The kagome superconductor family $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{Cs}$, K, Rb) emerged as an exciting platform to study exotic Fermi surface instabilities. Here, we use spectroscopic-imaging scanning tunneling microscopy (SI-STM) and angle-resolved photoemission spectroscopy (ARPES) to reveal how the surprising cascade of higher- and lower-dimensional density waves in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is intimately tied to a set of small reconstructed Fermi pockets. ARPES measurements visualize the formation of these pockets generated by a 3D charge density wave transition. The pockets are connected by dispersive $q^{*}$ wave vectors observed in Fourier transforms of STM differential conductance maps. As the additional 1D charge order emerges at a lower temperature, $q^{*}$ wave vectors become substantially renormalized, signaling further reconstruction of the Fermi pockets. Remarkably, in the superconducting state, the superconducting gap modulations give rise to an in-plane Cooper pair density wave at the same $q^{*}$ wave vectors. Our work demonstrates the intrinsic origin of the charge stripes and the pair density wave in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and their relationship to the Fermi pockets. These experiments uncover a unique scenario of how Fermi pockets generated by a parent charge density wave state can provide a favorable platform for the emergence of additional density waves.

Unveiling nonequilibrium dynamics of solitonic and topological defect structures in a multidimensional nonlinear medium is a current frontier across diverse fields. One of the quintessential objects is a ring dark soliton (RDS), whose dynamics are expected to display remarkable interplay between symmetry and self-patterned topological defect formation from a transverse (snake) instability, but it has thus far evaded full experimental observations. Here, we report an experimental realization of RDS generation in a two-dimensional atomic superfluid trapped in a circular box. By quenching the confining box potential, we observe an RDS emitted from the edge and its peculiar signature in the radial motion. As an RDS evolves, we observe transverse modulations at discrete azimuthal angles, which clearly result in a patterned formation of a circular vortex dipole array. Through collisions of the vortex dipoles with the box trap, we observe vortex unbinding, vortex pinning to the edge, and emission of rarefaction pulses. Our box-quench protocol opens a new way to study multidimensional dark solitons, structured formation of topological defects, and potentially the dynamics of ordered quantum vortex matter.

Most animal brains present two mirror-symmetric sides, but closer inspection reveals a range of asymmetries (in shape and function) that seem more salient in more cognitively complex species. Sustaining symmetric, redundant neural circuitry has associated metabolic costs, but it might aid in implementing computations within noisy environments or with faulty pieces. It has been suggested that the complexity of a computational task might play a role in breaking bilaterally symmetric circuits into fully lateralized ones; however, a rigorous, mathematically grounded theory of how this mechanism might work is missing. Here, we provide such a mathematical framework, starting with the simplest assumptions but extending our results to a comprehensive range of biologically relevant scenarios. We show mathematically that only fully lateralized or bilateral solutions are relevant within our framework (dismissing configurations in which circuits are only partially engaged). We provide maps that show when each configuration is preferred depending on costs, fitness contributed, circuit reliability, and task complexity. We discuss evolutionary paths leading from bilateral to lateralized configurations and other possible outcomes. The implications of these results for evolution, development, and rehabilitation of damaged or aging brains is discussed. Our work constitutes a limit case that should constrain and underlie similar mappings when other aspects (besides task complexity and circuit reliability) are considered.

We develop a theory of the nonlocal transport of two counterpropagating $\nu =1$ quantum Hall edges coupled via a narrow disordered superconductor. Contrary to the predictions developed for the clean case, the edge states proximitized in this way do not turn into a topological superconductor. Instead, they are naturally tuned to the critical point between trivial and topological phases. This occurs due to the competition between tunneling processes with and without particle-hole conversion. The critical conductance is a random, sample-specific quantity with a zero average and unusual bias dependence. The negative values of conductance are relatively stable against variations of the carrier density, which may make the critical state appear as a topological one. Our results offer an interpretation of recent experiments [G.-H. Lee , Nat. Phys. 13, 693 (2017); O. Gül , Phys. Rev. X 12, 021057 (2022)].

In this work, we lay down the ab initio many-body quantum theory of electrons and phonons in equilibrium as well as in steady-state or time-varying settings. Our focus is on the harmonic approximation, but the developed tools can readily incorporate anharmonic effects. We begin by showing the necessity of determining the ab initio Hamiltonian in a self-consistent manner to ensure the existence of an equilibrium state. We then identify the correct partitioning into a “noninteracting” and an “interacting” part to carry out diagrammatic expansions in terms of dressed propagators and screened interactions. The final outcome is the finite-temperature nonequilibrium extension of the Hedin equations, showcasing the emergence of the coupling between electrons and coherent phonons through the time-local Ehrenfest diagram. The Hedin equations have limited practical utility for real-time simulations of systems driven out of equilibrium by external fields. To overcome this limitation, we leverage the versatility of the diagrammatic approach to generate a closed system of differential equations for the dressed propagators and nuclear displacements. These are the Kadanoff-Baym equations for electrons and phonons. The formalism naturally merges with the theory of conserving approximations, which guarantee the satisfaction of the continuity equation and the conservation of total energy during time evolution. As an example, we show that the popular Born-Oppenheimer approximation is not conserving whereas its dynamical extension is conserving, provided that the electrons are treated in the Fan-Migdal approximation with a dynamically screened electron-phonon coupling. We also derive the formal solution of the Kadanoff-Baym equations for nonequilibrium steady states, which is useful for studies in photovoltaics and optoelectronics. Interestingly, the expansion of the phononic Green’s function around the quasiphonon energies points to a correlation-induced splitting of the phonon dispersion in materials with no time-reversal invariance.

The high-pressure (HP) behavior of dioxides is of interest due to their extensive polymorphism and role as analogs for ${\mathrm{SiO}}_2$, a phase expected to be important in the deep mantles of Earth and terrestrial exoplanets. Here we report on dynamic ramp compression of quartz-type germanium dioxide ${\mathrm{GeO}}_2$ to stresses up to 882 GPa, a higher peak stress than previous studies by a factor of 5. X-ray diffraction data show that $\mathrm{HP}\text{−}{\mathrm{PdF}}_2$-type ${\mathrm{GeO}}_2$ occurs under ramp loading from 154 to 440 GPa, and this phase persists to higher pressure than predicted by theory. Above 440 GPa, we observe evidence for transformation to a new phase of ${\mathrm{GeO}}_2$. Based on the diffraction data, the best candidate for this new phase is the cotunnite-type structure which has been predicted to be a stable phase of ${\mathrm{GeO}}_2$ above 300 GPa. The $\mathrm{HP}\text{−}{\mathrm{PdF}}_2$-type and cotunnite-type structures are important phases in a wide range of $A{X}_2$ compounds, including ${\mathrm{SiO}}_2$, at multihundred GPa stresses. Our results demonstrate that ramp compression can be an effective technique for synthesizing and characterizing such phases in oxides. In addition, we show that pulsed x-ray diffraction under ramp compression can be used to examine lower-symmetry phases in oxide materials.

Couplings between topological edge channels open electronic phases possessing nontrivial eigenmodes far beyond the noninteracting-edge picture. However, inelastic scatterings mask the eigenmodes’ inherent features, often preventing us from identifying the phases, as is the case for the quintessential Landau-level filling factor $\nu =2/3$ edge composed of the counterpropagating $\nu =1/3$ and 1 ($1/3–1$) channels. Here, we study the coherent-incoherent crossover of the $1/3–1$ channels by tuning the channel length in situ using a new device architecture comprising a junction of $\nu =1/3$ and 1 systems, the particle-hole conjugate of the $2/3$ edge. We successfully observed the concurrence of the fluctuating electrical conductance and the quantized thermal conductance in the crossover regime, the definitive hallmark of the eigenmodes in the disorder-dominated edge phase left experimentally unverified.

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization. Nevertheless, their experimental realization is challenging. Here we propose to study the XY* transition in quantum Hall bilayers at filling $({\nu }_1,{\nu }_2)=(\frac{1}{3},\frac{2}{3})$ where the exciton condensate (EC) phase plays the role of the superfluid. Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation. The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class. The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively. We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality. Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems. The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer. Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.

The negatively charged tin-vacancy (${\mathrm{SnV}}^{-}$) center in diamond is a promising solid-state qubit for applications in quantum networking due to its high quantum efficiency, strong zero phonon emission, and reduced sensitivity to electrical noise. The ${\mathrm{SnV}}^{-}$ has a large spin-orbit coupling, which allows for long spin lifetimes at elevated temperatures, but unfortunately suppresses the magnetic dipole transitions desired for quantum control. Here, by use of a naturally strained center, we overcome this limitation and achieve high-fidelity microwave spin control. We demonstrate a $\pi$-pulse fidelity of up to $99.51\pm 0.03\%$ and a Hahn-echo coherence time of $T_2^{\mathrm{echo}}=170.0\pm 2.8\mathrm{\mu }\mathrm{s}$, both the highest yet reported for ${\mathrm{SnV}}^{-}$ platform. This performance comes without compromise to optical stability, and is demonstrated at 1.7 K where ample cooling power is available to mitigate drive-induced heating. These results pave the way for ${\mathrm{SnV}}^{-}$ spins to be used as a building block for future quantum technologies.

The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a broad range of models. Exact solutions for dynamical, out-of-equilibrium properties of disordered systems are traditionally much harder to obtain. Even very basic questions such as the limiting energy of a fast quench are so far open. The dynamical cavity method partly fills this gap by considering short trajectories and leveraging the static cavity method. However, being limited to a couple of steps forward from the initialization, it typically does not capture dynamical properties related to attractors of the dynamics. We introduce the backtracking dynamical cavity method that instead of analyzing the trajectory forward from initialization, it analyzes the trajectories that are found by tracking them backward from attractors. We illustrate that this rather elementary twist on the dynamical cavity method leads to new insight into some of the very basic questions about the dynamics of complex disordered systems. This method is as versatile as the cavity method itself, and we hence anticipate that our paper will open many avenues for future research of dynamical, out-of-equilibrium properties in complex systems.

A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks) but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. It relies on implementing a time-reversal operation and injecting a small error signal on top of the echo dynamics. We show how the physical dynamics itself will then lead to the required gradient update of learnable parameters, independent of the details of the Hamiltonian. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields and other examples.

We perform a systematic symmetry classification of many-body Lindblad superoperators describing general (interacting) open quantum systems coupled to a Markovian environment. Our classification is based on the behavior of the many-body Lindbladian under antiunitary symmetries and unitary involutions. We find that Hermiticity preservation reduces the number of symmetry classes, while trace preservation and complete positivity do not, and that the set of admissible classes depends on the presence of additional unitary symmetries: in their absence or in symmetry sectors containing steady states, many-body Lindbladians belong to one of ten non-Hermitian symmetry classes; if however, there are additional symmetries and we consider non-steady-state sectors, they belong to a different set of 19 classes. In both cases, it does not include classes with Kramers degeneracy. Remarkably, our classification admits a straightforward generalization to the case of non-Markovian, and even non-trace-preserving, open quantum dynamics. While the abstract classification is completely general, we then apply it to general (long-range, interacting, spatially inhomogeneous) spin-$1/2$ chains. We explicitly build examples in all ten classes of Lindbladians in steady-state sectors, describing standard physical processes such as dephasing, spin injection and absorption, and incoherent hopping, thus illustrating the relevance of our classification for practical physics applications. Finally, we show that the examples in each class display unique random-matrix correlations. To fully resolve all symmetries, we employ the combined analysis of bulk complex spacing ratios and the overlap of eigenvector pairs related by symmetry operations. We further find that statistics of levels constrained onto the real and imaginary axes or close to the origin are not universal due to spontaneous breaking of Lindbladian $PT$ symmetry.

Collisional resonances of molecules can offer a deeper understanding of interaction potentials and collision complexes, and allow control of chemical reactions. Here, we experimentally map out the spectrum of Feshbach resonances in collisions between ultracold triplet rovibrational ground-state NaLi molecules and Na atoms over a range of 1400 G. Preparation of the spin-stretched state puts the system initially into the nonreactive quartet potential. A total of 25 resonances are observed, in qualitative agreement with quantum-chemistry calculations using a coupled-channels approach. Although the theory cannot predict the positions of resonances, it can account for several experimental findings and provide unprecedented insight into the nature and couplings of ultracold, strongly interacting complexes. Previous work has addressed only weakly bound complexes. We show that the main coupling mechanism results from spin-rotation and spin-spin couplings in combination with the anisotropic atom-molecule interaction, and that the collisional complexes which support the resonances have a size of $30a_0–40a_0$. This study illustrates the potential of a combined experimental and theoretical approach.

Over the recent years, coherent, time-periodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a long-ranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single-magnon excitations, but also composite magnon bound states. For long-range interactions with the experimentally realized power-law exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions, we observe bound states of these unconventional magnons which possess a nondiverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of bound-state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the nonequilibrium dynamics of quantum many-body systems.

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries, where quenched disorders locally break the symmetries, but restore the symmetries upon disorder averaging. An example would be crystalline SPT phases with imperfect lattices. Specifically, we define the notion of average SPT phase for disordered ensembles of quantum states. We then classify and characterize a large class of average SPT phases using a decorated domain wall approach, in which domain walls (and more general defects) of the average symmetries are decorated with lower-dimensional topological states. We then show that if the decorated domain walls have dimension higher than $(0+1)\mathrm{D}$, then the boundary states of such average SPT phases will almost certainly be long-range entangled, with probability approaching 1 as the system size approaches infinity. This generalizes the notion of t’Hooft anomaly to average symmetries, which we dub “average anomaly.” The average anomaly can also manifest as constraints on lattice systems similar to the Lieb-Schultz-Mattis theorems, but with only average lattice symmetries. We also generalize our problem to “quantum disorders” that can admit short-range entanglement on their own, and develop a theory of such generalized average SPT phases purely based on density matrices and quantum channels. Our results indicate that topological quantum phenomena associated with average symmetries can be at least as rich as those with ordinary exact symmetries.

Twisted graphene multilayers are highly tunable flatband systems for developing new phases of matter. Thus far, while orbital ferromagnetism has been observed in valley-polarized phases, the long-range orders of other correlated phases as well as the quantum phase transitions between different orders mostly remain unknown. Here, we report an observation of Coulomb-interaction-driven first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene (TDBG). At zero magnetic field, the transitions are revealed in a series of steplike abrupt resistance jumps with a prominent hysteresis loop when either the displacement field ($D$) or the carrier density ($n$) is tuned across a symmetry-breaking boundary near half filling, indicating a formation of ordered domains. It is worth noting that the good tunability and switching of these states give rise to a memory performance with a large on/off ratio. Moreover, when both spin and valley play the roles at finite magnetic field, we observe abundant first-order quantum phase transitions among normal metallic states from the charge-neutral point, orbital ferromagnetic states from quarter filling, and spin-polarized states from half filling. We interpret these first-order phase transitions in the picture of phase separations and spin-domain percolations driven by multifield tunable Coulomb interactions, in agreement with the Lifshitz transition and the Hartree-Fock calculations. The observed multifield tunable domain structure and its hysteresis resembles the characteristics of multiferroics, revealing intriguing magnetoelectric properties. Our result enriches the correlated phase diagram in TDBG for discovering novel exotic phases and quantum phase transitions, and it will benefit other twisted moiré systems as well.

Many recent studies of liquid-liquid phase separation in biology focus on phase separation as a dynamic control mechanism for cellular function, but it can also result in complex mesoscopic structures. We primarily investigate a model system consisting of DNA nanostars: finite-valence, self-assembled particles that form micron-scale liquid droplets via a binodal phase transition. We demonstrate that, upon phase separation, nanostar droplets spontaneously form hyperuniform structures, a type of disordered material with “hidden order” that combines the long-range order of crystals with the short-range isotropy of liquids. We find that the hyperuniformity of the DNA droplets reflects near-equilibrium dynamics, where phase separation drives the organization of droplets that then relax toward equilibrium via droplet Brownian motion. We engineer a two-species system of immiscible DNA droplets and find two distinctly hyperuniform structures in the same sample, but with random cross-species droplet correlations, which rules out explanations that rely on droplet-droplet hydrodynamic interactions. In addition, we perform experiments on the electrostatic coacervation of peptides and nucleotides which exhibit hyperuniform structures indistinguishable from DNA nanostars, indicating the phenomenon generally applies to phase-separating systems that experience Brownian motion. Our work on near-equilibrium droplet assembly and structure provides a foundation to investigate droplet organizational mechanisms in driven and/or biological environments. This approach also provides a path to implement phase-separated droplet patterns as exotic optical or mechanical metamaterials or as efficient biochemical reactors.

Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs) ensembles. The theory explains dynamics in closed, open, and time-dependent systems, provided that relevant pseudolocal quantities can be identified, and time-dependent Gibbs ensembles unify wide classes of quantum nonergodic and ergodic systems. The theory is applied to quantum many-body scars, continuous, discrete, and dissipative time crystals, Hilbert space fragmentation, lattice gauge theories, and disorder-free localization, among other cases. Novel pseudolocal classes of operators are introduced in the process: projected-local, which are local only for some states, cryptolocal, whose locality is not manifest in terms of any finite number of local densities, and transient ones, that dictate finite-time relaxation dynamics. An immediate corollary is proving saturation of the Mazur bound for the Drude weight. This proven theory is intuitively the rigorous algebraic counterpart of the weak eigenstate thermalization hypothesis and has deep implications for thermodynamics: Quantum many-body systems “out of equilibrium” are actually always in a time-dependent equilibrium state for any natural initial state. The work opens the possibility of designing novel out-of-equilibrium phases, with the newly identified scarring and fragmentation phase transitions being examples.

Continuous monitoring of driven-dissipative quantum-optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor. Saturation of the corresponding precision limit as defined by the quantum Cramér-Rao bound is typically not achieved by conventional, temporally local continuous-measurement schemes such as counting or homodyning. To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous-measurement strategy featuring temporally quasilocal measurement bases as captured by matrix-product states. Such a measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a “quantum-decoder” module, which “decodes” specific input matrix-product states into simple product states as its output field, and performing conventional continuous measurement at the output. We devise a universal recipe for the construction of the decoder by exploiting the time-reversal transformation of quantum-optical input-output channels, thereby establishing a universal method to achieve the quantum Cramér-Rao precision limit for generic sensor designs based on continuous measurement. As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic driven-dissipative open sensors. We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fiber-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections.

High harmonic generation (HHG) has developed in recent years as a promising tool for ultrafast materials spectroscopy. At the forefront of these advancements, several works proposed using HHG as an all-optical probe for topology of quantum matter by identifying its signatures in the emission spectra. However, it remains unclear if such spectral signatures are indeed a robust and general approach for probing topology. To address this point, we perform a fully ab initio study of HHG from prototypical two-dimensional topological insulators in the Kane-Mele quantum spin-Hall and anomalous-Hall phases. We analyze the spectra and previously proposed topological signatures by comparing HHG from the topological and trivial phases and across the phase transition. We demonstrate and provide detailed microscopic explanations of why, in these systems, none of the observables proposed thus far uniquely and universally probes material topology. Specifically, we find that the (i) HHG helicity, (ii) anomalous HHG ellipticity, (iii) HHG elliptical dichroism, and (iv) temporal delays in HHG emission are all unreliable signatures of topological phases. Our results suggest that extreme care must be taken when interpreting HHG spectra for topological signatures and that contributions from the crystal symmetries and chemical nature might be dominant over those from topology. They hint that a truly universal topological signature in nonlinear optics is unlikely and raise important questions regarding possible utilization and detection of topology in out-of-equilibrium systems.