An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ($e$-ph) interactions in quantum materials. Despite the growing importance of this area of research, the community lacks a complete understanding of how the RIXS process excites the lattice and how these excitations encode information about the $e$-ph interactions. Here, we present a detailed study of the RIXS spectra of the Hubbard-Holstein model defined on extended one-dimensional lattices. Using the density matrix renormalization group method, we compute the RIXS response while treating the electron mobility, many-body interactions, and core-hole interactions on an equal footing. The predicted spectra exhibit notable differences from those obtained using the commonly adopted Lang-Firsov models, with important implications for analyzing past and future experiments. Our results provide a deeper understanding of how RIXS probes $e$-ph interactions and set the stage for a more realistic analysis of future experiments.

The superconducting state of the heavy-fermion metal ${\mathrm{UTe}}_2$ has attracted considerable interest because of evidence of spin-triplet Cooper pairing and nontrivial topology. Progress on these questions requires identifying the presence or absence of nodes in the superconducting gap function and their dimension. In this article, we report a comprehensive study of the influence of disorder on the thermal transport in the superconducting state of ${\mathrm{UTe}}_2$. Through detailed measurements of the magnetic-field dependence of the thermal conductivity in the zero-temperature limit, we obtain clear evidence of the presence of point nodes in the superconducting gap for all samples with transition temperatures ranging from 1.6 to 2.1 K obtained by different synthesis methods, including a refined self-flux method. This robustness implies the presence of symmetry-imposed nodes throughout the range studied, further confirmed via disorder-dependent calculations of the thermal transport in a model with a single pair of nodes. In addition to capturing the temperature dependence of the thermal conductivity up to $T_c$, this model provides some information about the locations of the nodes, suggesting a $B_{1u}$ or $B_{2u}$ symmetry for the superconducting order parameter. Additionally, comparing the new, ultrahigh conductivity samples to older samples reveals a crossover between a low-field and a high-field regime at a single value of the magnetic field in all samples. In the high-field regime, the thermal conductivity at different disorder levels differs from each other by a simple offset, suggesting that some simple principle determines the physics of the mixed state, a fact which may illuminate trends observed in other clean nodal superconductors.

Song and Bernevig (SB) have recently proposed a topological heavy-fermion description of the physics of magic angle twisted bilayer graphene (MATBG), involving the hybridization of flat-band electrons with a relativistic conduction sea. Here, we explore the consequences of this model, seeking a synthesis of understanding drawn from heavy-fermion physics and MATBG experiments. Our work identifies a key discrepancy between measured and calculated on-site Coulomb interactions, implicating renormalization effects that are not contained in the current model. With these considerations in mind, we consider a SB model with a single, renormalized on-site interaction between the $f$ electrons, containing a phenomenological heavy-fermion binding potential on the moiré $AA$ sites. This feature allows the simplified model to capture the periodic reset of the chemical potential with filling and the observed stability of local moment behavior. We argue that a two-stage Kondo effect will develop in MATBG as a consequence of the relativistic conduction band: Kondo I occurs at high temperatures, establishing a coherent hybridization at the $\mathrm{\Gamma }$ points and a non-Fermi liquid of incoherent fermions at the moiré $K$ points; at much lower temperatures, Kondo II leads to a Fermi liquid in the flat band. Utilizing an auxiliary-rotor approach, we formulate a mean-field treatment of MATBG that captures this physics, describing the evolution of the normal state across a full range of filling factors. By contrasting the relative timescales of phonons and valence fluctuations in bulk heavy-fermion materials with that of MATBG, we are led to propose a valley-polaron origin to the Coulomb renormalization and the heavy-fermion binding potential identified from experiment. We also discuss the possibility that the two-fluid, non-Fermi liquid physics of the relativistic Kondo lattice is responsible for the strange-metal physics observed in MATBG.

Recent breakthrough experiments have demonstrated how it is now possible to explore the dynamics of quantum Hall states interacting with quantum electromagnetic cavity fields. While the impact of strongly coupled nonlocal cavity modes on integer quantum Hall physics has been recently addressed, the effects on fractional quantum Hall (FQH) liquids—and, more generally, fractionalized states of matter—remain largely unexplored. In this work, we develop a theoretical framework for the understanding of FQH states coupled to quantum light. In particular, combining analytical arguments with tensor network simulations, we study the dynamics of a $\nu =1/3$ Laughlin state in a single-mode cavity with finite electric field gradients. We find that the topological signatures of the FQH state remain robust against the nonlocal cavity vacuum fluctuations, as indicated by the endurance of the quantized Hall resistivity. The entanglement spectra, however, carry direct fingerprints of light-matter entanglement and topology, revealing peculiar polaritonic replicas of the U(1) counting. As a further response to cavity fluctuations, we also find a squeezed FQH geometry, encoded in long-wavelength correlations. By exploring the low-energy excited spectrum inside the FQH phase, we identify a new neutral quasiparticle, the graviton polariton, arising from the hybridization between quadrupolar FQH collective excitations (known as gravitons) and light. Pushing the light-matter interaction to ultrastrong-coupling regimes, we find other two important effects, a cavity vacuum-induced Stark shift for charged quasiparticles and a potential instability toward a density modulated stripe phase, competing against the phase separation driven by the Stark shift. Finally, we discuss the experimental implications of our findings and possible extension of our results to more complex scenarios.

Understanding nanoscale electronic and thermal transport of two-dimensional (2D) electron systems in the quantum Hall regime, particularly in the bulk insulating state, poses considerable challenges. One of the primary difficulties arises from the presence of chiral edge channels, whose transport behavior obscures the investigation of the insulating bulk. Using near-field optical and photocurrent nanoscopy, we probe real-space variations of the optical and thermal dynamics of graphene in the quantum Hall regime without relying on complex sample or electrode geometries. Near the charge-neutrality point, we detect strong optical and photothermal signals from resonant inter-Landau-level (LL) magnetoexciton excitations between the zeroth and $\pm 1$ st LLs, which gradually weaken with increasing doping due to Pauli blocking. Interestingly, at higher doping levels and full-integer LL fillings, photothermal signals reappear across the entire sample over an approximately $10\text{−}\mathrm{\mu }\mathrm{m}$ scale, indicating unexpectedly long cooling lengths and nonlocal photothermal heating through the insulating bulk. This observation suggests that thermal conductivity persists for the localized states even as electronic transport is suppressed—a clear violation of the Wiedemann-Franz law. Our experiments provide novel insights into nanoscale thermal and electronic transport in incompressible 2D gases, highlighting the roles of magnetoexcitons and chiral edge states in the thermo-optoelectric dynamics of the Dirac quantum Hall state.

The self-thinning of liquid bridges under the action of capillarity occurs in widespread processes like jetting, dripping, and spraying and gives rise to a strong extensional flow capable of stretching dissolved polymers. If the resulting elastic stress exceeds the viscous stress, an exponential “elastocapillary” (EC) thinning regime arises, yielding a timescale ${\tau }_{\mathrm{EC}}$ that is commonly considered equivalent to the longest relaxation time of the polymer $\lambda$. A long-standing question is why ${\tau }_{\mathrm{EC}}$ depends strongly on the polymer concentration, even at high dilutions where $\lambda$ should be constant in theory. To date, this is understood in terms of intermolecular interactions that arise due to “self-concentration” effects as polymers stretch. However, $\lambda$ depends on the polymer molecular weight $M$, and we show how the concentration dependence of ${\tau }_{\mathrm{EC}}$ can be explained by considering the molecular weight distribution (MWD) inherent in real polymer samples, without the need to invoke self-concentration. We demonstrate this by blending low-$M$ and high-$M$ polymer samples with narrow MWDs at dilute concentrations and in different proportions and by measuring ${\tau }_{\mathrm{EC}}$ for each blend in capillary thinning experiments. Through a simple model that qualitatively reproduces the experimental results, we show how elastic stresses generated by the polymer build up prior to the EC regime due to the sequential stretching of progressively decreasing molecular weight species in the MWD. Since the elastic stress generated by each species depends on its concentration, the fraction of the MWD that is required to stretch in order to induce the EC regime depends on the total polymer concentration $c$ in the solution. For higher $c$, the EC regime is induced by stretching of a higher-$M$ (longer $\lambda$) fraction of the MWD and results in a longer measurement of ${\tau }_{\mathrm{EC}}$. Our results have significant implications for the application of capillary thinning measurements to extensional rheometry, for the interpretation of such measurements, and for the understanding of elastocapillary thinning dynamics in general.

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.

Local random circuits scramble efficiently and, accordingly, have a range of applications in quantum information and quantum dynamics. With a global U(1) charge, however, the scrambling ability is reduced; for example, such random circuits do not generate the entire group of number-conserving unitaries. We establish two results using the statistical mechanics of $k$-fold replicated circuits. First, we show that finite moments cannot distinguish the ensemble that local random circuits generate from the Haar ensemble on the entire group of number-conserving unitaries. Specifically, the circuits form a $k_c$-design with $k_c=O(L^d)$ for a system in $d$ spatial dimensions with linear dimension $L$. Second, for $k<k_c$, we derive bounds on the depth $\tau$ required for the circuit to converge to an approximate $k$-design. The depth is lower bounded by diffusion $k{L}^2\ln (L)\lesssim \tau$. In contrast, without number conservation $\tau \sim \mathrm{poly}(k)L$. The convergence of the circuit ensemble is controlled by the low-energy properties of a frustration-free quantum statistical model which spontaneously breaks $k$ U(1) symmetries. We conjecture that the associated Goldstone modes set the spectral gap for arbitrary spatial and qudit dimensions, leading to an upper bound $\tau \lesssim k{L}^{d+2}$.

Competing interactions in frustrated magnets can give rise to highly degenerate ground states from which correlated liquidlike states of matter often emerge. The scaling of this degeneracy influences the ultimate ground state, with extensive degeneracies potentially yielding quantum spin liquids, while subextensive or smaller degeneracies yield static orders. A long-standing problem is to understand how ordered states precipitate from this degenerate manifold and what echoes of the degeneracy survive ordering. Here, we use neutron scattering to experimentally demonstrate a new “nodal-line” spin liquid, where spins collectively fluctuate within a subextensive manifold spanning one-dimensional lines in reciprocal space. Realized in the spin-orbit-coupled, face-centered-cubic iridate ${\mathrm{K}}_2{\mathrm{IrCl}}_6$, we show that the subextensive degeneracy is robust, but remains susceptible to fluctuations or longer-range interactions which cooperate to select a magnetic order at low temperatures. Proximity to the nodal-line spin liquid influences the ordered state, enhancing the effects of quantum fluctuations that in turn act to stabilize the sublattice magnetization through the self-consistent opening of a large spin-wave gap. Our results demonstrate how quantum fluctuations can act counterintuitively in frustrated materials: Even in a case where fluctuations are ineffective at selecting an ordered state from a degenerate manifold, at the brink of the nodal spin liquid, they can act to protect the ordered state and dictate its low-energy physics.

Monitored quantum systems undergo measurement-induced phase transitions (MiPTs) stemming from the interplay between measurements and unitary dynamics. When the detector readout is postselected to match a given value, the dynamics is generated by a non-Hermitian Hamiltonian with MiPTs characterized by different universal features. Here, we derive a partial postselected stochastic Schrödinger equation based on a microscopic description of continuous weak measurement. This formalism connects the monitored and postselected dynamics to a broader family of stochastic evolution. We apply the formalism to a chain of free fermions subject to partial postselected monitoring of local fermion parities. Within a two-replica approach, we obtain an effective bosonized Hamiltonian in the strong postselected limit. Using a renormalization group analysis, we find that the universality of the non-Hermitian MiPT is stable against a finite (weak) amount of stochasticity. We further show that the passage to the monitored universality occurs abruptly at finite partial postselection, which we confirm from the numerical finite size scaling of the MiPT. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories and provides a potential route to tackle the experimental postselected problem.

Quantum critical phenomena are widely studied across various materials families, from high-temperature superconductors to magnetic insulators. They occur when a thermodynamic phase transition is suppressed to zero temperature as a function of some tuning parameter such as pressure or magnetic field. This generally yields a point of instability—a so-called quantum critical point—at which the phase transition is driven exclusively by quantum fluctuations. Here, we show that the heavy fermion metamagnet ${\mathrm{UTe}}_2$ possesses a quantum phase transition at extreme magnetic field strengths of over 70 T. Rather than terminating at one singular point, we find that the phase boundary is sensitive to magnetic field components in each of the three Cartesian axes of magnetic field space. This results in the transition surface being bounded by a continuous ring of quantum critical points, the locus of which forms an extended line of quantum criticality—a novel form of quantum critical phase boundary. Within this quantum critical line sits a magnetic field-induced superconducting state in a toroidal shape, which persists to fields over 70 T. We model our data by a phenomenological free energy expansion and show how a quantum critical line—rather than a more conventional singular point of instability—anchors the remarkable high magnetic field phase landscape of ${\mathrm{UTe}}_2$.

The symmetry of superconducting and normal states is at the core of superconductivity research. Emergent electronic nematicity, which spontaneously breaks the rotational symmetry, has been found in the normal state of various types of unconventional superconductors. Here, we exploit the angle-resolved resistivity method to systematically measure the nematicity of the interface superconducting ${\mathrm{LaAlO}}_3/{\mathrm{KTaO}}_3(111)$ ($\mathrm{LAO}/\mathrm{KTO}$). Compared to the normal state, electronic nematicity is enhanced substantially by superconducting fluctuations around the superconducting temperature $T_{\mathrm{c}}$. More importantly, $T_{\mathrm{c}}$ is also anisotropic in plane and angle dependent. The nematicity consists of a dominant ${\mathrm{C}}_2$ component and a ${\mathrm{C}}_4$ component, which can be explained by the presence of nematic domains. After the superconductivity is suppressed by a magnetic field, the uncovered quantum metal state manifests significant nematicity that is contributed by residual nematic superconducting fluctuations. A coherent picture of nematic interface superconductivity can be retrieved from the measured nematicity phase diagram that is crucial for the understanding of quantum metal state, electronic nematicity, and interface superconductivity.

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of $ϵ$ in time that is $\mathrm{poly}({ϵ}^{-1})$ and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming $\mathrm{BQP}\ne \mathrm{BPP}$. We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming $\mathrm{BQP}\ne \mathrm{BPP}$, there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator.

A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell demons that achieve robust feedback-controlled chiral or helical transport against noise and decoherence. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control.

Ultrasound microscopy is the only technique that has the ability to monitor live-cell morphology over a long period of time without causing any damage to the cells, but its longer wavelength prevents one from obtaining high-resolution cell images. Here, we propose a deep-learning (DL) method for generating high-resolution acoustic images. By preparing datasets consisting of many pairs of acoustic and optical-microscope images for the same cells and training them, a high-resolution image comparable to optical microscopy is generated from an acoustic image. Importantly, the most accurate images are generated when three-layer (RGB) images containing not only high-frequency (approximately 180 MHz) images but also lower-frequency (approximately 100 MHz) images are used as the input images, which is attributed to enhanced acoustic absorption in the nucleus because the nucleus resonates in this low-frequency band. The DL scheme with the tri-frequency image input is applied to human mesenchymal stem cells and human induced pluripotent stem cells, and the high image-generation capability is demonstrated. As a result, high-resolution acoustic microscopy images are obtained for the same cells for over 24 h, without the typical cell damage encountered using optical imaging.

Through continuous progress in nuclear theory and experiment and an increasing number of neutron-star (NS) observations, a multitude of information about the equation of state (EOS) for matter at extreme densities is available. To constrain the EOS across its entire density range, this information needs to be combined consistently. However, the impact and model dependency of individual observations vary. Given their growing number, assessing the various methods is crucial to compare the respective effects on the EOS and discover potential biases. For this purpose, we present a broad compendium of different constraints and apply them individually to a large set of EOS candidates within a Bayesian framework. Specifically, we explore different ways of how chiral effective field theory and perturbative quantum chromodynamics can be used to place a likelihood on EOS candidates. We also investigate the impact of nuclear experimental constraints, as well as different radio and x-ray observations of NS masses and radii. This is augmented by reanalyses of the existing data from binary neutron star coalescences, in particular of GW170817, with improved models for the tidal waveform and kilonova light curves, which we also utilize to construct a tight upper limit of $2.39M_{\odot }$ on the TOV mass based on GW170817’s remnant. Our diverse set of constraints is eventually combined to obtain stringent limits on NS properties. We organize the combination in a way to distinguish between constraints where the systematic uncertainties are deemed small and those that rely on less conservative assumptions. For the former, we find the radius of the canonical $1.4M_{\odot }$ neutron star to be $R_{1.4}=12.26_{-0.91}^{+0.80}\mathrm{km}$ and the TOV mass at $M_{\mathrm{TOV}}=2.25_{-0.22}^{+0.42}{M}_{\odot }$ (95% credibility). Including all the presented constraints yields $R_{1.4}=12.20_{-0.48}^{+0.50}\mathrm{km}$ and $M_{\mathrm{TOV}}=2.30_{-0.20}^{+0.07}{M}_{\odot }$. When comparing these limits to individual data points, we find that the quoted radius of HESS J1731-347 displays noticeable tension with other constraints. Constraining microphysical properties of the EOS proves more challenging. For instance, the symmetry energy slope is restricted to $L_{\mathrm{sym}}={48}_{-25}^{+21}\mathrm{MeV}$, where this constraint is mainly dominated by our reanalysis of the PREX-II and CREX experiment.

Despite their importance in quantum theory, joint quantum measurements remain poorly understood. An intriguing conceptual and practical question is whether joint quantum measurements on separated systems can be performed without bringing them together. Remarkably, by using shared entanglement, this can be achieved perfectly when disregarding the postmeasurement state. However, existing localization protocols typically require unbounded entanglement. In this work, we address the fundamental question: “Which joint measurements can be localized with a finite amount of entanglement?” We develop finite-resource versions of teleportation-based schemes and analytically classify all two-qubit measurements that can be localized in the first levels of the resulting hierarchies. These levels include several measurements with exceptional properties and symmetries, such as the Bell state measurement and the elegant joint measurement. This leads us to propose a systematic classification of joint measurements based on entanglement cost, which we argue directly connects with the complexity of implementing those measurements. We illustrate how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.

Gravitational waves, detected a century after they were first theorized, are space-time distortions caused by some of the most cataclysmic events in the Universe, including black hole mergers and supernovae. The successful detection of these waves has been made possible by ingenious detectors designed by human experts. Beyond these successful designs, the vast space of experimental configurations remains largely unexplored, offering an exciting territory potentially rich in innovative and unconventional detection strategies. Here, we demonstrate an intelligent computational strategy to explore this enormous space, discovering unorthodox topologies for gravitational wave detectors that significantly outperform the currently best-known designs under realistic experimental constraints. This increases the potentially observable volume of the Universe by up to 50-fold. Moreover, by analyzing the best solutions from our superhuman algorithm, we uncover entirely new physics ideas at their core. At a bigger picture, our methodology can readily be extended to AI-driven design of experiments across wide domains of fundamental physics, opening fascinating new windows into the Universe.

Solid-state quantum registers consisting of optically active electron spins with nearby nuclear spins are promising building blocks for future quantum technologies. For electron spin-1 registers, dynamical decoupling (DD) quantum gates have been developed that enable the precise control of multiple nuclear spin qubits. However, for the important class of electron spin-$1/2$ systems, this control method suffers from intrinsic selectivity limitations, resulting in reduced nuclear spin gate fidelities. Here, we demonstrate improved control of single nuclear spins by an electron spin-$1/2$ using dynamically decoupled radio-frequency (DDRF) gates. We make use of the electron spin-$1/2$ of a diamond tin-vacancy center, showing high-fidelity single-qubit gates, single-shot readout, and spin coherence beyond a millisecond. The DD control is used as a benchmark to observe and control a single ${}^{1}3\mathrm{C}$ nuclear spin. Using the DDRF control method, we demonstrate improved control on that spin. In addition, we find and control an additional nuclear spin that is insensitive to the DD control method. Using these DDRF gates, we show entanglement between the electron and the nuclear spin with 72(3)% state fidelity. Our extensive simulations indicate that DDRF gate fidelities well in excess are feasible. Finally, we employ time-resolved photon detection during readout to quantify the hyperfine coupling for the electron’s optically excited state. Our work provides key insights into the challenges and opportunities for nuclear spin control in electron spin-$1/2$ systems, opening the door to multiqubit experiments on these promising qubit platforms.

Although spin and charge stripes in high-$T_c$ cuprates have been extensively studied, the exact range of carrier concentration over which they form a static order remains uncertain, complicating efforts to understand their significance. The problem is challenging due to the combined effects of quenched disorder and competition with superconductivity—both significant in cuprates—which add to the inherent difficulty of determining phase boundaries. In ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) and in zero external magnetic field, static spin stripes are confined to a doping range well below $p^{*}$, the pseudogap boundary at zero temperature. However, when high fields suppress the competing effect of superconductivity, spin-stripe order is found to extend up to $p^{*}$. Here, we investigate ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (Eu-LSCO) using ${}^{139}\mathrm{La}$ nuclear magnetic resonance and observe field-dependent spin fluctuations suggesting a similar competition between superconductivity and spin order as in LSCO. Nevertheless, we find that static spin stripes are present practically up to $p^{*}$ irrespective of field strength: The stronger stripe order in Eu-LSCO prevents superconductivity from enforcing a nonmagnetic ground state, except very close to $p^{*}$. Thus, spin-stripe order is consistently bounded by $p^{*}$ in both LSCO and Eu-LSCO, despite their differing balances between stripe order and superconductivity. This indicates that the canonical stripe order, where spins and charges are intertwined in a static pattern, is fundamentally tied to the pseudogap phase, though the exact nature of this connection has yet to be elucidated. Any stripe order beyond the pseudogap endpoint must then be of a different nature: Either spin and charge orders remain intertwined, but both fluctuating, or only spin order fluctuates while charge order remains static. The presence of spin-stripe order up to $p^{*}$ and the pervasive, slow, and field-dependent spin-stripe fluctuations, as well as the electronic inhomogeneity documented in this work, must all be carefully considered in discussions of Fermi surface transformations, putative quantum criticality, and strange metal behavior.