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.

Verified quantum information scrambling.

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout an entire system. This concept accompanies the dynamics of thermalization in closed quantum systems, and has recently emerged as a powerful tool for characterizing chaos in black holes1-4. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, because scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process5,6. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous test for whether scrambling has occurred, while simultaneously measuring an OTOC. We engineer quantum scrambling processes through a tunable three-qubit unitary operation as part of a seven-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically about 80 per cent, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

Observation of a discrete time crystal.

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a 'time crystal' was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a 'discrete time crystal'. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Nanometre-scale thermometry in a living cell.

Sensitive probing of temperature variations on nanometre scales is an outstanding challenge in many areas of modern science and technology. In particular, a thermometer capable of subdegree temperature resolution over a large range of temperatures as well as integration within a living system could provide a powerful new tool in many areas of biological, physical and chemical research. Possibilities range from the temperature-induced control of gene expression and tumour metabolism to the cell-selective treatment of disease and the study of heat dissipation in integrated circuits. By combining local light-induced heat sources with sensitive nanoscale thermometry, it may also be possible to engineer biological processes at the subcellular level. Here we demonstrate a new approach to nanoscale thermometry that uses coherent manipulation of the electronic spin associated with nitrogen-vacancy colour centres in diamond. Our technique makes it possible to detect temperature variations as small as 1.8 mK (a sensitivity of 9 mK Hz(-1/2)) in an ultrapure bulk diamond sample. Using nitrogen-vacancy centres in diamond nanocrystals (nanodiamonds), we directly measure the local thermal environment on length scales as short as 200 nanometres. Finally, by introducing both nanodiamonds and gold nanoparticles into a single human embryonic fibroblast, we demonstrate temperature-gradient control and mapping at the subcellular level, enabling unique potential applications in life sciences.

Critical Thermalization of a Disordered Dipolar Spin System in Diamond.

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

Imaging the Local Charge Environment of Nitrogen-Vacancy Centers in Diamond.

Characterizing the local internal environment surrounding solid-state spin defects is crucial to harnessing them as nanoscale sensors of external fields. This is especially germane to the case of defect ensembles which can exhibit a complex interplay between interactions, internal fields, and lattice strain. Working with the nitrogen-vacancy (NV) center in diamond, we demonstrate that local electric fields dominate the magnetic resonance behavior of NV ensembles at a low magnetic field. We introduce a simple microscopic model that quantitatively captures the observed spectra for samples with NV concentrations spanning more than two orders of magnitude. Motivated by this understanding, we propose and implement a novel method for the nanoscale localization of individual charges within the diamond lattice; our approach relies upon the fact that the charge induces a NV dark state which depends on the electric field orientation.

Erratum: Discrete Time Crystals: Rigidity, Criticality, and Realizations [Phys. Rev. Lett. 118, 030401 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.030401.

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks.

The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase, we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems.

We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.

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.

Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers.

We report direct measurement of population dynamics in the excited state manifold of a nitrogen-vacancy (NV) center in diamond. We quantify the phonon-induced mixing rate and demonstrate that it can be completely suppressed at low temperatures. Further, we measure the intersystem crossing (ISC) rate for different excited states and develop a theoretical model that unifies the phonon-induced mixing and ISC mechanisms. We find that our model is in excellent agreement with experiment and that it can be used to predict unknown elements of the NV center's electronic structure. We discuss the model's implications for enhancing the NV center's performance as a room-temperature sensor.

Enhanced antiferromagnetic exchange between magnetic impurities in a superconducting host.

It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than the superconducting coherence length (r ≲ ξ), this exchange is thought to be dominated by Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, identical to the those in a normal metallic host. This perception is based on a perturbative treatment of the exchange interaction. Here, we provide a nonperturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong 1/r(2) antiferromagnetic interaction that can dominate over conventional RKKY even at distances significantly smaller than the coherence length (r ≪ ξ). Experimental signatures, implications, and applications are discussed.

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.

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.

Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing.

We propose and analyze a novel mechanism for long-range spin-spin interactions in diamond nanostructures. The interactions between electronic spins, associated with nitrogen-vacancy centers in diamond, are mediated by their coupling via strain to the vibrational mode of a diamond mechanical nanoresonator. This coupling results in phonon-mediated effective spin-spin interactions that can be used to generate squeezed states of a spin ensemble. We show that spin dephasing and relaxation can be largely suppressed, allowing for substantial spin squeezing under realistic experimental conditions. Our approach has implications for spin-ensemble magnetometry, as well as phonon-mediated quantum information processing with spin qubits.

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.

Probing many-body dynamics in a two-dimensional dipolar spin ensemble.

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.