Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity. In external electric and magnetic fields, the drag effect enables electrical control of excitons and may pave the way for the implementation of gauge fields for excitons and polaritons. Moreover, a reciprocal effect may facilitate optical manipulation of electron transport. Our findings establish transport measurements as a novel, powerful tool for probing the many-body physics of mobile quantum impurities.

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green’s functions grow linearly with rate $\alpha$ in generic systems, with an extra logarithmic correction in 1D. The rate $\alpha$—an experimental observable—governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents ${\lambda }_L\le 2\alpha$, which complements and improves the known universal low-temperature bound ${\lambda }_L\le 2\pi T$. We illustrate our results in paradigmatic examples such as nonintegrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally, we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

As electrical control of Néel order opens the door to reliable antiferromagnetic spintronic devices, understanding the microscopic mechanisms of antiferromagnetic switching is crucial. Spatially resolved studies are necessary to distinguish multiple nonuniform switching mechanisms; however, progress has been hindered by the lack of tabletop techniques to image the Néel order. We demonstrate spin Seebeck microscopy as a sensitive tabletop method for imaging antiferromagnetism in thin films and apply this technique to study spin-torque switching in $\mathrm{Pt}/\mathrm{NiO}$ and $\mathrm{Pt}/\mathrm{NiO}/\mathrm{Pt}$ heterostructures. We establish the interfacial antiferromagnetic spin Seebeck effect in NiO as a probe of surface Néel order. By imaging before and after applying current-induced spin torque, we resolve spin domain rotation and domain wall motion. We correlate the changes in spin Seebeck images with electrical measurements of the average Néel orientation through the spin Hall magnetoresistance, confirming that we image antiferromagnetic order.

Non-Hermiticity enriches topological phases beyond the existing Hermitian framework. Whereas their unusual features with no Hermitian counterparts were extensively explored, a full understanding about the role of symmetry in non-Hermitian physics has still been elusive, and there remains an urgent need to establish their topological classification in view of rapid theoretical and experimental progress. Here, we develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge conjugation is defined in terms of transposition rather than complex conjugation due to the lack of Hermiticity, and hence chiral symmetry becomes distinct from sublattice symmetry. It is also shown that non-Hermiticity enables a Hermitian-conjugate counterpart of the Altland-Zirnbauer symmetry. Taking into account sublattice symmetry or pseudo-Hermiticity as an additional symmetry, the total number of symmetry classes is 38 instead of 10, which describe intrinsic non-Hermitian topological phases as well as non-Hermitian random matrices. Furthermore, due to the complex nature of energy spectra, non-Hermitian systems feature two different types of complex-energy gaps, pointlike and linelike vacant regions. On the basis of these concepts and $K$-theory, we complete classification of non-Hermitian topological phases in arbitrary dimensions and symmetry classes. Remarkably, non-Hermitian topology depends on the type of complex-energy gaps, and multiple topological structures appear for each symmetry class and each spatial dimension, which are also illustrated in detail with concrete examples. Moreover, the bulk-boundary correspondence in non-Hermitian systems is elucidated within our framework, and symmetries preventing the non-Hermitian skin effect are identified. Our classification not only categorizes recently observed lasing and transport topological phenomena, but also predicts a new type of symmetry-protected topological lasers with lasing helical edge states and dissipative topological superconductors with nonorthogonal Majorana edge states. Furthermore, our theory provides topological classification of Hermitian and non-Hermitian free bosons. Our work establishes a theoretical framework for the fundamental and comprehensive understanding of non-Hermitian topological phases and paves the way toward uncovering unique phenomena and functionalities that emerge from the interplay of non-Hermiticity and topology.

Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is experienced only by one of the components. The second nondisordered “clean” component plays the role of a bath of adjustable size that is collisionally coupled to the “dirty” component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling, and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.

The surprising insulating and superconducting states of narrow-band graphene twisted bilayers have been mostly discussed so far in terms of strong electron correlation, with little or no attention to phonons and electron-phonon effects. We found that, among the 33 492 phonons of a fully relaxed $\theta =1.08°$ twisted bilayer, there are few special, hard, and nearly dispersionless modes that resemble global vibrations of the moiré supercell, as if it were a single, ultralarge molecule. One of them, doubly degenerate at $\mathbf{\Gamma }$ with symmetry $A_1+B_1$, couples very strongly with the valley degrees of freedom, also doubly degenerate, realizing a so-called $E\otimes e$ Jahn-Teller (JT) coupling. The JT coupling lifts very efficiently all degeneracies which arise from the valley symmetry, and may lead, for an average atomic displacement as small as 0.5 m Å, to an insulating state at charge neutrality. This insulator possesses a nontrivial topology testified by the odd winding of the Wilson loop. In addition, freezing the same phonon at a zone boundary point brings about insulating states at most integer occupancies of the four ultraflat electronic bands. Following that line, we further study the properties of the superconducting state that might be stabilized by these modes. Since the JT coupling modulates the hopping between $AB$ and $BA$ stacked regions, pairing occurs in the spin-singlet Cooper channel at the inter-($AB\text{−}BA$) scale, which may condense a superconducting order parameter in the extended $s$-wave and/or $d\pm id$-wave symmetry.

We propose a systematic approach to the nonequilibrium dynamics of strongly interacting many-body quantum systems, building upon the standard perturbative expansion in the Coulomb interaction. High-order series are derived from the Keldysh version of the determinantal diagrammatic quantum Monte Carlo algorithm, and the reconstruction beyond the weak-coupling regime of physical quantities is obtained by considering them as analytic functions of a complex-valued interaction $U$. Our advances rely on two crucial ingredients: (i) a conformal change of variable, based on the approximate location of the singularities of these functions in the complex $U$ plane, and (ii) a Bayesian inference technique, that takes into account additional known nonperturbative relations, in order to control the amplification of noise occurring at large $U$. This general methodology is applied to the strongly correlated Anderson quantum impurity model and is thoroughly tested both in and out of equilibrium. In the situation of a finite voltage bias, our method is able to extend previous studies, by bridging with the regime of unitary conductance and by dealing with energy offsets from particle-hole symmetry. We also confirm the existence of a voltage splitting of the impurity density of states and find that it is tied to a nontrivial behavior of the nonequilibrium distribution function. Beyond impurity problems, our approach could be directly applied to Hubbard-like models, as well as other types of expansions.

A single quantum of excitation of a mechanical oscillator is a textbook example of the principles of quantum physics. But mechanical oscillators, despite their pervasive presence in nature and modern technology, do not generically exist in an excited Fock state. In the past few years, careful isolation of gigahertz-frequency nanoscale oscillators has allowed experimenters to prepare such states at millikelvin temperatures. These developments illustrate the tension between the basic predictions of quantum mechanics—which should apply to all mechanical oscillators even at ambient conditions—and the extreme conditions required to observe those predictions. We resolve the tension by creating a single Fock state of a 40-THz vibrational mode in a crystal at room temperature and atmospheric pressure. After exciting a bulk diamond with a femtosecond laser pulse and detecting a Stokes-shifted photon, the Raman-active vibrational mode is prepared in the Fock state $|1⟩$ with 98.5% probability. The vibrational state is then mapped onto the anti-Stokes sideband of a subsequent pulse, which when subjected to a Hanbury Brown–Twiss intensity correlation measurement reveals the sub-Poisson number statistics of the vibrational mode. By controlling the delay between the two pulses, we are able to witness the decay of the vibrational Fock state over its 3.9-ps lifetime at ambient conditions. Our technique is agnostic to specific selection rules, and should thus be applicable to any Raman-active medium, opening a new general approach to the experimental study of quantum effects related to vibrational degrees of freedom in molecules and solid-state systems.

There is growing interest in heat pumps based on materials that show thermal changes when phase transitions are driven by changes of electric, magnetic, or stress field. Importantly, regeneration permits sinks and loads to be thermally separated by many times the changes of temperature that can arise in the materials themselves. However, performance and parameterization are compromised by net heat transfer between caloric working bodies and heat-transfer fluids. Here, we show that this net transfer can be avoided—resulting in true, balanced regeneration—if one varies the applied electric field while an electrocaloric (EC) working body dumps heat on traversing a passive fluid regenerator. Our EC working body is represented by bulk ${\mathrm{PbSc}}_{0.5}{\mathrm{Ta}}_{0.5}{\mathrm{O}}_3$ near its first-order ferroelectric phase transition, where we record directly measured adiabatic temperature changes of up to 2.2 K. Indirectly measured adiabatic temperature changes of similar magnitude are identified, unlike normal, from adiabatic measurements of polarization, at nearby measurement set temperatures, without assuming a constant heat capacity. The resulting high-resolution field-temperature-entropy maps of our material, and a small clamped companion sample, are used to construct cooling cycles that assume the use of an ideal passive regenerator in order to span $\le 20\mathrm{K}$. These cooling cycles possess well-defined coefficients of performance that are bounded by well-defined Carnot limits, resulting in large ($>50\%$) well-defined efficiencies that are not unduly compromised by a small field hysteresis. Our approach permits the limiting performance of any caloric material in a passive regenerator to be established, optimized, and compared; provides a recipe for true regeneration in prototype cooling devices; and could be extended to balance active regeneration.

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic oscillator modes associated with the tightly confined channel, and hence, the corresponding “lattice sites” are intimately related to the energy of the system. We analyze the quantum-transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension combined with the quasienergy spectrum of the periodically driven channel allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.

Understanding the material parameters that control the superconducting transition temperature $T_c$ is a problem of fundamental importance. In many novel superconductors phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean-field theory fails. For a simple parabolic band in 2D with Fermi energy $E_F$, we find that $k_B{T}_c\le E_F/8$, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases. Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum $T_c$ to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on $T_c$ in 3D.

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large-$N$ models exhibiting exponential growth of OTOCs and a sharp chaos wave front and other random circuit models showing a diffusively broadened wave front. In this paper, we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large-$N$ limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wave front. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a crossover to a diffusively broadened wave front. At small $N$, we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively broadened wave front.

Magnetic moments arranged at the corners of a honeycomb lattice are predicted to form a novel state of matter, the Kitaev quantum spin liquid, under the influence of frustration effects between bond-dependent Ising interactions. Some layered honeycomb iridates and related materials, such as ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ and $\alpha \text{−}{\mathrm{RuCl}}_3$, are proximate to the Kitaev quantum spin liquid, but bosonic spin-wave excitations associated with undesirable antiferromagnetic long-range order mask the inherent properties of the Kitaev Hamiltonian. Here, we use ${}^{63}\mathrm{Cu}$ nuclear quadrupole resonance to uncover the low-energy spin excitations in the nearly ideal honeycomb lattice of effective spin $S=1/2$ at the ${\mathrm{Ir}}^{4+}$ sites in ${\mathrm{Cu}}_2{\mathrm{IrO}}_3$. We demonstrate that, unlike ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, Ir spin fluctuations exhibit no evidence for critical slowing-down toward magnetic long-range order in zero external magnetic field. Moreover, the low-energy spin excitation spectrum is dominated by a mode that has a large excitation gap comparable to the Ising interactions, a signature expected for Majorana fermions of the Kitaev quantum spin liquid.

Spins associated with single defects in solids provide promising qubits for quantum-information processing and quantum networks. Recent experiments have demonstrated long coherence times, high-fidelity operations, and long-range entanglement. However, control has so far been limited to a few qubits, with entangled states of three spins demonstrated. Realizing larger multiqubit registers is challenging due to the need for quantum gates that avoid cross talk and protect the coherence of the complete register. In this paper, we present novel decoherence-protected gates that combine dynamical decoupling of an electron spin with selective phase-controlled driving of nuclear spins. We use these gates to realize a ten-qubit quantum register consisting of the electron spin of a nitrogen-vacancy center and nine nuclear spins in diamond. We show that the register is fully connected by generating entanglement between all 45 possible qubit pairs and realize genuine multipartite entangled states with up to seven qubits. Finally, we investigate the register as a multiqubit memory. We demonstrate the protection of an arbitrary single-qubit state for over 75 s—the longest reported for a single solid-state qubit—and show that two-qubit entanglement can be preserved for over 10 s. Our results enable the control of large quantum registers with long coherence times and therefore open the door to advanced quantum algorithms and quantum networks with solid-state spin qubits.

Although charge density waves (CDWs) are omnipresent in cuprate high-temperature superconductors, they occur at significantly different wave vectors, confounding efforts to understand their formation mechanism. Here, we use resonant inelastic x-ray scattering to investigate the doping- and temperature-dependent CDW evolution in ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ ($x=0.115–0.155$). We discover that the CDW develops in two stages with decreasing temperature. A precursor CDW with a quasicommensurate wave vector emerges first at high temperature. This doping-independent precursor CDW correlation originates from the CDW phase mode coupled with a phonon and “seeds” the low-temperature CDW with a strongly doping-dependent wave vector. Our observation reveals the precursor CDW and its phase mode as the building blocks of the highly intertwined electronic ground state in the cuprates.

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and optimizes them using gradient search. The concept emerges from deep learning but is not limited to training neural networks. We present the theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher-order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed-point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second-order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient-based variational optimization of infinite projected entangled pair states for the quantum antiferromagnetic Heisenberg model and obtain state-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.

Charge transport of topological semimetals is the focus of intensive investigations because of their nontrivial band topology. Heat transport of these materials, on the other hand, is largely unexplored and remains elusive. Here, we report on an observation of unprecedented, giant magnetic quantum oscillations of thermal conductivity in the prototypical Weyl semimetal TaAs. The oscillations are antiphase with the quantum oscillating electronic density of states of a Weyl pocket, and their amplitudes amount to 2 orders of magnitude of the estimation based on the Wiedemann-Franz law. Our analyses show that all the conventional heat-transport mechanisms through diffusions of propagating electrons, phonons, and electron-hole bipolar excitations are far inadequate to account for these phenomena. Taking further experimental facts that the parallel field configuration favors much-higher magnetothermal conductivity, we propose that the newly proposed chiral zero sound provides a reasonable explanation to these exotic phenomena. More work focusing on other topological semimetals along the same line is badly called for.

We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of charged excitations, fracton phases of both types as well as various Symmetry-protected topological phases emerge. Finally, the relation between the present approach and the formalism based on polynomials over finite fields is discussed.

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Because of the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.

Since the early 1960s, alloys are commonly grouped into two classes that feature either bound states in the band gap (I) or additional, nondiscrete band states (II). Consequently, one can observe either excitons bound to isoelectronic impurities or the typical band edge emission of a semiconductor that shifts and broadens with rising isoelectronic doping concentration. Microscopic parameters for class I alloys can directly be extracted from photoluminescence (PL) spectra, whereas any conclusions drawn for class II alloys usually remain limited to macroscopic assertions. Nonetheless, we present a spectroscopic study on exciton localization in a mixed-crystal alloy (class II) that allows us to access microscopic alloy parameters. In order to illustrate our approach, we study bulk ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ epilayers at the onset of alloying ($0\le x\le 2.4\%$) in order to understand their robustness to point and structural defects. Through an in-depth PL analysis it is demonstrated how different excitonic complexes (free, bound, and complex bound excitons) can serve as a probe to monitor the dilute limit of class II alloys. From an $x$-dependent linewidth analysis we extract the length scales at which excitons become increasingly localized, i.e., their conversion from a free to a bound particle upon alloy formation. Already at $x=2.4\%$ the exciton diffusion length is reduced to $5.7\pm 1.3\mathrm{nm}$ at a temperature of 12 K; hence, detrimental exciton transfer mechanisms toward nonradiative defects are suppressed. In addition, the associated low-temperature PL data suggest that a single indium atom cannot permanently capture an exciton. The low density of silicon impurities in our samples even allows studying their local indium-enriched environment at the scale of the exciton Bohr radius based on impurity bound excitons. The associated temperature-dependent PL data reveal an alloying dependence for the exciton-phonon coupling. Thus, the formation of the random alloy can not only be monitored by the emission of various excitonic complexes, but also more indirectly via the associated coupling(s) to the phonon bath. Micro-PL spectra even give access to a probing of silicon bound excitons embedded in a particular environment of indium atoms thanks to the emergence of a series of individual and energetically sharp emission lines (full width at half maximum $\approx 300\mu \mathrm{eV}$). Consequently, the present study allows us to extract microscopic properties formerly mostly only accessible for class I alloys.