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An outstanding challenge in large-scale quantum platforms is to simultaneously achieve strong interactions, giving rise to the most interesting behaviors, and local addressing -that can probe them. In the context of correlated phases, local addressing enables one to directly probe the nature of the system's order. Meanwhile, for out-ofequilibrium dynamics, such addressing allows the study of quantum information spreading and operator growth. Here, we introduce a novel technique that enables the measurement of local correlation functions, down to single-site resolution, despite access to only global controls. Our approach leverages the intrinsic disorder present in a solid-state spin ensemble to dephase the nonlocal components of the correlation function. Utilizing this toolset, we measure both the spin and energy transport in nuclear spin chains. By tuning the interaction Hamiltonian via Floquet engineering, we investigate the cross-over between ballistic and diffusive hydrodynamics. Interestingly, when the system is both interacting and (nearly-)integrable, we observe the coexistence of diffusive spin transport with ballistic energy transport., main text 5 pages, 4 figures; SM 10 pages 5 figures

Moire superlattices in van der Waals (vdW) heterostructures form by stacking atomically thin layers on top of one another with a twist angle or lattice mismatch. The resulting moire potential leads to a strong modification of the band structure, which can give rise to exotic quantum phenomena ranging from correlated insulators and superconductors to moire excitons and Wigner crystals. Here, we demonstrate the dynamic tuning of moire potential in a WSe2/WS2 heterostructure at cryogenic temperature. We utilize the optical fiber tip of a cryogenic scanning near-field optical microscope (SNOM) to locally deform the heterostructure and measure its near-field optical response simultaneously. The deformation of the heterostructure increases the moire potential, which leads to a red shift of the moire exciton resonances. We observe the interlayer exciton resonance shifts up to 20 meV, while the intralayer exciton resonances shift up to 17 meV.

Systems of spins engineered with tunable density and reduced dimensionality enable a number of advancements in quantum sensing and simulation. Defects in diamond, such as nitrogen-vacancy (NV) centers and substitutional nitrogen (P1 centers), are particularly promising solid-state platforms to explore. However, the ability to controllably create coherent, two-dimensional spin systems and characterize their properties, such as density, depth confinement, and coherence is an outstanding materials challenge. We present a refined approach to engineer dense ($\gtrsim$1 ppm$\cdot$nm), 2D nitrogen and NV layers in diamond using delta-doping during plasma-enhanced chemical vapor deposition (PECVD) epitaxial growth. We employ both traditional materials techniques, e.g. secondary ion mass spectrometry (SIMS), alongside NV spin decoherence-based measurements to characterize the density and dimensionality of the P1 and NV layers. We find P1 densities of 5-10 ppm$\cdot$nm, NV densities between 1 and 3.5 ppm$\cdot$nm tuned via electron irradiation dosage, and depth confinement of the spin layer down to 1.6 nm. We also observe high (up to 0.74) ratios of P1 to NV centers and reproducibly long NV coherence times, dominated by dipolar interactions with the engineered P1 and NV spin baths.

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter., 9 + 10 pages, 3 + 6 figures

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically-driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems., Comment: 7+13 pages, 3+13 figures

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase. Here, we realize a two-dimensional dipolar XY model -- which exhibits a continuous spin-rotational symmetry -- utilizing a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works utilizing the Rydberg-blockade mechanism to realize Ising-type interactions exhibiting discrete spin rotation symmetry., Comment: 18 pages, 3 figures in main text, 9 figures in supplemental methods

Moiré superlattices in van der Waals (vdW) heterostructures form by stacking atomically thin layers on top of one another with a twist angle or lattice mismatch. The resulting moiré potential leads to a strong modification of the band structure, which can give rise to exotic quantum phenomena ranging from correlated insulators and superconductors to moiré excitons and Wigner crystals. Here, we demonstrate the dynamic tuning of moiré potential in a WSe

Nitrogen-vacancy (NV) centers in diamond have shown promise as inherently localized electric-field sensors, capable of detecting individual charges with nanometer resolution. Working with NV ensembles, we demonstrate that a detailed understanding of the internal electric field environment enables enhanced sensitivity in the detection of external electric fields. We follow this logic along two complementary paths. First, using excitation tuned near the NV's zero-phonon line, we perform optically detected magnetic resonance (ODMR) spectroscopy at cryogenic temperatures in order to precisely measure the NV center's excited-state susceptibility to electric fields. In doing so, we demonstrate that the characteristically observed contrast inversion arises from an interplay between spin-selective optical pumping and the NV centers' local charge distribution. Second, motivated by this understanding, we propose and analyze a novel scheme for optically-enhanced electric-field sensing using NV ensembles; we estimate that our approach should enable order of magnitude improvements in the DC electric-field sensitivity., Comment: 6+10 pages, 3+6 figures

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We test this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We find that domain-wall relaxation is indeed governed by the KPZ dynamical exponent $z = 3/2$, and that the occurrence of KPZ scaling requires both integrability and a non-abelian SU(2) symmetry. Finally, we leverage the single-spin-sensitive detection enabled by the quantum-gas microscope to measure a novel observable based on spin-transport statistics, which yields a clear signature of the non-linearity that is a hallmark of KPZ universality., 8 pages, 5 figures + 13 pages Supplementary Information

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In a companion manuscript [2105.10504], we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of $^{40}$K$^{87}$Rb., 6 + 7 pages, 3 figures. See companion manuscript arxiv:2105.10504 for additional numerics and a detailed experimental proposal for realizing the Hopf insulator

We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range spin-orbit coupled hoppings for its realization. While these ingredients have so far precluded its realization in solid state systems and other quantum simulation architectures, in a companion manuscript [1901.08597] we predict that Hopf insulators can in fact arise naturally in dipolar interacting systems. Here, we investigate a specific such architecture in lattices of polar molecules, where the effective `spin' is formed from sublattice degrees of freedom. We introduce two techniques that allow one to optimize dipolar Hopf insulators with large band gaps, and which should also be readily applicable to the simulation of other exotic bandstructures. First, we describe the use of Floquet engineering to control the range and functional form of dipolar hoppings and second, we demonstrate that molecular AC polarizabilities (under circularly polarized light) can be used to precisely tune the resonance condition between different rotational states. To verify that this latter technique is amenable to current generation experiments, we calculate from first principles the AC polarizability for $\sigma^+$ light for ${}^{40}$K$^{87}$Rb. Finally, we show that experiments are capable of detecting the unconventional topology of the Hopf insulator by varying the termination of the lattice at its edges, which gives rise to three distinct classes of edge mode spectra., Comment: 15 pages, 8 figures. See companion manuscript arxiv:1901.08597 for an overview on realizing the Hopf insulator via dipolar interactions

The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power-laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power-law, we demonstrate that long-range interactions give rise to a continuum of non-conformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power-law., 6+10 pages, 3+9 figures

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted in silicon quantum wells due to strain and electronic confinement, but the "valley splitting" of the two lowest lying valleys is known to be sensitive to atomic-scale disorder. Large valley splittings are desirable to have a well-defined spin qubit. In addition, an understanding of the inter-valley tunnel coupling that couples different valleys in adjacent quantum dots is extremely important, as the resulting gaps in the energy level diagram may affect the fidelity of charge and spin transfer protocols in silicon quantum dot arrays. Here we use microwave spectroscopy to probe spatial variations in the valley splitting, and the intra- and inter-valley tunnel couplings ($t_{ij}$ and $t'_{ij}$) that couple dots $i$ and $j$ in a triple quantum dot (TQD). We uncover large spatial variations in the ratio of inter-valley to intra-valley tunnel couplings $t_{12}'/t_{12}=0.90$ and $t_{23}'/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that $t'_{ij}$ scales linearly with $t_{ij}$, as expected from theory. The results indicate strong interactions between different valley states on neighboring dots, which we attribute to local inhomogeneities in the silicon quantum well.

The theory of quantum information provides a common language which links disciplines ranging from cosmology to condensed-matter physics. For example, the delocalization of quantum information in strongly-interacting many-body systems, known as quantum information scrambling, has recently begun to unite our understanding of black hole dynamics, transport in exotic non-Fermi liquids, and many-body analogs of quantum chaos. To date, verified experimental implementations of scrambling have dealt only with systems comprised of two-level qubits. Higher-dimensional quantum systems, however, may exhibit different scrambling modalities and are predicted to saturate conjectured speed limits on the rate of quantum information scrambling. We take the first steps toward accessing such phenomena, by realizing a quantum processor based on superconducting qutrits (three-level quantum systems). We implement two-qutrit scrambling operations and embed them in a five-qutrit teleportation algorithm to directly measure the associated out of-time-ordered correlation functions. Measured teleportation fidelities, Favg = 0.568 +- 0001, confirm the occurrence of scrambling even in the presence of experimental imperfections. Our teleportation algorithm, which connects to recent proposals for studying traversable wormholes in the laboratory, demonstrates how quantum information processing technology based on higher dimensional systems can exploit a larger and more connected state space to achieve the resource efficient encoding of complex quantum circuits.

We analyze a method for preparing low-entropy many-body states in isolated quantum optical systems of atoms, ions and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite temperature, time-dependent matrix product state calculations reveal that even moderately sized "bath" regions can remove enough energy and entropy density to expose coherent low temperature physics. The protocol is particularly natural in systems with long-range interactions such lattice-trapped polar molecules and Rydberg dressed atoms where the magnitude of the Hamiltonian scales directly with the density. To this end, we propose a simple implementation of conformal cooling quenches in a dilutely-filled optical lattice, where signatures of quantum magnetism can be observed., Comment: 10 pages, 9 figures. V2: Modified discussion of experimental implementation and added references

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed., Comment: 8+7 pages and 3+6 figures

A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its 1/T1 relaxation rate due to magnetic noise created by electric current fluctuations in the material. We analyze this technique as a wireless probe of superconductivity in atomically thin two-dimensional materials. At temperatures T≲Tc, the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations. We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature. We show that scaling of the noise with sample-probe distance provides a window into the nonlocal quasistatic conductivity of superconductors, both clean and disordered. At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers. Potential experimental implications are discussed., Physical Review Research, 4 (1), ISSN:2643-1564

We propose nanoscale magnetometry via isolated single-spin qubits as a probe of superconductivity in two-dimensional materials. We characterize the magnetic field noise at the qubit location, arising from current and spin fluctuations in the sample and leading to measurable polarization decay of the qubit. We show that the noise due to transverse current fluctuations studied as a function of temperature and sample-probe distance can be used to extract useful information about the transition to a superconducting phase and the pairing symmetry of the superconductor. Surprisingly, at low temperatures, the dominant contribution to the magnetic noise arises from longitudinal current fluctuations and can be used to probe collective modes such as monolayer plasmons and bilayer Josephson plasmons. We also characterize the noise due to spin fluctuations, which allows probing the spin structure of the pairing wave function. Our results provide a non-invasive route to probe the rich physics of two-dimensional superconductors., Comment: 15 + 14 pages, 7 figures; (v2) Minor edits

Cold atoms in an optical lattice provide an ideal platform for studying Bloch oscillations. Here, we extend Bloch oscillations to two superposed optical lattices that are accelerated away from one another, and for the first time show that these symmetric Bloch oscillations can split, reflect and recombine matter waves coherently. Using the momentum parity-symmetry of the Hamiltonian, we map out the energy band structure of the process and show that superpositions of momentum states are created by adiabatically following the ground state of the Hamiltonian. The relative phase and velocity of the two lattices completely determines the trajectories of different branches of the matter wave. Experimentally, we demonstrate symmetric Bloch oscillations using cold Cesium atoms where we form interferometers with up to $240\hbar k$ momentum splitting, one of the largest coherent momentum splittings achieved to date. This work has applications in macroscopic tests of quantum mechanics, measurements of fundamental constants, and searches for new physics., Comment: 15 pages, 12 figures

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in 1D systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau et al. [Nature Physics 11, 566 (2015)]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first order phase transitions and in symmetry protected topological phases. Our study is motived by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near) degenerate manifolds. The rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines accurate, well-ordered energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG., 8+4 pages, 2+5 figures

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent "classical" properties of a system (e.g. diffusivity, viscosity, compressibility) from a generic microscopic quantum Hamiltonian. Here, we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconventional spin diffusion at nanometer length scales. In particular, the combination of positional disorder and on-site random fields leads to diffusive dynamics that are Fickian yet non-Gaussian. Finally, by tuning the underlying parameters within the spin Hamiltonian via a combination of static and driven fields, we demonstrate direct control over the emergent spin diffusion coefficient. Our work opens the door to investigating hydrodynamics in many-body quantum spin systems., Comment: 25+20+15 pages, 3+15+7 figures

In this work, we prove a new family of Lieb-Robinson bounds for lattice spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power-law greater than $kd$, where $d$ is the dimension of the system. More precisely, we require that the sum of the norm of terms with diameter greater than or equal to $R$, acting on any one site, decays as a power-law $1/R^\alpha$, with $\alpha > d$. These new bounds allow us to prove that, at any fixed time, the spatial decay of quantum information follows arbitrarily closely to $1/r^{\alpha}$. Moreover, we define a new light-cone for power-law interacting quantum systems, which captures the region of the system where changing the Hamiltonian can affect the evolution of a local operator. In short-range interacting systems, this light-cone agrees with the conventional definition. However, in long-range interacting systems, our definition yields a stricter light-cone, which is more relevant in most physical contexts., Comment: 26 pages

We prove the existence of nonequilibrium phases of matter in the prethermal regime of periodically driven, long-range interacting systems, with power-law exponent α>d, where d is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension—a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart. ©2020, DARPA DRINQS program (Grant No. D18AC00033), Gordon and Betty Moore Foundation (Grant no. GBMF4303)

We present a scalable and matrix-free eigensolver for studying two-level quantum spin chain models with nearest-neighbor XX +YY interactions plus Z terms. In particular, we focus on the Heisenberg interaction plus random on-site fields, a model that is commonly used to study the many-body localization (MBL) transition. This type of problem is computationally challenging because the vector space dimension grows exponentially with the physical system size, and the solve must be iterated many times to average over different configurations of the random disorder. For each eigenvalue problem, eigenvalues from different regions of the spectrum and their corresponding eigenvectors need to be computed. Traditionally, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large number of spins L, e.g., one needs thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The new matrix-free approach, proposed in this paper, does not suffer from this memory bottleneck and even allows for simulating spin chains up to L = 24 spins on a single compute node. We discuss the OpenMP and hybrid MPI--OpenMP implementations of matrix-free block matrix-vector operations that are the key components of the new approach. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates in a massively parallel fashion, and analyzing their entanglement entropy to gain insight into the MBL transition.

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N = 60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $\lambda$, across a wide range in temperatures, including in the regime where $\lambda$ approaches the universal bound, $\lambda = 2\pi/\beta$., Comment: 6+15 pages, 3+11 figures. v3 published version, with corrected prefactor in Eq. 1

We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum many-body ground state wavefunction on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$, along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one dimensional spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and non-integrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low depth quantum circuits., Comment: 14 pages, 6 figures

Quantum spin liquids are a new class of magnetic ground state in which spins are quantum mechanically entangled over macroscopic scales. Motivated by recent advances in the control of polar molecules, we show that dipolar interactions between S=1/2 moments stabilize spin liquids on the triangular and kagome lattices. In the latter case, the moments spontaneously break time-reversal, forming a chiral spin liquid with robust edge modes and emergent semions. We propose a simple route toward synthesizing a dipolar Heisenberg antiferromagnet from lattice-trapped polar molecules using only a single pair of rotational states and a constant electric field., 11 pages, 8 figures

We predict the existence of a novel Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf $\mathbb{Z}$ invariant, a linking number characterizing the (non-driven) Hopf topological insulator. The second invariant is an intrinsically Floquet $\mathbb{Z}_2$ invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time-evolution, subject to a process in which defects at different quasienergy exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0- or $\pi$-quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators., Comment: 6 + 9 pages, 3 + 1 figures

The $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry protected topological (SPT) phase hosts a robust boundary qubit at zero temperature. At finite energy density, the SPT phase is destroyed and bulk observables equilibrate in finite time. Nevertheless, we predict parametric regimes in which the boundary qubit survives to arbitrarily high temperature, with an exponentially longer coherence time than that of the thermal bulk degrees of freedom. In a dual picture, the persistence of the qubit stems from the inability of the bulk to absorb the virtual $\mathbb{Z}_2 \times \mathbb{Z}_2$ domain walls emitted by the edge during the relaxation process. We confirm the long coherence time by exact diagonalization and connect it to the presence of a pair of conjugate almost strong zero modes. Our results provide a route to experimentally construct long-lived coherent boundary qubits at infinite temperature in disorder-free systems., 6 pages, 3 figures

The Dicke model—a paradigmatic example of superradiance in quantum optics—describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative nature of these interactions, the system’s dynamics is captured by the behavior of a single mean-field, collective spin. In this mean-field limit, it has recently been shown that the interplay between photon losses and periodic driving of light–matter coupling can lead to time-crystalline-like behavior of the collective spin (Gong et al 2018 Phys. Rev. Lett. 120 040404). In this work, we investigate whether such a Dicke time crystal (TC) is stable to perturbations that explicitly break the mean-field solvability of the conventional Dicke model. In particular, we consider the addition of short-range interactions between the atoms which breaks the collective coupling and leads to complex many-body dynamics. In this context, the interplay between periodic driving, dissipation and interactions yields a rich set of dynamical responses, including long-lived and metastable Dicke-TCs, where losses can cool down the many-body heating resulting from the continuous pump of energy from the periodic drive. Specifically, when the additional short-range interactions are ferromagnetic, we observe time crystalline behavior at non-perturbative values of the coupling strength, suggesting the possible existence of stable dynamical order in a driven-dissipative quantum many-body system. These findings illustrate the rich nature of novel dynamical responses with many-body character in quantum optics platforms.

A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed `density matrix truncation' (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system's dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (un-driven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L = 100), we are able to directly extract the energy diffusion coefficient., 6+21 pages, 4+23 figures

We propose a method to probe and control the interactions between an ensemble of magnetic impurities in a superconductor via microwave radiation. Our method relies upon the presence of sub-gap Yu-Shiba-Rusinov (YSR) states associated with the impurities. Depending on the sign of the detuning, radiation generates either a ferro- or antiferromagnetic contribution to the exchange interaction. This contribution can bias the statistics of the random exchange constants stemming from the RKKY interaction. Moreover, by measuring the microwave response at the YSR resonance, one gains information about the magnetic order of the impurities. To this end, we estimate the absorption coefficient as well as the achievable strength of the microwave-induced YSR-interactions using off-resonant radiation. The ability to utilize microwave fields to both probe and control impurity spins in a superconducting host may open new paths to studying metallic spin glasses., Comment: 11 pages, 3 figures

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including the Su-Schrieffer-Heeger model, $p$-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground state) exhibits a more natural route for direct experimental detection. To this end, we build upon recent work [F. Grusdt, et al., Nat. Commun. 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.

We produce a trimerized kagome lattice for ultracold atoms using an optical superlattice formed by overlaying triangular lattices generated with two colors of light at a 2:1 wavelength ratio. Adjusting the depth of each lattice tunes the strong intratrimer ($J$) and weak intertrimer (${J}^{\ensuremath{'}}$) tunneling energies, and also the on-site interaction energy $U$. Two different trimerization patterns are distinguished using matter-wave diffraction. We characterize the coherence of a strongly interacting Bose gas in this lattice, observing persistent nearest-neighbor spatial coherence in the large $U/{J}^{\ensuremath{'}}$ limit, and that such coherence displays asymmetry between the strongly and the weakly coupled bonds.

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity and gravity. Here, we extend the framework for exploring information scrambling to infinite dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: i) scrambling in the phase space of a single mode and ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct `types' of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out and quasi scrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed., Comment: 31 pages, 19 figures