The properties of the isotropic incompressible $\nu =5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+i{p}_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $\nu =5/2$. This finding motivates us to consider an inhomogeneous paired state—a $p_x+i{p}_y$ pair-density wave (PDW)—whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and antidomain walls of the $p_x+i{p}_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and antidomain walls) where the order parameter changes sign, support a pair of symmetry-protected counterpropagating Majorana modes. The coupling behavior of the domain-wall Majorana modes crucially depends on the interplay of the Fermi energy $E_F$ and the PDW pairing energy $E_{\mathrm{P}\mathrm{D}\mathrm{W}}$. The analysis of this interplay yields a rich set of topological states: (1) In the weak-coupling regime ($E_F>E_{\mathrm{P}\mathrm{D}\mathrm{W}}$), the hybridization of domain walls leads to a Majorana Fermi surface (MFS), which is protected by inversion and particle-hole symmetries. (2) As the MFS shrinks towards degenerate Dirac points, lattice effects render it unstable towards an Abelian stripe phase with two copropagating Majorana modes at the boundary. (3) A uniform component of the order parameter, which breaks inversion symmetry, gaps the MFS and causes the system to enter a non-Abelian FQH state supporting a chiral Majorana edge state. (4) In the strong-coupling regime, $E_F<E_{\mathrm{P}\mathrm{D}\mathrm{W}}$, the bulk fermionic spectrum becomes gapped; this is a trivial phase with no chiral Majorana edge states, which is in the universality class of an Abelian Halperin paired state. The pair-density-wave order state in a paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases—as well as transitions thereof—tuned by the strength of the paired liquid crystalline order.

With the help of quantum key distribution (QKD), two distant peers are able to share information-theoretical secure key bits. Increasing the key rate is ultimately significant for the applications of QKD in the lossy channel. However, it has been proven that there is a fundamental rate-distance limit, called the linear bound, which restricts the performance of all existing repeaterless protocols and realizations. Surprisingly, a recently proposed protocol, called twin-field (TF) QKD, can beat the linear bound with no need for quantum repeaters. Here, we present one of the first implementations of the TF-QKD protocol and demonstrate its advantage of beating the linear bound at a channel distance of 300 km. In our experiment, a modified TF-QKD protocol that does not assume phase postselection is considered, and thus a higher key rate than the original one is expected. After controlling the phase evolution of the twin fields traveling through hundreds of kilometers of optical fibers, the implemented system achieves high-visibility single-photon interference and allows stable and high-rate measurement-device-independent QKD. Our experimental demonstration and results confirm the feasibility of the TF-QKD protocol and its prominent superiority in long-distance key distribution services.

Gates in error-prone quantum information processors are often modeled using sets of one- and two-qubit process matrices, the standard model of quantum errors. However, the results of quantum circuits on real processors often depend on additional external “context” variables. Such contexts may include the state of a spectator qubit, the time of data collection, or the temperature of control electronics. In this article, we demonstrate a suite of simple, widely applicable, and statistically rigorous methods for detecting context dependence in quantum-circuit experiments. They can be used on any data that comprise two or more “pools” of measurement results obtained by repeating the same set of quantum circuits in different contexts. These tools may be integrated seamlessly into standard quantum device characterization techniques, like randomized benchmarking or tomography. We experimentally demonstrate these methods by detecting and quantifying crosstalk and drift on the publicly accessible 16-qubit ibmqx3.

The effects of uniaxial compressive stress on the normal state ${}^{17}\mathrm{O}$ nuclear-magnetic-resonance properties of the unconventional superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal $\mathbf{a}$-axis strain ${ϵ}_{aa}\equiv {ϵ}_v$ that maximizes the superconducting transition temperature $T_c$. The spin susceptibility weakly increases on lowering the temperature below $T\simeq 10\mathrm{K}$, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the $\gamma$ band formed by the Ru $d_{xy}$ states hybridized with in-plane O $p_{\pi }$ orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalization $S$ by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.

We study a large-$N$ tensor model with $O(N{)}^3$ symmetry containing two flavors of Majorana fermions, ${\psi }_1^{abc}$ and ${\psi }_2^{abc}$. We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev (SYK) models, each containing $N_{\mathrm{SYK}}$ Majorana fermions. In these models, we assume tetrahedral quartic Hamiltonians which depend on a real coupling parameter $\alpha$. We find a duality relation between two Hamiltonians with different values of $\alpha$, which allows us to restrict the model to the range of $-1\le \alpha \le 1/3$. The scaling dimension of the fermion number operator $Q=i{\psi }_1^{abc}{\psi }_2^{abc}$ is complex and of the form $1/2+if(\alpha )$ in the range $-1\le \alpha <0$, indicating an instability of the conformal phase. Using Schwinger-Dyson equations to solve for the Green functions, we show that in the true low-temperature phase this operator acquires an expectation value, which demonstrates the breaking of an antiunitary particle-hole symmetry and other discrete symmetries. We also calculate spectra of the coupled SYK models for values of $N_{\mathrm{SYK}}$ where exact diagonalizations are possible. For negative $\alpha$, we find a gap separating the two lowest energy states from the rest of the spectrum, leading to an exponential decay of the zero-temperature correlation functions. For $N_{\mathrm{SYK}}$ divisible by 4, the two lowest states have a small splitting. They become degenerate in the large-$N_{\mathrm{SYK}}$ limit, as expected from the spontaneous breaking of a ${\mathbb{Z}}_2$ symmetry.

One important yet exceedingly rare property of the cuprate high-temperature superconductors is the presence of a single correlated $d$ band in the low-energy spectrum, leading to the one-band Hubbard model as the minimal description. In order to search for materials with interesting strong correlation physics as well as possible benchmark systems for the one-band Hubbard model, here we present a new approach to find one-band correlated materials analogous to the cuprates by leveraging the emerging area of materials informatics. Using the composition, structure, and formation energy of more than half a million real and hypothetical inorganic crystalline materials in the Open Quantum Materials Database, we search for synthesizable materials whose nominal transition-metal $d$ electron count and crystal field are compatible with achieving an isolated half-filled $d$ band. Thirteen Cu compounds, including bromide, oxide, selenate, borate, pyrophosphate, hydrogen phosphate, and pyrosilicate chemistries, and one Fe oxide compound are shown to successfully achieve the one-band electronic structure based on density-functional theory band structure calculations. Further calculations including magnetism and explicit on-site Coulomb interaction, performed for a representative subset of five candidate materials, reveal significant evidence for strong correlation physics, including Mott insulating behavior and antiferromagnetism. The success of our data-driven approach to discovering new correlated materials opens up new avenues to design and discover materials with rare electronic properties.

The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault tolerance of the Bacon-Shor code.

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states to spatial dimensions $d\ge 2$. By construction, they are Euclidean invariant and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending projected entangled-pair states, we propose a generalization bearing similarities with the continuum multiscale entanglement renormalization ansatz.

We demonstrate full quantum state control of two species of single atoms using optical tweezers and assemble the atoms into a molecule. Our demonstration includes 3D ground-state cooling of a single atom (Cs) in an optical tweezer, transport by several microns with minimal heating, and merging with a single Na atom. Subsequently, both atoms occupy the simultaneous motional ground state with 61(4)% probability. This realizes a sample of exactly two cotrapped atoms near the phase-space-density limit of one, and allows for efficient stimulated-Raman transfer of a pair of atoms into a molecular bound state of the triplet electronic ground potential $a^3{\mathrm{\Sigma }}^{+}$. The results are key steps toward coherent creation of single ultracold molecules for future exploration of quantum simulation and quantum information processing.

Charge transport in $\pi$-conjugated polymers is characterized by a strong degree of disorder in both the energy of conjugated segments and the electronic coupling between adjacent sites. This disorder arises from variations in the structure and conformation of molecular units, as well as the weak intermolecular binding interactions. Although disorder in molecular conformation can be expected to influence the density of states (DOS) distribution—and hence, optoelectronic properties of the material—until now, there has been no direct study of the relationship between a distinct conformational defect and the charge transport properties of a conjugated polymer. Here, we investigate the impact of introducing an extended, planarized chain geometry, known as the “$\beta$-phase,” on hole transport through otherwise amorphous films of poly(9,9-dioctylfluorene) (PFO). We show that while $\beta$-phase introduces a striking drop of about a hundredfold in time-of-flight (TOF) hole mobility (${\mu }_h$) at room temperature, it reduces the steady-state ${\mu }_h$ measured from hole-only devices by a factor of less than about 5. In order to reconcile these observations, we combine high-dynamic-range TOF photocurrent spectroscopy and energy-resolved electrochemical impedance spectroscopy to extract the hole DOS of the conjugated polymer. Both methods show that the effect of the $\beta$-phase content is to introduce a sharp sub-bandgap feature into the DOS of glassy PFO lying about 0.3 eV above the highest occupied molecular orbital. The observed energy of the conformational trap is consistent with electronic structure calculations using a tight-binding approach. Using the obtained DOS with a drift-diffusion model capable of resolving charge carriers in both time and energy, we show how the seemingly contradictory transport phenomena obtained via the time-resolved, frequency-resolved, and steady-state methods are reconciled. The results highlight the significance of energetic redistribution of charge carriers in affecting transport behavior. This work demonstrates how charge-carrier mobility in organic semiconductors can be controlled via molecular conformation, and it resolves a long-standing debate over how different (equilibrium versus nonequilibrium) transport techniques reveal electronic properties of disordered solids in a unified manner.

We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency—and drive strength—regimes that are usually inaccessible via high-frequency $\omega$ expansions in the parameter $h/\omega$, where $h$ is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems.

The recent development of ultrashort laser pulses allows for optical control of structural and electronic properties of complex quantum materials. The layered transition-metal dichalcogenide ${\mathrm{MoTe}}_2$, which can crystallize into several different structures with distinct topological and electronic properties, provides possibilities to control or switch between different phases. In this study, we report a photoinduced subpicosecond structural transition between the type-II Weyl semimetal phase and normal-semimetal phase in bulk crystalline ${\mathrm{MoTe}}_2$ by using ultrafast pump-probe and time-resolved second-harmonic-generation spectroscopy. The phase transition is most clearly characterized by the dramatic change of the shear oscillation mode and the intensity loss of second-harmonic generation. This work opens up new possibilities for ultrafast manipulation of the topological properties of solids, enabling potentially practical applications for a topological switch device with ultrafast excitations.

A fluid is said to be scale invariant when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross-Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies, and interaction parameters by a scaling transform. Finally, we show that some specific initial shapes—uniformly filled triangles or disks—may lead to a periodic evolution corresponding to a novel type of breather for the two-dimensional Gross-Pitaevskii equation.

Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of $2+1$-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases. In this paper, we present several examples of deconfined quantum critical points between SPT phases in $3+1$-D for both bosonic and fermionic systems. These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points. We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility—which we dub “unnecessary quantum critical points”—of stable generic continuous phase transitions within the same phase. We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible $3+1$-D field theory duality between $SU(2)$ gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of “maximally chaotic,” periodically driven, quantum spin chains. Specifically, we consider the so-called “self-dual” kicked Ising chains initialized in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the maximally chaotic models considered: Their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so-called “minimal cut” bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel “duality-based” numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is nonintegrable.

Recent success in deep neural networks has generated strong interest in hardware accelerators to improve speed and energy consumption. This paper presents a new type of photonic accelerator based on coherent detection that is scalable to large ($N\gtrsim {10}^6$) networks and can be operated at high (gigahertz) speeds and very low (subattojoule) energies per multiply and accumulate (MAC), using the massive spatial multiplexing enabled by standard free-space optical components. In contrast to previous approaches, both weights and inputs are optically encoded so that the network can be reprogrammed and trained on the fly. Simulations of the network using models for digit and image classification reveal a “standard quantum limit” for optical neural networks, set by photodetector shot noise. This bound, which can be as low as $50\mathrm{zJ}/\mathrm{MAC}$, suggests that performance below the thermodynamic (Landauer) limit for digital irreversible computation is theoretically possible in this device. The proposed accelerator can implement both fully connected and convolutional networks. We also present a scheme for backpropagation and training that can be performed in the same hardware. This architecture will enable a new class of ultralow-energy processors for deep learning.

Transformation of light carrying spin angular momentum (SAM) to optical field vortices carrying orbital angular momentum (OAM) has been of wide interest in recent years. The interactions between two optical fields, each carrying one of those degrees of freedom, and furthermore, the transfer of the resulting angular momentum product to matter are seldom discussed. Here, we measure the interaction between 3D light carrying axial SAM and 2D plasmon-polariton vortices carrying high-order transverse OAM. The interaction is mediated by two-photon absorption within a gold surface, imprinting the resulting angular-momentum mixing into matter by excitation of electrons that are photo-emitted into vacuum. Interestingly, the spatial distribution of the emitted electrons carries the signature of a subtraction of the spin from the orbit angular momenta. We show experimentally and theoretically that the absorptive nature of this interaction leads to both single and double photon-plasmon angular momentum mixing processes by one- and two- photon interactions. Our results demonstrate high order angular momenta light-matter interactions, provide a glimpse into specific electronic excitation routes, and may be applied in future electronic sources and coherent control.

The quantum coherence of electronic quasiparticles underpins many of the emerging transport properties of conductors at small scales. Novel electronic implementations of quantum optics devices are now available with perspectives such as “flying-qubit” manipulations. However, electronic quantum interferences in conductors remained up to now limited to propagation paths shorter than $30\mu \mathrm{m}$ independent of the material. Here we demonstrate strong electronic quantum interferences after a propagation along two 0.1-mm-long pathways in a circuit. Interferences of visibility as high as 80% and 40% are observed on electronic analogues of the Mach-Zehnder interferometer of, respectively, $24\text{−}\mu \mathrm{m}$ and 0.1-mm arm length, consistently corresponding to a 0.25-mm electronic phase coherence length. While such devices perform best in the integer quantum Hall regime at filling factor 2, the electronic interferences are restricted by the Coulomb interaction between copropagating edge channels. We overcome this limitation by closing the inner channel in micron-scale loops of frozen internal degrees of freedom combined with a loop-closing strategy providing an essential isolation from the environment.

We report on experimental results in a new regime of relativistic light-matter interaction employing midinfrared ($3.9\text{−}\mu \mathrm{m}$ wavelength) high-intensity femtosecond laser pulses. In the laser-generated plasma, electrons reach relativistic energies already for rather low intensities due to the fortunate ${\lambda }^2$ scaling of the kinetic energy with the laser wavelength. The lower intensity efficiently suppresses optical field ionization and creation of the preplasma at the rising edge of the laser pulse, enabling an enhanced efficient vacuum heating of the plasma. The lower critical plasma density for long-wavelength radiation can be surmounted by using nanowires instead of flat targets. Numerical simulations, which are in a good agreement with experimental results, suggest that $\approx 80\%$ of the incident laser energy has been absorbed resulting in a long-living, keV-temperature, high-charge-state plasma with a density more than 3 orders of magnitude above the critical value. Our results pave the way to laser-driven experiments on laboratory astrophysics and nuclear physics at a high repetition rate.