_c=0.34$), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much larger than the average intergalaxy separation, implying that they lie in the same universality class. We also show that the distribution of galaxies is a highly correlated disordered system (relative to the uncorrelated Poisson distribution), as measured by the $\tau$ order metric. Finally, we consider the ability of large-scale clustering statistics to constrain cosmological parameters, such as the Universe’s expansion rate, using simulation-based inference. Both the nearest-neighbor distribution and pair-connectedness function (which includes contributions from correlation functions of all order) are found to considerably tighten bounds on the amplitude of quantum-mechanical fluctuations from inflation at a level equivalent to observing 25 times more galaxies. The pair-connectedness function in particular provides a useful alternative to the standard three-particle correlation, since it contains similar large-scale information to the three-point function, can be computed highly efficiently, and can be straightforwardly extended to small scales (though likely requires simulation-based modeling). This work provides the first application of such techniques to cosmology, providing both a novel system to test heterogeneous media descriptors and a tranche of new tools for cosmological analyses. A range of extensions are possible, including implementation on observational data; this will require further study on various observational effects, necessitating high-resolution simulations.

We investigate the electronic structure of ${\mathrm{LaCoO}}_3$ across the gradual spin-state and insulator-to-metal transitions using bulk-sensitive hard x-ray photoelectron and soft x-ray absorption spectroscopies. The spectra exhibit strong variations with temperature. The energy gap is reduced by about 0.6 eV in going from 80 to 650 K but the near Fermi level intensity remains small, classifying ${\mathrm{LaCoO}}_3$ as a bad metal even in the metallic phase. We are able to explain the spectra in terms of incoherent sums of low-spin and high-spin ${\mathrm{Co}}^{3+}$ spectra. We also find that the energy parameters for the two Co sites are very different, revealing that paramagnetic ${\mathrm{LaCoO}}_3$ is a highly inhomogeneous system with local lattice relaxations that are spin-state-specific. This, in turn, provides a natural explanation for the much-debated temperature dependence of the activation energy for the transitions.

Multipolar spindles are very rare in normal tissues, but they are much more prevalent in many tumors, which might be induced by the mechanical confinements from overcrowding microenvironments in tumors. However, little is known about what the difference is between various forms of mechanical confinements that cells encounter in normal tissues and tumor tissues, and how they affect multipolarity and chromosome segregation fidelity. Here, we use microchannels with different heights and widths to mimic diverse forms and degrees of mechanical constraints within the tissue architecture. We find that multipolar spindles occur frequently under two-wall confinement but that they are rare under four-wall confinement, suggesting that multipolar-spindle assembly depends on the form of the three-dimensional mechanical confinement. We reveal that two-wall confinement leads to an increased fraction of multipolar spindles by pole splitting, while four-wall confinement restrains multipolarity by the enhancement of pole clustering and the inhibition of pole splitting. We further conduct numerical simulations and develop a theoretical model to investigate how mechanical confinement influences pole splitting and clustering. By exploring the energy landscape of pole-pole interactions and pole-cortex interactions and treating pole splitting and clustering as reversible reactions, we demonstrate that mechanical confinement controls cell shape and pole-cortex interactions, which, in turn, change the energy barriers of pole splitting and clustering as well as the probability of multipolar mitosis. Further experiments confirm the theoretical prediction that the pole-cortex interaction determines the probability of the multipolar spindles under various mechanical confinements. Our findings demonstrate the extent to which extracellular microenvironments and tissue architecture can affect complex cellular behaviors, indicating that normal tissue architecture may have the ability to suppress the progress of cancers. Thus, our findings would provide essential cues for cancer therapies targeting the tumor microenvironment.

Weyl electrons are intensely studied due to novel charge transport phenomena such as chiral anomaly, Fermi arcs, and photogalvanic effect. Recent theoretical works suggest that Weyl electrons can also participate in magnetic interactions, and the Weyl-mediated indirect exchange coupling between local moments is proposed as a new mechanism to induce spiral magnetic ordering by involving chiral Weyl electrons. Here, we present evidence of Weyl-mediated spiral magnetism in SmAlSi from neutron diffraction, transport, and thermodynamic data. We show that the spiral order in SmAlSi results from the nesting between topologically nontrivial Fermi pockets and weak magnetocrystalline anisotropy, unlike related materials (Ce,Pr,Nd)AlSi, where a strong anisotropy prevents the spins from freely rotating. We map the magnetic phase diagram of SmAlSi and reveal an $A$ phase where topological magnetic excitations may exist. Within the $A$ phase, we find a large topological Hall effect whose variation with the magnetic field direction suggests a dominant helical instead of cycloidal character, as theoretically predicted for the Weyl-induced spiral order.

We elucidate the fate of classical symmetries which suffer from Abelian Adler-Bell-Jackiw anomalies. Instead of being completely destroyed, these symmetries survive as noninvertible topological global symmetry defects with world volume anyon degrees of freedom that couple to the bulk through a magnetic 1-form global symmetry as in the fractional Hall effect. These noninvertible chiral symmetries imply selection rules on correlation functions and arise in familiar models of massless quantum electrodynamics and models of axions (as well as their non-Abelian generalizations). When the associated bulk magnetic 1-form symmetry is broken by the propagation of dynamical magnetic monopoles, the selection rules of the noninvertible chiral symmetry defects are violated nonperturbatively. This leads to technically natural exponential hierarchies in axion potentials and fermion masses.

Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a long-lived superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. While generic strong deformations of the PXP model indeed restore diffusive transport, adding a strong chemical potential intriguingly gives rise to a well-converged superdiffusive exponent $z\approx 3/2$. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the suppression of some form of symmetry-breaking order to zero temperature has received particular attention. The key question is how the strength of the electron pairs changes near the QCP, and this can be verified by high-field experiments. However, such studies are limited mainly to superconductors with magnetic QCPs, and the possibility of unconventional mechanisms by which nonmagnetic QCP promotes strong pairing remains a nontrivial issue. Here, we report systematic measurements of the upper critical field $H_{c2}$ in nonmagnetic ${\mathrm{FeSe}}_{1-x}{\mathrm{Te}}_x$ superconductors, which exhibit a pure QCP of electronic nematicity characterized by spontaneous rotational-symmetry breaking. As the magnetic field increases, the superconducting phase of ${\mathrm{FeSe}}_{1-x}{\mathrm{Te}}_x$ shrinks to a narrower dome surrounding the nematic QCP. The analysis of $H_{c2}$ reveals that the Pauli-limiting field is enhanced toward the QCP, implying that the pairing interaction is significantly strengthened via nematic fluctuations emanating from the QCP. Remarkably, this nematic QCP is not accompanied by a divergent effective mass, distinct from the magnetically mediated pairing. Our observation opens up a nematic route to high-temperature superconductivity.

Anyon collision experiments have recently demonstrated the ability to discriminate between fermionic and anyonic statistics. However, only one type of anyons associated with the simple Laughlin state at filling factor $\nu =1/3$ has been probed so far. It is now important to establish anyon collisions as quantitative probes of fractional statistics for more complex topological orders, with the ability to distinguish between different species of anyons with different statistics. In this work, we use the anyon collider to compare the Laughlin $\nu =1/3$ state, which is used as the reference state, with the more complex Jain state at $\nu =2/5$, where low energy excitations are carried by two copropagating edge channels. We demonstrate that anyons generated on the outer channel of the $\nu =2/5$ state (with a fractional charge $e^{*}=e/3$) have a similar behavior compared to $\nu =1/3$, showing the robustness of anyon collision signals for anyons of the same type. In contrast, anyons emitted on the inner channel of $\nu =2/5$ (with a fractional charge $e^{*}=e/5$) exhibit a reduced degree of bunching compared to the $\nu =1/3$ case, demonstrating the ability of the anyon collider to discriminate not only between anyons and fermions, but also between different species of anyons associated with different topological orders of the bulk. Our experimental results for the inner channel of $\nu =2/5$ also point toward an influence of interchannel interactions in anyon collision experiments when several copropagating edge channels are present. A quantitative understanding of these effects will be important for extensions of anyon collisions to non-Abelian topological orders, where several charged and neutral modes propagate at the edge.

Recent pioneering works have set the stage for exploring anyon braiding statistics from negative current cross-correlations along two intersecting quasiparticle beams. In such a dual-source-analyzer quantum point contact setup, also referred to as “collider,” the anyon exchange phase of fractional quantum Hall quasiparticles is predicted to be imprinted into the cross-correlations characterized by an effective Fano factor $P$. In the case of symmetric incoming quasiparticle beams, conventional fermions result in a vanishing $P$. In marked contrast, we observe signatures of anyon statistics in the negative $P$ found both for the $e/3$ Laughlin quasiparticles at filling factor $\nu =1/3$ ($P\approx -2$, corroborating previous findings) and for the $e/5$ quasiparticles in the hierarchical state $\nu =2/5$ ($P\approx -1$). Nevertheless, we argue that the quantitative connection between a numerical value of $P\ne 0$ and a specific fractional exchange phase is hampered by the influence of the analyzer conductance dependence on the voltages used to generate the quasiparticles. Finally, we address the important challenge how to distinguish at $\nu =1/3$ between negative cross-correlations induced by a fractional braid phase and those resulting from a different Andreev-like mechanism. Although with symmetric sources $P$ does not exhibit signatures of a crossover when the analyzer is progressively detuned to favor Andreev processes, we demonstrate that changing the balance between sources provides a means to discriminate between the two mechanisms.

When mobile impurities are introduced and coupled to a Fermi sea, new quasiparticles known as Fermi polarons are formed. There are two interesting, yet drastically different regimes of the Fermi polaron problem: (i) the attractive polaron (AP) branch connected to pairing phenomena spanning the crossover from BCS superfluidity to the Bose-Einstein condensation of molecules and (ii) the repulsive branch (RP), which underlies the physics responsible for Stoner’s itinerant ferromagnetism. Here, we study Fermi polarons in two-dimensional systems, where many questions and debates regarding their nature persist. The model system we investigate is a doped ${\mathrm{MoSe}}_2$ monolayer. We find the observed AP-RP energy splitting and the quantum dynamics of attractive polarons agree with the predictions of polaron theory. As the doping density increases, the quantum dephasing of the attractive polarons remains constant, indicative of stable quasiparticles, while the repulsive polaron dephasing rate increases nearly quadratically. The dynamics of Fermi polarons are of critical importance for understanding the pairing and magnetic instabilities that lead to the formation of rich quantum phases found in a wide range of physical systems including nuclei, cold atomic gases, and solids.