We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around $g_s/2\pi =40\mathrm{MHz}$. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around $2J/2\pi =20\mathrm{MHz}$. In addition, photon-number states are resolved from the shift $2{\chi }_s/2\pi =-13\mathrm{MHz}$ that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

The material $\alpha \text{−}{\mathrm{RuCl}}_3$ has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low-energy excitations. In practice, $\alpha \text{−}{\mathrm{RuCl}}_3$ undergoes a transition to a state with antiferromagnetic order below a temperature $T_N\approx 7\mathrm{K}$, but this order can be suppressed by applying an external in-plane magnetic field of $H_{\parallel }=7\mathrm{T}$. Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at $H_{\parallel }>7\mathrm{T}$ by Kasahara and co-workers [Nature (London) 559, 227 (2018)] has been interpreted as evidence of itinerant Majorana fermions in the Kitaev quantum spin liquid state. In this study, we reexamine the origin of the thermal Hall conductivity ${\kappa }_{xy}$ in $\alpha \text{−}{\mathrm{RuCl}}_3$. Our measurements of ${\kappa }_{xy}(T)$ on several different crystals yield a temperature dependence very similar to that of the phonon-dominated longitudinal thermal conductivity ${\kappa }_{xx}(T)$, for which the natural explanation is that ${\kappa }_{xy}$ is also mostly carried by phonons. Upon cooling, ${\kappa }_{xx}$ peaks at $T\simeq 20\mathrm{K}$, then drops until $T_N$, whereupon it suddenly increases again. The abrupt increase below $T_N$ is attributed to a sudden reduction in the scattering of phonons by low-energy spin fluctuations as these become partially gapped when the system orders. The fact that ${\kappa }_{xy}$ also increases suddenly below $T_N$ is strong evidence that the thermal Hall effect in $\alpha \text{−}{\mathrm{RuCl}}_3$ is also carried predominantly by phonons. This implies that any quantized signal from Majorana edge modes would have to come on top of a sizable—and sample-dependent—phonon background.

Response to elongational flow is fundamental to soft matter and directly impacts new developments in a broad range of technologies form polymer processing and microfluidics to controlled flow in biosystems. Of particular significance are the effects of elongational flow on self-assembled systems where the interactions between the fundamental building blocks control their adaptation. Here we probe the effects of associating groups on the structure and dynamics of linear polymer melts in uniaxial elongation using molecular dynamics simulations. We study model polymers with randomly incorporated backbone associations with interaction strengths varying from $1k_{B}T$ to $10k_{B}T$. These associating groups drive the formation of clusters in equilibrium with an average size that increases with interaction strength. Flow drives these clusters to continuously break and reform as chains stretch. These flow-driven cluster dynamics drive a qualitative transition in polymer elongation dynamics from homogeneous to nanoscale localized yield and cavitation as the association strength increases.

We study the relation between angular spectral absorptivity and emissivity for any thermal emitter, which consists of any linear media that can be dispersive, inhomogeneous, bianisotropic, or nonreciprocal. First, we establish an adjoint Kirchhoff’s law for mutually adjoint emitters. This law is based on generalized reciprocity and is a natural generalization of conventional Kirchhoff’s law for reciprocal emitters. Using this law, we derive all the relations between absorptivity and emissivity for an arbitrary thermal emitter We reveal that such relations are determined by the symmetries of the system, which are characterized by a Shubnikov point group. We classify all thermal emitters based on their symmetries using the known list of all three-dimensional Shubnikov point groups. Each class possesses its own set of laws that relates the absorptivity and emissivity. We numerically verify our theory for all three types of Shubnikov point groups: Gray groups, colorless groups, and black and white groups. We also verify the theory for both planar and nonplanar structures with single or multiple diffraction channels. Our theory provides a theoretical foundation for further exploration of thermal radiation in general media.

Many inexplicable phenomena in low-temperature many-body physics are a result of macroscopic quantum effects. Such macroscopic quantumness is often evaluated via long-range entanglement, that is, entanglement in the macroscopic length scale. Long-range entanglement is employed to characterize novel quantum phases and serves as a critical resource for quantum computation. However, the conditions under which long-range entanglement is stable, even at room temperatures, remain unclear. In this regard, this study demonstrates the unstable nature of bipartite long-range entanglement at arbitrary temperatures, which exponentially decays with distance. The proposed theorem is a no-go theorem pertaining to the existence of long-range entanglement. The obtained results are consistent with existing observations, indicating that long-range entanglement at nonzero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. The derivation in this study introduces a quantum correlation defined by the convex roof of the standard correlation function. Further, an exponential clustering theorem for generic quantum many-body systems under such a quantum correlation at arbitrary temperatures is established, which yields the primary result by relating quantum correlation with quantum entanglement. Moreover, a simple application of analytical techniques is demonstrated by deriving a general limit on the Wigner-Yanase-Dyson skew and quantum Fisher information; this is expected to attract significant attention in the field of quantum metrology. Notably, this study reveals the novel, general aspects of low-temperature quantum physics and clarifies the characterization of long-range entanglement.

A central question of quantum computing is determining the source of the advantage of quantum computation over classical computation. Even though simulating quantum dynamics on a classical computer is thought to require exponential overhead in the worst case, efficient simulations are known to exist in several special cases. It was widely assumed that these easy-to-simulate cases as well as any yet-undiscovered ones could be avoided by choosing a quantum circuit at random. We prove that this intuition is false by showing that certain families of constant-depth, 2D random circuits can be approximately simulated on a classical computer in time only linear in the number of qubits and gates, even though the same families are capable of universal quantum computation and are hard to exactly simulate in the worst case (under standard hardness assumptions). While our proof applies to specific random circuit families, we demonstrate numerically that typical instances of more general families of sufficiently shallow constant-depth 2D random circuits are also efficiently simulable. We propose two classical simulation algorithms. One is based on first simulating spatially local regions which are then “stitched” together via recovery maps. The other reduces the 2D simulation problem to a problem of simulating a form of 1D dynamics consisting of alternating rounds of random local unitaries and weak measurements. Similar processes have recently been the subject of an intensive research focus, which has observed that the dynamics generally undergo a phase transition from a low-entanglement (and efficient-to-simulate) regime to a high-entanglement (and inefficient-to-simulate) regime as measurement strength is varied. Via a mapping from random quantum circuits to classical statistical mechanical models, we give analytical evidence that a similar computational phase transition occurs for both of our algorithms as parameters of the circuit architecture like the local Hilbert space dimension and circuit depth are varied and, additionally, that the effective 1D dynamics corresponding to sufficiently shallow random quantum circuits falls within the efficient-to-simulate regime. Implementing the latter algorithm for the depth-3 “brickwork” architecture, for which exact simulation is hard, we find that a laptop could simulate typical instances on a $409\times 409$ grid with a total variation distance error less than 0.01 in approximately one minute per sample, a task intractable for previously known circuit simulation algorithms. Numerical results support our analytic evidence that the algorithm is asymptotically efficient.

The study of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ sits at the confluence of simplicity and complexity: on one hand, the model for Ising chains—the building blocks of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$—in a transverse field can be exactly solved and, thus, serves as an archetype of quantum criticality; on the other hand, the weak but nonzero interchain coupling adds geometric frustration to the stage, substantially complicating the phase diagram. Here we utilize low-temperature specific heat and thermal conductivity measurements to study the low-lying magnetic excitations in ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ and its spin-1 analog ${\mathrm{NiNb}}_2{\mathrm{O}}_6$. The thermal conductivity is found to be suppressed around the quantum critical point, where the specific heat is enhanced due to gapless magnetic excitations, pointing to the localized nature of the latter. These results highlight the predominant role of frustration in determining the quantum critical magnetic excitations of spin chains, which may furthermore underlie the remarkable similarities between the phenomenology of these spin-$1/2$ and spin-1 systems.

Supersolids are a fundamental quantum phase of matter where the global phase and translational symmetries are spontaneously broken. The recently discovered supersolidity in quantum gases of strongly magnetic atoms gives the opportunity to explore in depth how superfluidity and crystalline order are mixed in this fascinating phase. The dipolar supersolid is usually created from a Bose-Einstein condensate, i.e., a standard superfluid, crossing a quantum phase transition that is related to the crystallization transitions of ordinary matter. In this work, we assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition. We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first- and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively. The dimensional crossover is peculiar to supersolids, is controlled via the transverse confinement and the atom number, and can be justified on the general ground of the Landau theory of phase transitions. The quasiadiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.

Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted-trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions $\nu$ of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of $\nu$ and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality $\nu =0$, with additional spin polarization being present at quarter ($\nu =-2$) or three-quarter ($\nu =+2$) fillings of the quasiflat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost-flat bands and dispersive Dirac cones in twisted-trilayer graphene.

We investigate a model system for the rotational dynamics of inertial many-particle clustering, in which submillimeter objects are acoustically levitated in air. Driven by scattered sound, levitated grains self-assemble into a monolayer of particles, forming mesoscopic granular rafts with both an acoustic binding energy and a bending rigidity. Detuning the acoustic trap can give rise to stochastic forces and torques that impart angular momentum to levitated objects. As the angular momentum of a quasi-two-dimensional granular raft is increased, the raft deforms from a disk to an ellipse, eventually pinching off into multiple separate rafts, in a mechanism that resembles the breakup of a liquid drop. We extract the raft effective surface tension and elastic modulus and show that nonpairwise acoustic forces give rise to effective elastic moduli that scale with the raft size. We also show that the raft size controls the microstructural basis of plastic deformation, resulting in a transition from fracture to ductile failure.

Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed-matter systems. Here, by combining symmetry analysis and model calculations, we elucidate that the crystallographic symmetry groups of a vast number of magnetic materials with light elements, in which the neglect of relativistic spin-orbit coupling (SOC) is an appropriate approximation, are considerably larger than the conventional magnetic groups. Thus, a symmetry description that involves partially decoupled spin and spatial rotations, dubbed spin group, is required. We derive the classifications of spin point groups describing coplanar and collinear magnetic structures, and the irreducible corepresentations of spin space groups illustrating more energy degeneracies that are disallowed by magnetic groups. One consequence of the spin group is the new antiunitary symmetries that protect SOC-free $Z_2$ topological phases with unprecedented surface-node structures. Our work not only manifests the physical reality of materials with weak SOC, but also sheds light on the understanding of all solids with and without SOC by a unified group theory.

The ${\mathrm{Ce}}^{3+}$ pseudospin-$1/2$ degrees of freedom in the pyrochlore magnet ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ are known to possess dipole-octupole character, making it a candidate for novel quantum spin liquid ground states at low temperatures. We report new polarized neutron diffraction at low temperatures, as well as heat capacity ($C_p$) measurements on single crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$. The former bears both similarities and differences with that measured from the canonical dipolar spin ice compound ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, while the latter rises sharply at low temperatures, initially plateauing near 0.08 K, before falling off toward a high temperature zero beyond 3 K. $\text{Above}\sim 0.5\mathrm{K}$, the $C_p$ dataset can be fit to the results of a quantum numerical linked cluster calculation, carried out to fourth order, that allows estimates for the terms in the near-neighbor XYZ Hamiltonian expected for such dipole-octupole pyrochlore systems. Fits of the same theory to the temperature dependence of the magnetic susceptibility and unpolarized neutron scattering complement this analysis. A comparison between the resulting best-fit numerical linked cluster calculation and the polarized neutron diffraction shows both agreement and discrepancies, mostly in the form of zone-boundary diffuse scattering in the non-spin-flip channel, which are attributed to interactions beyond near neighbors. The lack of an observed thermodynamic anomaly and the constraints on the near-neighbor XYZ Hamiltonian suggest that ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ realizes a ${\mathrm{U}(1)}_{\pi }$ quantum spin liquid state at low temperatures, and one that likely resides near the boundary between dipolar and octupolar character.

Driving a many-body system out of equilibrium induces phenomena such as the emergence and decay of transient states, which can manifest itself as pattern and domain formation. The understanding of these phenomena expands the scope of established thermodynamics into the out-of-equilibrium domain. Here, we experimentally and theoretically study the out-of-equilibrium dynamics of a bosonic lattice model subjected to a strong dc field, realized as ultracold atoms in a strongly tilted triangular optical lattice. We observe the emergence of pronounced density-wave patterns—which spontaneously break the underlying lattice symmetry—using a novel single-shot imaging technique with two-dimensional single-site resolution in three-dimensional systems, which also resolves the domain structure. Our study suggests that the short-time dynamics arises from resonant pair tunneling processes within an effective description of the tilted Hubbard model. More broadly, we establish the far out-of-equilibrium regime of lattice models subjected to a strong dc field, as an exemplary and paradigmatic scenario for transient pattern formation.

The second law of thermodynamics states that work cannot be extracted from thermal equilibrium, whose quantum formulation is known as complete passivity; a state is called completely passive if work cannot be extracted from any number of copies of the state by any unitary operations. It has been established that a quantum state is completely passive if and only if it is a Gibbs ensemble. In physically plausible setups, however, the class of possible operations is often restricted by fundamental constraints such as symmetries imposed on the system. In the present work, we investigate the concept of complete passivity under symmetry constraints. Specifically, we prove that a quantum state is completely passive under a symmetry constraint described by a connected compact Lie group, if and only if it is a generalized Gibbs ensemble including conserved charges associated with the symmetry. Remarkably, our result applies to noncommutative symmetry such as SU(2) symmetry, suggesting an unconventional extension of the notion of generalized Gibbs ensemble. Furthermore, we consider the setup where a quantum work storage is explicitly included, and prove that the characterization of complete passivity remains unchanged. Our result extends the notion of thermal equilibrium to systems protected by symmetries, and would lead to flexible design principles of quantum heat engines and batteries. Moreover, our approach serves as a foundation of the resource theory of thermodynamics in the presence of symmetries.

We consider a two-dimensional quantum memory of qubits on a torus which encode the extended Fibonacci string-net code and devise strategies for error correction when those qubits are subjected to depolarizing noise. Building on the concept of tube algebras, we construct a set of measurements and of quantum gates which map arbitrary qubit errors to the string-net subspace and allow for the characterization of the resulting error syndrome in terms of doubled Fibonacci anyons. Tensor network techniques then allow us to quantitatively study the action of Pauli noise on the string-net subspace. We perform Monte Carlo simulations of error correction in this Fibonacci code and compare the performance of several decoders. For the case of a fixed-rate sampling depolarizing noise model, we find an error correction threshold of 4.7% using a clustering decoder.

Novel phenomena in magnetically intercalated graphite have been the subject of much research, pioneered and promoted by M. S. and G. Dresselhaus and many others in the 1980s. Among the most enigmatic findings of that era was the dramatic, roller-coaster-like behavior of the magnetoresistivity in a ${\mathrm{EuC}}_6$ compound, in which magnetic ${\mathrm{Eu}}^{2+}$ ions form a triangular lattice that is commensurate to graphite honeycomb planes. In this study, we provide a long-awaited microscopic explanation of this behavior, demonstrating that the resistivity of ${\mathrm{EuC}}_6$ is dominated by spin excitations in Eu planes and their highly nontrivial evolution with the magnetic field. Together with our theoretical analysis, the present study showcases the power of the synthetic 2D materials as a source of potentially significant insights into the nature of exotic spin excitations.

One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum. Prior to the inverse level spacing time, random matrix theory predicts a “ramp” of increasing variance in the connected part of the spectral form factor. However, in realistic quantum chaotic systems, the finite-time dynamics of the spectral form factor is much richer, with the pure random matrix ramp appearing only at sufficiently late time. In this article, we present a hydrodynamic theory of the connected spectral form factor prior to the inverse level spacing time. We first derive a general formula for the spectral form factor of a system with almost-conserved sectors in terms of return probabilities and spectral form factors within each sector. Next we argue that the theory of fluctuating hydrodynamics can be adapted from the usual Schwinger-Keldysh contour to the periodic time setting needed for the spectral form factor, and we show explicitly that the general formula is recovered in the case of energy diffusion. We also initiate a study of interaction effects in this modified hydrodynamic framework and show how the Thouless time defined as the time required for the spectral form factor to approach the pure random matrix result is controlled by the slow hydrodynamics modes. We then extend the formalism to Floquet systems, where a ramp is expected but with a different coefficient, and we derive a crossover formula from the Hamiltonian ramp to the Floquet ramp when the Floquet drive is weak. Taken together, these results establish an effective field theory of chaotic spectral correlations which predicts the random matrix ramp at late time and computes corrections to it at earlier times.

The low-energy physics of fractional quantum Hall (FQH) states—a paradigm of strongly correlated topological phases of matter—to a large extent is captured by weakly interacting quasiparticles known as composite fermions. In this paper, based on numerical simulations and effective field theory, we argue that some high-energy states in the FQH spectra necessitate a different description based on parton quasiparticles. We show that Jain states at filling factor $\nu =n/(2pn\pm 1)$ with integers $n$, $p\ge 2$ support two kinds of collective modes: In addition to the well-known Girvin-MacDonald-Platzman (GMP) mode, they host a high-energy collective mode, which we interpret as the GMP mode of partons. We elucidate observable signatures of the parton mode in the dynamics following a geometric quench. We construct a microscopic wave function for the parton mode and demonstrate agreement between its variational energy and exact diagonalization. Using the parton construction, we derive a field theory of the Jain states and show that the previously proposed effective theories follow from our approach. Our results point to partons being “real” quasiparticles which, in a way reminiscent of quarks, become observable only at sufficiently high energies.

Waves traveling in weakly disordered media possessing long-range correlations experience a universal phenomenon known as branched flow, where the waves split and form channels (branches) of enhanced intensity that keep dividing as the waves propagate. Branched flow effects have been studied experimentally in various systems, thus far always with coherent waves. We present the first experimental observation of branched flow of spatially incoherent light. We show that the primary effect of branching occurs for both coherent and incoherent light, but each pronounced branch is accompanied by sidelobes arising from interference, which disappear when the waves are incoherent. The position of the first caustic, where the branches reach peak intensity, remains the same as the coherence is reduced, but the branch statistics changes and some branches blur or disappear.

We observe the emission of bunches of $k\ge 1$ photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted at specific values $V_k$ of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly $k$ photons in the resonator. The latter is a microfabricated spiral coil which resonates and leaks photons at 4.4 GHz in a measurement line. Its characteristic impedance of $1.97\mathrm{k}\mathrm{\Omega }$ is high enough to reach a strong junction-resonator coupling and a bright emission of the $k$-photon bunches. We show that a rotating-wave approximation treatment of the system accounts quantitatively for the observed radiation intensity, from $k=1$ to 6, and over 3 orders of magnitude when varying the Josephson energy $E_J$. We also measure the second-order correlation function of the radiated microwave to determine its Fano factor $F_k$, which in the low $E_J$ limit confirms with $F_k\simeq k$ the emission of $k$-photon bunches. At larger $E_J$, a more complex behavior is observed in quantitative agreement with numerical simulations.