Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction that degrades the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction, we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum-dot system. We probe the derivative of the Stark shift, $g$-factor and $g$-factor difference for two single-electron quantum-dot qubits as a function of external magnetic field and find that they are dominated by spin-orbit interactions originating from the vector potential, consistent with recent theoretical predictions. Conversely, by populating the double dot with two electrons, we probe the mixing of singlet and spin-polarized triplet states during electron tunneling, which we conclude is dominated by momentum-term spin-orbit interactions that vary from 1.85 MHz up to 27.5 MHz depending on the magnetic field orientation. Finally, we exploit the tunability of the derivative of the Stark shift of one of the dots to reduce its sensitivity to electric noise and observe an 80% increase in $T_2^{*}$. We conclude that the tuning of the spin-orbit interaction will be crucial for scalable quantum computing in silicon and that the optimal setting will depend on the exact mode of qubit operations used.

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a—possibly nonintegrable—reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order $g^{-2}$, where $g$ is the perturbation strength. We also describe the leading correction to the time-dependent reference equilibrium state, which is, in general, of order $g$. The theory is well confirmed in numerical calculations of model Hamiltonians, for which we use a numerical linked cluster expansion and full exact diagonalization.

Dipolar coupling plays a fundamental role in the interaction between electrically or magnetically polarized species such as magnetic atoms and dipolar molecules in a gas or dipolar excitons in the solid state. Unlike Coulomb or contactlike interactions found in many atomic, molecular, and condensed-matter systems, this interaction is long-ranged and highly anisotropic, as it changes from repulsive to attractive depending on the relative positions and orientation of the dipoles. Because of this unique property, many exotic, symmetry-breaking collective states have been recently predicted for cold dipolar gases, but only a few have been experimentally detected and only in dilute atomic dipolar Bose-Einstein condensates. Here, we report on the first observation of attractive dipolar coupling between excitonic dipoles using a new design of stacked semiconductor bilayers. We show that the presence of a dipolar exciton fluid in one bilayer modifies the spatial distribution and increases the binding energy of excitonic dipoles in a vertically remote layer. The binding energy changes are explained using a many-body polaron model describing the deformation of the exciton cloud due to its interaction with a remote dipolar exciton. The surprising nonmonotonic dependence on the cloud density indicates the important role of dipolar correlations, which is unique to dense, strongly interacting dipolar solid-state systems. Our concept provides a route for the realization of dipolar lattices with strong anisotropic interactions in semiconductor systems, which open the way for the observation of theoretically predicted new and exotic collective phases, as well as for engineering and sensing their collective excitations.

We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperatures even in a common case of predominantly orbital suppression of superconductivity when the Zeeman spin splitting is expected to have a relatively weak effect. The maximum relative FFLO temperature is given by the ratio of the superconducting transition temperature and the Fermi energy. This maximum is realized when the ratio of the spin-spitting energy and the Landau-level separation is half-integer. These results imply that the FFLO states may exist not only in the Pauli-limited superconductors but also in very clean materials with small Zeeman spin-splitting energy. We expect that the described quantization-promoted FFLO instability is a general phenomenon, which may be found in materials with different electronic spectra and order-parameter symmetries.

Using molecular dynamics simulations and theoretical analysis of velocity-autocorrelation functions, we study ion transport mechanisms in typical room-temperature ionic liquids. We show that ions may reside in two states: free and bound with an interstate exchange. We investigate quantitatively the exchange process and reveal new qualitative features of this process. To this end, we propose a dynamic criterion for free and bound ions based on the ion trajectory density and demonstrate that this criterion is consistent with a static one based on interionic distances. Analyzing the trajectories of individual cations and anions, we estimate the time that ions spend in bound “clustered states” and when they move quasifreely. Using this method, we evaluate the average portion of “free” ions as approximately 15%–25%, increasing with temperature in the range of 300–600 K. The ion diffusion coefficients and conductivities as a function of the temperature calculated from the velocity and electrical-current autocorrelation functions reproduce the reported experimental data very well. The experimental data for the direct-current conductivity (constant ionic current) is in good agreement with theoretical predictions of the Nernst-Einstein equation based on the concentrations and diffusion coefficients of free ions obtained in our simulations. In analogy with electronic semiconductors, we scrutinize an “ionic semiconductor” model for ionic liquids, with valence and conduction “bands” for ions separated by an energy gap. The obtained band gap for the ionic liquid is small, around 26 meV, allowing for easy interchange between the two dynamic states. Moreover, we discuss the underscreening paradox in the context of the amount of free charge carriers, showing that the obtained results do not yet approve its simplistic resolution.

Many experiments that interrogate fundamental theories require detectors whose sensitivities are limited by the laws of quantum mechanics. In cavity-based searches for axionic dark matter, vacuum fluctuations in the two quadratures of the cavity electromagnetic field limit the sensitivity to an axion-induced field. In an apparatus designed to partially mimic existing axion detectors, we demonstrate experimentally that such quantum limits can be overcome through the use of squeezed states. By preparing a microwave cavity in a squeezed state and measuring just the squeezed quadrature, we enhance the spectral scan rate by a factor of $2.12\pm 0.08$. This enhancement is in excellent quantitative agreement with a theoretical model accounting for both imperfect squeezing and measurement.

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $\mathrm{U}(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)\mathrm{D}$ is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetry-breaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors $N_f=4$, our data suggest a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

In cuprates, the strong correlations in proximity to the antiferromagnetic Mott insulating state give rise to an array of unconventional phenomena beyond high-temperature superconductivity. Developing a complete description of the ground-state evolution is crucial to decoding the complex phase diagram. Here we use the structure of broken translational symmetry, namely, $d$-form factor charge modulations in $(\mathrm{Bi},\mathrm{Pb}{)}_2(\mathrm{Sr},\mathrm{La}{)}_2{\mathrm{CuO}}_{6+\delta }$ as a probe of the ground-state reorganization that occurs at the transition from truncated Fermi arcs to a large Fermi surface. We use real space imaging of nanoscale electronic inhomogeneity as a tool to access a range of dopings within each sample, and we definitively validate the spectral gap $\mathrm{\Delta }$ as a proxy for local hole doping. From the $\mathrm{\Delta }$ dependence of the charge modulation wave vector, we discover a commensurate-to-incommensurate transition that is coincident with the Fermi-surface transition from arcs to large hole pocket, demonstrating the qualitatively distinct nature of the electronic correlations governing the two sides of this quantum phase transition. Furthermore, the doping dependence of the incommensurate wave vector on the overdoped side is at odds with a simple Fermi-surface-driven instability.

Ultrafast photodoping of the Mott insulators, possessing strong correlation between electronic and magnetic degrees of freedom, holds promise for launching an ultrafast dynamics of spins which cannot be described in terms of conventional models of ultrafast magnetism. Here we study the ultrafast laser-induced dynamics of the magnetic order in a novel spin-orbit Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ featuring an uncompensated pattern of antiferromagnetic spin ordering. Using the transient magneto-optical Kerr effect sensitive to the net magnetization, we reveal that photodoping by femtosecond laser pulses with photon energy above the Mott gap launches melting of the antiferromagnetic order seen as ultrafast demagnetization with a characteristic time of 300 fs followed by a sub-10-ps recovery. Nonequilibrium dynamical mean-field theory calculations based on the single-band Hubbard model confirm that ultrafast demagnetization is primarily governed by the laser-induced generation of electron-hole pairs, although the precise simulated time dependencies are rather different from the experimentally observed ones. To describe the experimental results, here we suggest a phenomenological model which is based on Onsager’s formalism and accounts for the photogenerated electron-hole pairs using the concepts of holons and doublons.

Nitrogen-vacancy (NV) centers in diamond are appealing nanoscale quantum sensors for temperature, strain, electric fields, and, most notably, magnetic fields. However, the cryogenic temperatures required for low-noise single-shot readout that have enabled the most sensitive NV magnetometry reported to date are impractical for key applications, e.g., biological sensing. Overcoming the noisy readout at room temperature has until now demanded the repeated collection of fluorescent photons, which increases the time cost of the procedure, thus reducing its sensitivity. Here, we show how machine learning can process the noisy readout of a single NV center at room temperature, requiring on average only one photon per algorithm step, to sense magnetic-field strength with a precision comparable to those reported for cryogenic experiments. Analyzing large datasets from NV centers in bulk diamond, we report absolute sensitivities of $60\mathrm{nT}{\mathrm{s}}^{1/2}$ including initialization, readout, and computational overheads. We show that dephasing times can be simultaneously estimated and that time-dependent fields can be dynamically tracked at room temperature. Our results dramatically increase the practicality of early-term single-spin sensors.

We study the yielding behavior of a model glass under cyclic athermal quasistatic deformation and at finite rate and temperature, computationally, and show that yielding is characterized by the discontinuous appearance of shear bands, whose width is about ten particle diameters at their initiation, in which the strain gets localized. Strain localization is accompanied by a corresponding change in the energies and a decrease in the density in the shear band. We show that the glass remains well annealed outside the shear band, whereas the energies correspond to the highest possible energy minima at the given density within the shear band. Diffusive motion of particles characterizing the yielded state are confined to the shear bands, whose mean positions display movement over repeated cycles. Outside the shear band, particle motions are subdiffusive but remain finite. Despite the discontinuous nature of their appearance, shear bands are reversible in the sense that a reduction in the amplitude of cyclic deformation to values below yielding leads to the healing and disappearance of the shear bands.

We present an extensive overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on an ideal nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases of the corresponding model: ferromagnetic, Néel, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach, and we highlight the benefits of the former while outlining the shortcomings of the latter. Some of the transitions are direct and others occur via intermediate phases with more complicated forms of ordering. The spin-wave spectrum in the Néel phase is obtained and is shown to be nonreciprocal, ${ϵ}_{\alpha ,\mathbf{k}}\ne {ϵ}_{\alpha ,-\mathbf{k}}$, in the presence of anisotropic bond-dependent interactions. In a portion of the Néel phase, we find spin-wave instabilities to a long-range spiral-like state. This transition boundary is similar to that of the spin-liquid phase of the $S=1/2$ model discovered in our prior work, suggesting a possible connection between the two. Further, in the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for the $S=1/2$ case. However, for a two-dimensional surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an enigmatic accidental degeneracy manifested by pseudo-Goldstone modes. As a result, despite the nearly classical ground state, the ordering transition temperature in a wide region of the phase diagram is significantly suppressed from the mean-field expectation. We identify this accidental degeneracy as due to an exact correspondence to an extended Kitaev-Heisenberg model with emergent symmetries that naturally lead to the pseudo-Goldstone modes. There are previously studied dualities within the Kitaev-Heisenberg model on the triangular lattice that are exposed here in a wider parameter space. One important implication of this correspondence for the $S=1/2$ case is the existence of a region of the spin-liquid phase that is dual to the spin-liquid phase discovered recently by us. We complement our studies by the density-matrix renormalization group of the $S=1/2$ model to confirm some of the duality relations and to verify the existence of the dual spin-liquid phase.

Single-photon generation is an important proof of the underlying quantum nature of a physical process and a ubiquitous tool for scientific exploration, with applications ranging from spectroscopy and metrology to quantum computing. In the microwave regime, emission of antibunched radiation has so far relied on coherent control of Josephson qubits requiring precisely calibrated microwave pulses. In this work, we experimentally demonstrate the operation of a bright on-demand source of quantum microwave radiation driven by a simple dc voltage bias across a Josephson junction. Our source is based on photon emission into a microwave resonator through inelastic Cooper pair tunneling regulated by a high-impedance $RC$ circuit preventing simultaneous tunnel events. It is characterized by its normalized second-order correlation function of $g^{(2)}(0)\approx 0.43$ corresponding to antibunching in the single-photon regime. Our device can be triggered, and its in situ tunable emission rate exceeds those obtained with current microwave single-photon sources by more than 1 order of magnitude.

Using a coarse-grained molecular dynamics model, we simulate the self-assembly of PbSe nanocrystals (NCs) adsorbed at a flat fluid-fluid interface. The model includes all key forces involved: NC-NC short-range facet-specific attractive and repulsive interactions, entropic effects, and forces due to the NC adsorption at fluid-fluid interfaces. Realistic values are used for the input parameters regulating the various forces. The interface-adsorption parameters are estimated using a recently introduced sharp-interface numerical method which includes capillary deformation effects. We find that the final structure in which the NCs self-assemble is drastically affected by the input values of the parameters of our coarse-grained model. In particular, by slightly tuning just a few parameters of the model, we can induce NC self-assembly into either silicene-honeycomb superstructures, where all NCs have a $\{111\}$ facet parallel to the fluid-fluid interface plane, or square superstructures, where all NCs have a $\{100\}$ facet parallel to the interface plane. Both of these nanostructures have been observed experimentally. However, it is still not clear their formation mechanism, and, in particular, which are the factors directing the NC self-assembly into one or another structure. In this work, we identify and quantify such factors, showing illustrative assembled-phase diagrams obtained from our simulations. In addition, with our model, we can study the self-assembly dynamics, simulating how the NCs’ structures evolve from few-NCs aggregates to gradually larger domains. For example, we observe linear chains, where all NCs have a $\{110\}$ facet parallel to the interface plane as typical precursors of the square superstructure, and zigzag aggregates, where all NCs have a $\{111\}$ facet parallel to the interface plane as typical precursors of the silicene-honeycomb superstructure. Both of these aggregates have also been observed experimentally. Finally, we show indications that our method can be applied to study defects of the obtained superstructures.

The results of the renormalization group are commonly advertised as the existence of power-law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a case-by-case basis. We use the mathematics of normal form theory to systematically group these into universality families of seemingly unrelated systems united by common scaling variables. We recover and explain the existing literature and predict the nonlinear generalization for the universal homogeneous scaling functions. We show that this procedure leads to a better handling of the singularity even in classic cases and elaborate our framework using several examples.

We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two-dimensional real fermions in systems with space-time inversion $I_{\mathrm{ST}}$ symmetry. The Euler class is an integer topological invariant classifying real two-band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{\mathrm{ST}}$-symmetric Wannier representation. Moreover, a two-band system with the Euler class $e_2$ has band crossing points whose total winding number is equal to $2e_2$. Thus the conventional Nielsen-Ninomiya theorem fails in systems with a nonzero Euler class. We propose that the topological phase transition between two insulators carrying distinct Euler classes can be described in terms of the pair creation and annihilation of vortices accompanied by winding number changes across Dirac strings. When the number of bands is bigger than two, there is a $Z_2$ topological invariant classifying the band topology, that is, the second Stiefel Whitney class ($w_2$). Two bands with an even (odd) Euler class turn into a system with $w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the nontrivial second Stiefel-Whitney class remains robust against adding trivial bands, it does not impose a Wannier obstruction when the number of bands is bigger than two. However, when the resulting multiband system with the nontrivial second Stiefel-Whitney class is supplemented by additional chiral symmetry, a nontrivial second-order topology and the associated corner charges are guaranteed.

By combining theory and experiments, we demonstrate that dipolar quantum gases of both ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well-defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in ${}^{166}\mathrm{Er}$ the supersolid behavior survives only a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in ${}^{164}\mathrm{Dy}$. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.

We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system, here giving a 92% fidelity estimate for the controlled-$Z$ gate. Interestingly, with character randomized benchmarking, the two-qubit gate fidelity can be obtained by studying the additional decay induced by interleaving the two-qubit gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation.

We introduce a class of gapped three-dimensional models, dubbed “cage-net fracton models,” which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional string-net models, whose spectrum includes non-Abelian anyons, we condense extended one-dimensional “flux strings” built out of pointlike excitations. Flux-string condensation generalizes the concept of anyon condensation familiar from conventional topological order and allows us to establish properties of the fracton-ordered (equivalently, flux-string-condensed) phase, such as its ground-state wave function and spectrum of excitations. Through the examples of doubled-Ising and ${\mathrm{SU}(2)}_k$ cage-net models, we demonstrate the existence of strictly immobile Abelian fractons and of non-Abelian particles restricted to move only along one dimension. In the doubled-Ising cage-net model, we show that these restricted-mobility non-Abelian excitations are a fundamentally three-dimensional phenomenon, as they cannot be understood as bound states among two-dimensional non-Abelian anyons and Abelian particles. We further show that the ground-state wave function of such phases can be understood as a fluctuating network of extended objects—cages—and strings, which we dub a cage-net condensate. Besides having implications for topological quantum computation in three dimensions, our work may also point the way towards more general insights into quantum phases of matter with fracton order.

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by fluctuating forces which stem from active processes in the system, such as self-propulsion or collisions with other active particles. These active fluctuations do not fulfill a fluctuation-dissipation relation and therefore play the role of a nonequilibrium environment, which keeps the system permanently out of thermal equilibrium even in the absence of external forces. We investigate how the out-of-equilibrium character of the active matter system and the associated irreversibility is reflected in the trajectories of the Brownian particle. Specifically, we analyze the log ratio of path probabilities for observing a certain particle trajectory forward in time versus observing its time-reversed twin trajectory. For passive Brownian motion, it is well known that this path probability ratio quantifies irreversibility in terms of entropy production. For active Brownian motion, we show that in addition to the usual entropy produced in the thermal environment, the path probability ratio contains a contribution to irreversibility from mutual information “production” between the particle trajectory and the history of the nonequilibrium environment. The resulting irreversibility measure fulfills an integral fluctuation theorem and a second-law-like relation. When deriving and discussing these relations, we keep in mind that the active fluctuations can occur either due to a suspension of active particles pushing around a passive colloid or due to active self-propulsion of the particle itself; we point out the similarities and differences between these two situations. We obtain explicit expressions for active fluctuations modeled by an Ornstein-Uhlenbeck process. Finally, we illustrate our general results by analyzing a Brownian particle which is trapped in a static or moving harmonic potential.