Imaging the Meissner effect in hydride superconductors using quantum sensors.

By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena1. The megabar regime represents an interesting frontier, in which recent discoveries include high-temperature superconductors, as well as structural and valence phase transitions2-6. However, at such high pressures, many conventional measurement techniques fail. Here we demonstrate the ability to perform local magnetometry inside a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach uses a shallow layer of nitrogen-vacancy colour centres implanted directly within the anvil7-9; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the nitrogen-vacancy centre to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH9 (ref. 10). By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping both the diamagnetic response and flux trapping, we directly image the geometry of superconducting regions, showing marked inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed-loop optimization of superhydride materials synthesis.

Emergent hydrodynamics in a strongly interacting dipolar spin ensemble.

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws1-7. 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 (for example, diffusivity, viscosity and compressibility) from a generic microscopic quantum Hamiltonian7-14. 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 nanometre length scales. In particular, the combination of positional disorder and on-site random fields leads to diffusive dynamics that are Fickian yet non-Gaussian15-20. 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 enables the investigation of hydrodynamics in many-body quantum spin systems.

Universal Entanglement of Typical States in Constrained Systems.

Constraints play an important role in the entanglement dynamics of many quantum systems. We develop a diagrammatic formalism to exactly evaluate the entanglement spectrum of random pure states in large constrained Hilbert spaces. The resulting spectra may be classified into universal "phases" depending on their singularities. The simplest class of local constraints reveals a nontrivial phase diagram with a Marchenko-Pastur phase which terminates in a critical point with new singularities. We propose a certain quantum defect chain as a microscopic realization of the critical point. The much studied Rydberg-blockaded or Fibonacci chain lies in the Marchenko-Pastur phase with a modified Page correction to the entanglement entropy. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained Floquet spin chains, as we confirm numerically.

Quasiperiodic Quantum Ising Transitions in 1D.

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν=1^{+} (exact) and z≈1.9, Δ_{σ}≈0.16, and Δ_{γ}≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.

Thermal inclusions: how one spin can destroy a many-body localized phase.

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N≫1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale Jc(N)∼1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either 'on' (strongly entangled) or 'off' (weakly entangled) in eigenstates. The clusters of 'on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Clustering of Nonergodic Eigenstates in Quantum Spin Glasses.

The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p-spin models of the spin-glass theory, eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.

Quasi-Many-Body Localization in Translation-Invariant Systems.

We examine localization phenomena associated with generic, high entropy, states of a translation-invariant, one-dimensional spin ladder. At early times, we find slow growth of entanglement entropy consistent with the known phenomenology of many-body localization in disordered, interacting systems. At intermediate times, however, anomalous diffusion sets in, leading to full spin polarization decay on an exponentially activated time scale. We identify a single length scale which parametrically controls both the spin transport times and the apparent divergence of the susceptibility to spin glass ordering. Ultimately, at the latest times, the exponentially slow anomalous diffusion gives way to diffusive thermal behavior. We dub the intermediate dynamical behavior, which persists over many orders of magnitude in time, quasi-many-body localization.

Continuous Preparation of a Fractional Chern Insulator.

We present evidence of a direct, continuous quantum phase transition between a Bose superfluid and the ν=1/2 fractional Chern insulator in a microscopic lattice model. In the process, we develop a detailed field theoretic description of this transition in terms of the low energy vortex dynamics. The theory explicitly accounts for the structure of lattice symmetries and predicts a Landau forbidden transition that is protected by inversion. That the transition is continuous enables the quasiadiabatic preparation of the fractional Chern insulator in nonequilibrium, quantum optical systems.

Many-body localization in dipolar systems.

Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities.

Many-body mobility edge in a mean-field quantum spin glass.

The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

Interferometric probes of many-body localization.

We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems.

Realizing fractional Chern insulators in dipolar spin systems.

Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν = 1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultracold polar molecules trapped in a deep optical lattice. With the motion of the molecules pinned, under certain conditions, these rotational excitations form a fractional Chern insulating state. We present a detailed experimental blueprint for its realization and demonstrate that the implementation is consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications.

Topologically protected quantum state transfer in a chiral spin liquid.

Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the current-carrying edge states associated with the quantum Hall and the quantum spin Hall effects to topologically protected quantum memory and quantum logic operations. Here we propose and analyse a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed.

Detecting non-Abelian anyons by charging spectroscopy.

Observation of non-Abelian statistics for the e/4 quasiparticles in the ν = 5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localized quasiparticles, and, hence, an additional low temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, V(G), provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the V(G)-T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.

Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions.

Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first-order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.

Topological flat bands from dipolar spin systems.

We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S=1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hard-core bosons, namely, the dressed spin flips. These gauge fields result in topological band structures, whose band gap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultracold polar molecules or spins in the solid state is considered.