The ability to engineer nonreciprocal interactions is an essential tool in modern communication technology as well as a powerful resource for building quantum networks. Aside from large reverse isolation, a nonreciprocal device suitable for applications must also have high efficiency (low insertion loss) and low output noise. Recent theoretical and experimental studies have shown that nonreciprocal behavior can be achieved in optomechanical systems, but performance in these last two attributes has been limited. Here, we demonstrate an efficient, frequency-converting microwave isolator based on the optomechanical interactions between electromagnetic fields and a mechanically compliant vacuum-gap capacitor. We achieve simultaneous reverse isolation of more than 20 dB and insertion loss less than 1.5 dB. We characterize the nonreciprocal noise performance of the device, observing that the residual thermal noise from the mechanical environments is routed solely to the input of the isolator. Our measurements show quantitative agreement with a general coupled-mode theory. Unlike conventional isolators and circulators, these compact nonreciprocal devices do not require a static magnetic field, and they allow for dynamic control of the direction of isolation. With these advantages, similar devices could enable programmable, high-efficiency connections between disparate nodes of quantum networks, even efficiently bridging the microwave and optical domains.

The pulse duration, and, more generally, the temporal intensity profile of free-electron laser (FEL) pulses, is of utmost importance for exploring the new perspectives offered by FELs; it is a nontrivial experimental parameter that needs to be characterized. We measured the pulse shape of an extreme ultraviolet externally seeded FEL operating in high-gain harmonic generation mode. Two different methods based on the cross-correlation of the FEL pulses with an external optical laser were used. The two methods, one capable of single-shot performance, may both be implemented as online diagnostics in FEL facilities. The measurements were carried out at the seeded FEL facility FERMI. The FEL temporal pulse characteristics were measured and studied in a range of FEL wavelengths and machine settings, and they were compared to the predictions of a theoretical model. The measurements allowed a direct observation of the pulse lengthening and splitting at saturation, in agreement with the proposed theory.

Virtually all interactions that are relevant for atomic and condensed matter physics are mediated by quantum fluctuations of the electromagnetic field vacuum. Consequently, controlling the vacuum fluctuations can be used to engineer the strength and the range of interactions. Recent experiments have used this premise to demonstrate novel quantum phases or entangling gates by embedding electric dipoles in photonic cavities or wave guides, which modify the electromagnetic fluctuations. Here, we show theoretically that the enhanced fluctuations in the antisqueezed quadrature of a squeezed vacuum state allow for engineering interactions between electric dipoles without the need for a photonic structure. Thus, the strength and range of the interactions can be engineered in a time-dependent way by changing the spatial profile of the squeezed vacuum in a traveling-wave geometry, which also allows the implementation of chiral dissipative interactions. Using experimentally realized squeezing parameters and including realistic losses, we predict single-atom cooperativities $C$ of up to 10 for the squeezed-vacuum-enhanced interactions.

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field, the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $\pi$, the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to $\pi$, at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field and is therefore a natural diagnostic of the transition. We point out that in the presence of a symmetry under a mirror reflection followed by time reversal, the system belongs to a higher symmetry class, and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.

Geometrical frustration arises when the lattice geometry prevents local interaction energies from minimizing simultaneously. Whether and how geometrically frustrated spins or charges in clean crystals exhibit glassy dynamics remain elusive due to the lack of measurements on microscopic dynamics. Here, we employ buckled monolayer colloidal crystals to mimic frustrated antiferromagnetic Ising spins on triangular lattices and measure single-spin dynamics using video microscopy. Both attractive and repulsive colloidal crystals buckled into zigzag stripes with glassy dynamics at low effective temperatures in experiment and simulation. The simple local spin configurations enable uncovering correlations among structure, dynamics, and soft vibrational modes. Machine learning analysis further reveals facilitated dynamics to be an important mechanism of structural relaxation. Moreover, our simulation reveals a similar structure and dynamics in lattice Coulomb liquids. Hence, spin-lattice coupling and long-range interaction can similarly lift degeneracy, induce a rugged landscape, and, thus, produce glassy dynamics.

The strong light-matter interaction and the valley selective optical selection rules make monolayer (ML) ${\mathrm{MoS}}_2$ an exciting 2D material for fundamental physics and optoelectronics applications. But, so far, optical transition linewidths even at low temperature are typically as large as a few tens of meV and contain homogeneous and inhomogeneous contributions. This prevented in-depth studies, in contrast to the better-characterized ML materials ${\mathrm{MoSe}}_2$ and ${\mathrm{WSe}}_2$. In this work, we show that encapsulation of ML ${\mathrm{MoS}}_2$ in hexagonal boron nitride can efficiently suppress the inhomogeneous contribution to the exciton linewidth, as we measure in photoluminescence and reflectivity a FWHM down to 2 meV at $T=4\mathrm{K}$. Narrow optical transition linewidths are also observed in encapsulated ${\mathrm{WS}}_2$, ${\mathrm{WSe}}_2$, and ${\mathrm{MoSe}}_2$ MLs. This indicates that surface protection and substrate flatness are key ingredients for obtaining stable, high-quality samples. Among the new possibilities offered by the well-defined optical transitions, we measure the homogeneous broadening induced by the interaction with phonons in temperature-dependent experiments. We uncover new information on spin and valley physics and present the rotation of valley coherence in applied magnetic fields perpendicular to the ML.

We demonstrate optimization of thermal conductance across nanostructures by developing a method combining atomistic Green’s function and Bayesian optimization. With an aim to minimize and maximize the interfacial thermal conductance (ITC) across Si-Si and Si-Ge interfaces by means of the $\mathrm{Si}/\mathrm{Ge}$ composite interfacial structure, the method identifies the optimal structures from calculations of only a few percent of the entire candidates (over 60 000 structures). The obtained optimal interfacial structures are nonintuitive and impacting: the minimum ITC structure is an aperiodic superlattice that realizes 50% reduction from the best periodic superlattice. The physical mechanism of the minimum ITC can be understood in terms of the crossover of the two effects on phonon transport: as the layer thickness in the superlattice increases, the impact of Fabry-Pérot interference increases, and the rate of reflection at the layer interfaces decreases. An aperiodic superlattice with spatial variation in the layer thickness has a degree of freedom to realize optimal balance between the above two competing mechanisms. Furthermore, the spatial variation enables weakening the impact of constructive phonon interference relative to that of destructive interference. The present work shows the effectiveness and advantage of material informatics in designing nanostructures to control heat conduction, which can be extended to other nanostructures and properties.

Machine learning, one of today’s most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states has recently become highly desirable in the applications of machine-learning techniques to quantum many-body physics. In this paper, we explore the data structures that encode the physical features in the network states by studying the quantum entanglement properties, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement entropy of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states, we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing quantum states with massive entanglement. Strikingly, the neural-network representation for these states is remarkably efficient, in the sense that the number of nonzero parameters scales only linearly with the system size. We further examine the entanglement properties of generic RBM states by randomly sampling the weight parameters of the RBM. We find that their averaged entanglement entropy obeys volume-law scaling, and the meantime strongly deviates from the Page entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with a long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states regardless of how much entanglement they possess, which paves a novel way to bridge computer-science-based machine-learning techniques to outstanding quantum condensed-matter physics problems.

We show that the previously predicted “cubic Dirac fermion,” composed of six conventional Weyl fermions including three with left-handed and three with right-handed chirality, is realized in a specific, stable solid state system that has been made years ago, but was not appreciated as a “cubically dispersed Dirac semimetal” (CDSM). We identify the crystal symmetry constraints and find the space group $\mathrm{P}{6}_3/\mathrm{m}$ as one of the two that can support a CDSM, of which the characteristic band crossing has linear dispersion along the principle axis but cubic dispersion in the plane perpendicular to it. We then conduct a material search using density functional theory, identifying a group of quasi-one-dimensional molybdenum monochalcogenide compounds ${\mathrm{A}}^{\mathrm{I}}{({\mathrm{MoX}}^{\mathrm{VI}})}_3$ (${\mathrm{A}}^{\mathrm{I}}=\mathrm{Na}$, K, Rb, In, Tl; ${\mathrm{X}}^{\mathrm{VI}}=\mathrm{S}$, Se, Te) as ideal CDSM candidates. Studying the stability of the $\mathrm{A}{(\mathrm{MoX})}_3$ family reveals a few candidates such as $\mathrm{Rb}{(\mathrm{MoTe})}_3$ and $\mathrm{Tl}{(\mathrm{MoTe})}_3$ that are predicted to be resilient to Peierls distortion, thus retaining the metallic character. Furthermore, the combination of one dimensionality and metallic nature in this family provides a platform for unusual optical signature—polarization-dependent metallic vs insulating response.

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of $\ell$ contiguous sites. We argue that this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random-field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites, and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.

Emission of high-order harmonics from solids provides a new avenue in attosecond science. On the one hand, it allows us to investigate fundamental processes of the nonlinear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic-generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomenon of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine in any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process and hence precisely addresses the question of localization of harmonic emission in solids. We apply this model to investigate HHG in a ZnO crystal for two different orientations, corresponding to wider and narrower valence and conduction bands, respectively. Interestingly, for narrower bands, the HHG process shows significant localization, similar to harmonic generation in atoms. For all cases, the delocalized contributions to HHG emission are highest near the band-gap energy. Our results pave the way to controlling localized contributions to HHG in a solid crystal.

The higher the energy of a particle is above equilibrium, the faster it relaxes because of the growing phase space of available electronic states it can interact with. In the relaxation process, phase coherence is lost, thus limiting high-energy quantum control and manipulation. In one-dimensional systems, high relaxation rates are expected to destabilize electronic quasiparticles. Here, we show that the decoherence induced by relaxation of hot electrons in one-dimensional semiconducting nanowires evolves nonmonotonically with energy such that above a certain threshold hot electrons regain stability with increasing energy. We directly observe this phenomenon by visualizing, for the first time, the interference patterns of the quasi-one-dimensional electrons using scanning tunneling microscopy. We visualize the phase coherence length of the one-dimensional electrons, as well as their phase coherence time, captured by crystallographic Fabry-Pèrot resonators. A remarkable agreement with a theoretical model reveals that the nonmonotonic behavior is driven by the unique manner in which one-dimensional hot electrons interact with the cold electrons occupying the Fermi sea. This newly discovered relaxation profile suggests a high-energy regime for operating quantum applications that necessitate extended coherence or long thermalization times, and may stabilize electronic quasiparticles in one dimension.

The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition that lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of this transition at finite sizes in one dimension. We find that the entanglement entropy of small subsystems looks strongly subthermal in the quantum critical regime, which indicates that it varies discontinuously across the transition as the system size is taken to infinity, even though many other aspects of the transition look continuous. We also study the variance of the half-chain entanglement entropy, which shows a peak near the transition, and find substantial variation in the entropy across eigenstates of the same sample. Furthermore, the sample-to-sample variations in this quantity are strongly growing and are larger than the intrasample variations. We posit that these results are consistent with a picture in which the transition to the thermal phase is driven by an eigenstate-dependent sparse resonant “backbone” of long-range entanglement, which just barely gains enough strength to thermalize the system on the thermal side of the transition as the system size is taken to infinity. This discontinuity in a global quantity—the presence of a fully functional bath—in turn implies a discontinuity even for local properties. We discuss how this picture compares with existing renormalization group treatments of the transition.

Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency $f_J$ rather than conventional emission at $f_J$. Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency $f_J/2$. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the $f_J/2$ line, much shorter than for the $f_J$ line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI) case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting $XXZ$-like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.

In the presence of disorder, an interacting closed quantum system can undergo many-body localization (MBL) and fail to thermalize. However, over long times, even weak couplings to any thermal environment will necessarily thermalize the system and erase all signatures of MBL. This presents a challenge for experimental investigations of MBL since no realistic system can ever be fully closed. In this work, we experimentally explore the thermalization dynamics of a localized system in the presence of controlled dissipation. Specifically, we find that photon scattering results in a stretched exponential decay of an initial density pattern with a rate that depends linearly on the scattering rate. We find that the resulting susceptibility increases significantly close to the phase transition point. In this regime, which is inaccessible to current numerical studies, we also find a strong dependence on interactions. Our work provides a basis for systematic studies of MBL in open systems and opens a route towards extrapolation of closed-system properties from experiments.

A new type of topological state in strongly correlated condensed matter systems, the heavy Weyl fermion state, has been found in a heavy fermion material, ${\mathrm{CeRu}}_4{\mathrm{Sn}}_6$, which has no inversion symmetry. Two different types of Weyl points, types I and II, can be found in the quasiparticle band structure obtained by the $\mathrm{LDA}+\mathrm{Gutzwiller}$ calculations, which can treat the strong correlation effects among the $f$ electrons from cerium atoms. The surface calculations indicate that the topologically protected Fermi arc states exist on the (010) but not on the (001) surface.

In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed “Floquet time crystals.” We show that such phases of matter can exist in the prethermal regime of periodically driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder, which limited previous constructions. We prove a theorem that states that such a prethermal regime persists until times that are nearly exponentially long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems that spontaneously break continuous time-translation symmetry. Furthermore, we argue that for driven systems coupled to a cold bath, the prethermal regime could potentially persist to infinite time.

The synthesis of transition metal heterostructures is currently one of the most vivid fields in the design of novel functional materials. In this paper, we propose a simple scheme to predict band alignment and charge transfer in complex oxide interfaces. For semiconductor heterostructures, band-alignment rules like the well-known Anderson or Schottky-Mott rule are based on comparison of the work function or electron affinity of the bulk components. This scheme breaks down for oxides because of the invalidity of a single work-function approximation as recently shown in [Phys. Rev. B 93, 235116 (2016); Adv. Funct. Mater. 26, 5471 (2016)]. Here, we propose a new scheme that is built on a continuity condition of valence states originating in the compounds’ shared network of oxygen. It allows for the prediction of sign and relative amplitude of the intrinsic charge transfer, taking as input only information about the bulk properties of the components. We support our claims by numerical density functional theory simulations as well as (where available) experimental evidence. Specific applications include (i) controlled doping of ${\mathrm{SrTiO}}_3$ layers with the use of $4d$ and $5d$ transition metal oxides and (ii) the control of magnetic ordering in manganites through tuned charge transfer.