What do the typical entangled states of two black holes look like? Do they contain semiclassical interiors? We approach these questions constructively, providing ensembles of states that densely explore the black hole Hilbert space. The states contain very long Einstein-Rosen caterpillars: semiclassical wormholes with large numbers of matter inhomogeneities. Distinguishing these ensembles from the typical entangled states of the black holes is hard. We quantify this by deriving the correspondence between a microscopic notion of quantum randomness and the geometric length of the wormhole. This formalizes a “complexity $=$ geometry” relation.

Using $e^{+}{e}^{-}$ annihilation data corresponding to a total integrated luminosity of $7.33{\mathrm{fb}}^{-1}$ collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, we provide the first amplitude analysis and absolute branching fraction measurement of the hadronic decay $D_s^{+}\to K_S^0{K}_L^0{\pi }^{+}$. The branching fraction of $D_s^{+}\to K_S^0{K}_L^0{\pi }^{+}$ is determined to be $(1.86\pm 0.06_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}})\%$. Combining the $\mathcal{B}[D_s^{+}\to \varphi (\to K_S^0{K}_L^0){\pi }^{+}]$ obtained in this Letter and the world average of $\mathcal{B}[D_s^{+}\to \varphi (\to K^{+}{K}^{-}){\pi }^{+}]$, we measure the relative branching fraction $\mathcal{B}(\varphi \to K_S^0{K}_L^0)/\mathcal{B}(\varphi \to K^{+}{K}^{-})=(0.593\pm 0.023_{\mathrm{stat}}\pm 0.014_{\mathrm{syst}}\pm 0.016_{\varphi \pi })$, where the third error is due to the uncertainty of the $\mathcal{B}(D_s^{+}\to \varphi {\pi }^{+},\varphi \to K^{+}{K}^{-})$. Our result deviates from the Particle Data Group value by more than $3\sigma$. Furthermore, the asymmetry of the branching fractions of $D_s^{+}\to K_S^0{K}^{*}(892{)}^{+}$ and $D_s^{+}\to K_L^0{K}^{*}(892{)}^{+}$, $\mathbf{(}\{\mathcal{B}[D_s^{+}\to K_S^0{K}^{*}(892{)}^{+}]-\mathcal{B}[D_s^{+}\to K_L^0{K}^{*}(892{)}^{+}]\}/\{\mathcal{B}[D_s^{+}\to K_S^0{K}^{*}(892{)}^{+}]+\mathcal{B}[D_s^{+}\to K_L^0{K}^{*}(892{)}^{+}]\}\mathbf{)}$, is determined to be $(-14.5\pm {5.1}_{\mathrm{stat}}\pm {1.8}_{\mathrm{syst}})\%$.

We report on a calculation of open heavy-flavor production at hadron colliders which extends to next-to-next-to-leading order (NNLO) accuracy the classic NLO-accurate formalism developed almost 30 years ago under the acronym FONLL. The approach retains the exact heavy-flavor mass dependence at low transverse momentum, $p_T$, and resums collinear logarithms through next-to-next-to-leading log (NNLL) at high $p_T$. Provided are predictions for $B$ hadrons as well as $B$-decay products like $J/\mathrm{\Psi }$ and muons. The main features of the $\mathrm{NNLO}+\mathrm{NNLL}$ results are reduced scale dependence and moderate NNLO correction, consistent with perturbative convergence in a wide range of kinematic scales from few GeV up to asymptotically large values of $p_T$. The new calculation significantly improves the agreement with data for $B$ hadrons and muons. We uncover an intriguing discrepancy in $J/\mathrm{\Psi }$ final states which may point to a lower value of the $B\to J/\mathrm{\Psi }$ decay rate.

The thermalization of quark-gluon plasma created in heavy-ion collisions is crucial for understanding its behavior as a relativistic fluid and the thermodynamic properties of the quantum chromodynamics (QCD). This study investigates the role of fluctuations in the relationship between transverse momentum and particle multiplicity, with a particular focus on their impact on extracting the QCD speed of sound. In a thermalized quark-gluon plasma, these fluctuations mostly originate from quantum fluctuations in the colliding nuclei, and exhibit a Gaussian distribution as a consequence of their independence from thermodynamic response. In contrast, nonthermalized systems display non-Gaussian fluctuations, reflecting the breakdown of thermalization. By leveraging the Gaussianity condition of quantum-initiated fluctuations, the physical value of the speed of sound can be extracted statistically, even in the presence of significant event-by-event fluctuations. This framework provides a robust diagnostic tool for probing thermalization and extracting thermodynamic properties in both large and small collision systems.

A comprehensive reevaluation of the root-mean-square nuclear charge radius is presented for the doubly magic ${}^{208}\mathrm{Pb}$ extracted from muonic spectroscopy measurements. By integrating rigorous theoretical quantum electrodynamics calculations, state-of-the-art numerical methods, and a systematic reanalysis of the uncertainties, we reduced the long-standing muonic fine-structure anomaly and improved the goodness of fit by a factor of 20. The resulting value of 5.5062(5) fm for a Fermi distribution is fairly consistent with the previously reported muonic spectroscopy value, and 3 standard deviations larger than the commonly used compilation data, which indicates that the current value and its uncertainty could be significantly underestimated. Attributing the remaining discrepancy to theory errors which cannot be rigorously calculated, we suggest the rms charge radius with reduced model dependence to be 5.5062(17) fm. This Letter sets an improved benchmark for charge radius extraction in heavy nuclei and paves a path for systematic reevaluations across the nuclear chart.

Circularly polarized light offers opportunities to probe symmetry-dependent properties of matter such as chirality and spin. Circular-dichroic measurements typically require further intrinsic or extrinsic breaking of symmetry by, e.g., enantiomeric excess, orientation, magnetic fields, or direction-sensitive detectors. Here we introduce circular-dichroic attosecond transient absorption spectroscopy by leveraging the angular momentum of two circularly polarized pulses, both pump and probe, in an isotropic medium, optically orienting the angular momentum of excited states on an attosecond timescale. We investigate a circular-dichroic measurement of the attosecond transient absorption of He Rydberg states. By limiting the allowed pathways via dipole selection rules for co- and counterrotating circularly polarized near-infrared and extreme ultraviolet (XUV) pulses, different spectral reshapings of the XUV transient absorption due to the AC Stark effect are observed. Paired with time-dependent Schrödinger equation calculations, the results show the role of selection and propensity rules and open up new opportunities to study coupling pathways of excited states as well as spin-dependent dynamics in atoms and beyond via attosecond optical orientation.

In resonance fluorescence excitation experiments, light emitted from solid-state quantum emitters is typically filtered to eliminate the laser photons, ensuring that only red-shifted Stokes photons are detected. However, theoretical analyses of the fluorescence intensity correlation often model emitters as two-level systems, focusing on light emitted exclusively from the purely electronic transition (the zero-phonon line), or they rely on statistical approaches based on conditional probabilities that neglect the quantum coherence between the emitters and the coherence between the electric fields they generate. Here, we propose a model to characterize the correlation of either zero-phonon line photons or Stokes-shifted photons. This model successfully reproduces the experimental correlation of Stokes-shifted photons emitted from two interacting molecules and predicts that this correlation is affected by quantum coherence. Besides, we analyze the role of quantum coherence in the Stokes-shifted emission from two distant emitters, showing a sharp peak at zero time delay due to the Hanbury Brown–Twiss effect.

Recent developments in nonequilibrium and nonlinear terahertz (THz) spectroscopies have significantly advanced the understanding of collective excitations in superconductors. However, there is ongoing debate regarding the identification of Higgs, Leggett modes, and BCS charge fluctuations in the two-band superconductor ${\mathrm{MgB}}_2$. To address this issue, we have demonstrated the selective excitation of collective modes in ${\mathrm{MgB}}_2$ by systematically adjusting THz pump pulse characteristics. Using multicycle THz pump-probe spectroscopy, we distinguish various nonlinear processes through two-dimensional scans. The $\pi$-band Higgs mode is identified through its characteristic resonant enhancement at the temperatures where the pump frequency ${\omega }_{\mathrm{p}}$ matches the $\pi$-band superconductivity gap $2{\mathrm{\Delta }}_{\pi }(\mathrm{T})$. In contrast, employing single-cycle THz pulses that satisfy nonadiabatic excitation conditions reveals a heavily damped oscillation corresponding to the Leggett mode. Our observed mode-selective responses in ${\mathrm{MgB}}_2$ under tailored excitation provide a clear experimental route to discriminate between the modes, helping to reconcile existing controversies while highlighting the critical role of interband coupling in collective mode observation for multiband superconductors.

The discovery of 15.1 K superconductivity in first-stage ${\mathrm{CaC}}_6$ reignited interest in searching for high-temperature superconductors in graphite intercalation compounds (GICs). However, despite nearly two decades of intensive research, progress in exploring high-temperature superconductivity in GIC materials has remained stagnant. Currently, research on the superconductivity of GICs mainly focuses on first-stage GICs, while the superconductivity of high-stage GICs has been largely overlooked. Here, we report an experimental discovery of superconductivity with maximum critical temperature ($T_c$) of approximately 28 K in sodium carbide at about 14 GPa evidenced by a sharp drop of resistance and a characteristic decrease of $T_c$ under magnetic fields up to 6 T. The upper critical field ${\mu }_0{H}_{c2}(0)$ was estimated to be 8.8 T based on fitting with the Ginzburg-Landau superconducting model while the coherent length is approximately $61.2\AA$. X-ray diffraction measurements combined with crystal structure predictions identified the superconducting candidate material as the second-stage GIC ${\mathrm{NaC}}_8$, in which sodium atoms occupy the interlayer spaces between AA-stacked bilayer graphene. The current findings not only achieve the long-sought high-$T_c$ GICs, but more importantly, open up a new avenue for exploring high-temperature superconductors in light-element compounds.

Elucidating the mechanisms of negative thermal expansion (NTE) not only identifies the determining factors of this phenomenon but also provides guidance for the precise regulation of the coefficient of thermal expansion (CTE). However, accurately quantifying these determining factors during CTE modulation remains a critical challenge. In this Letter, we quantitatively determine the respective contributions of phonon-derived Grüneisen parameters (axial values and their difference) and elastic compliance tensors to the tuning of axial NTE in the $M{\mathrm{Zr}}_2$ system. Through temperature dependence of the neutron total scattering data (for neutron powder diffraction and neutron pair distribution function analyses), extended x-ray absorption fine structure, synchrotron x-ray diffraction, and first-principles calculations, it provides insight into the quantified roles of phonons and anisotropic elasticity in controlling the broad-range CTE. As the number of $M\text{−}3d$ electrons grows, phonons, which are the dominant factors, weaken NTE, while elasticity, playing a cross-linking coefficient, enhances NTE. The current study not only provides deep insights into the origins of NTE in the $M{\mathrm{Zr}}_2$ system, but it also offers a novel perspective on the quantifiable control of NTE in anisotropic materials.

Unconventional superconductors that spontaneously break space-group symmetries of their underlying crystal lattice are distinguished by spatial modulations of superconducting order parameter. These states have recently captured significant attention in various strongly correlated materials, where the translational or intra-unit-cell symmetry breaking results in the emergence of pair density waves with wavelength extending across one or multiple unit cells. Here, we employ a spectroscopic-imaging scanning tunneling microscopy to reveal sublattice modulations of the superconducting gap magnitude, coherence strength, and subgap states in tunable $1T^{\prime }\text{−}{\text{MoTe}}_2$ monolayer. These modulations are uniquely oriented perpendicular to the zigzag Mo chains at the scale of half a unit cell and coexist with three-unit-cell pair density wave modulations along the Mo chains, both of which attenuate with increasing temperature and external magnetic fields. Importantly, we find that the superconductivity modulations are strongly linked to unconventional electron pairing mechanisms, which significantly deviate from the Cooper pairing observed in conventional Bardeen-Cooper-Schrieffer superconductors. Our findings advance the knowledge of Cooper-pair density modulations and their intricate interplay with other symmetry-breaking states in strongly correlated superconductors.

The radiative heat transfer in the extreme near-field regime, i.e., for distances below 10 nm, remains poorly understood. There are competing experimental results in this regime, with some in good agreement with theoretical predictions, while others report drastically elevated heat fluxes, orders of magnitude larger than what theory suggests. Whether the theory of fluctuational electrodynamics can predict the radiative heat transfer in this extreme near-field regime or not remains a matter of active debate. In this Letter, a radiative heat transfer measurement is presented between a gold-coated sphere and a gold film sample in the transition regime between the near-field and the extreme near-field regime just before contact. The radiative heat flux measurement is made by using a near-field scanning thermal microscope equipped with a temperature sensor at a sharp tip as a heat flux sensor. We find an excellent agreement with the theoretical predictions of fluctuational electrodynamics in the near-field regime. In the extreme near-field regime, however, a highly increased radiative heat flux is observed with values about 100 times larger than the theoretical predictions, indicating that fluctuational electrodynamics fails to capture the radiative heat flux in this regime.

Electron spin resonance can provide unique insights into charge transport processes in organic semiconductors in a regime in which charge motion determines spin relaxation. In particular, electrically detected magnetic resonance (EDMR) probes directly the changes in charge transport properties that are sensitive to magnetic resonance excitation. Here, we present a systematic study of continuous-wave EDMR on conjugated polymer field-effect transistors (FETs) that can be operated in both unipolar as well as ambipolar regimes. We show that, in addition to a narrow, electron-hole recombination-induced EDMR signal that can only be detected in the ambipolar regime, there is also a broad EDMR signal when devices are operated in both unipolar and ambipolar regions. We attribute this signal to a spin blockade mechanism induced when mobile carriers encounter trapped charges along the charge transport percolation pathways and study its dependence on biasing conditions and temperature. The spin-blockade EDMR signature is also observed in conjugated polymer FETs that exhibit only unipolar operation. Our findings show that EDMR provides a powerful technique to study the role of spin blockade and bipolaron formation on the charge transport properties of a wide range of conjugated polymers.

We introduce a class of interacting fermionic quantum models in $d$ dimensions with nodal interactions that exhibit superdiffusive transport. We establish nonperturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength $\omega (q)\sim q^z$ with dynamical exponent $z=\min [(2n+d)/2n,2]$, where $n$ is the order of the nodal point in momentum space. We verify our predictions in one-dimensional systems using tensor-network techniques.

A normal metal proximitized by a superconductor can exhibit a gapless superconducting state characterized by segmented Fermi surfaces, as confirmed experimentally. In this state, quasiparticle states remain gapless along one direction, while a superconducting gap opens in the perpendicular direction. We show that this anisotropic phase enables an unconventional Hall effect in gapless superconductors, termed the superconducting Hall effect (ScHE), in which a longitudinal quasiparticle current is converted into a dissipationless transverse supercurrent without a phase transition. Using both the thermodynamic approach for bulk systems and quantum transport theory for a four-probe setup, we demonstrate the existence of this effect and reveal its intrinsic origin as the quasiparticle Berry curvature. The predicted ScHE can be experimentally verified via angular-dependent Hall measurements performed on gapless superconductors, such as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ proximitized by superconducting ${\mathrm{NbSe}}_2$ as well as altermagnetic materials coupled to superconductors.

Recently, the dc shot noise (DSN) of photocurrents has been proposed as its complementary probe to quantify the nonmagnetic gapped quantum materials. In this Letter, we have discovered two novel DSN terms that are crucial for understanding the properties of magnetically insulating quantum materials: linear magnetic shift DSN and circular magnetic injection DSN. Both magnetic shift and injection DSNs inherit quantum geometric information of Bloch states. Interestingly, these terms can appear only when the system breaks parity-time ($\mathcal{P}\mathcal{T}$) symmetry. Leveraging this unique symmetry sensitivity, we propose DSN as a noninvasive, symmetry-resolved diagnostic capable of distinguishing magnetic properties. We demonstrate the viability of this approach through both minimal altermagnet models and first-principles calculations of realistic monolayer and bilayer ${\mathrm{CrI}}_3$ in various magnetic configurations. We show that magnetic DSN not only captures the spin-split band structure of altermagnets, but also differentiates magnetic phases and parity of the number of layers in two-dimensional ${\mathrm{CrI}}_3$. This establishes DSN as a powerful tool for probing symmetry, quantum geometry, and spin textures in magnetic quantum materials.

We experimentally and theoretically demonstrate that nonlinear spin-wave dynamics can induce an effective resonant interaction between nonresonant magnon modes in a yttrium iron garnet disk. Under strong pumping near the ferromagnetic resonance mode, we observe a spectral splitting that emerges with increasing drive amplitude. This phenomenon is well captured by a theoretical framework based on the linearization of a magnon three-wave mixing Hamiltonian, which at high power leads to parametric Suhl instabilities. The access and control of nonlinear magnon-parametric processes enable the development of experimental platforms in an unexplored parameter regime for both classical and quantum computation protocols.

Structured optical cavities have advanced as a powerful test bed to study lattice Hamiltonians in general, and topological phenomena in particular. The in situ tuning of topological modes, enabled via substantial modifications of emulated lattice potentials, has remained out of experimental reach due to the commonly utilized monolithic cavity samples. Here, we study the Su-Schrieffer-Heeger (SSH) lattice Hamiltonian, which we emulate in a widely tunable open optical cavity strongly coupled to excitons in an integrated ${\mathrm{WS}}_2$ monolayer. The potential landscape comprises a topological domain boundary hosting a topological, exponentially localized mode at the interface between two lattices characterized by different Zak phases. The mode is spectrally tunable over 80 meV. Moreover, we use the unique tilt tunability of our implementation to transform the SSH lattice into a Stark ladder. This transformation couples the topologically protected defect mode to propagating lattice modes and effectively changes the symmetry of the system. Furthermore, it allows us to directly quantify the Zak-phase difference ${\mathrm{\Delta }}_{Zak}=(1.07\pm 0.11)\pi$ between the two topological phases. Our Letter constitutes an important step toward in situ tuning topological lattices to control and guide light on nonlinear chips.