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.

Eliminating Leakage Errors in Hyperfine Qubits.

Population leakage outside the qubit subspace presents a particularly harmful source of error that cannot be handled by standard error correction methods. Using a trapped ^{171}Yb^{+} ion, we demonstrate an optical pumping scheme to suppress leakage errors in atomic hyperfine qubits. The selection rules and narrow linewidth of a quadrupole transition are used to selectively pump population out of leakage states and back into the qubit subspace. Each pumping cycle reduces the leakage population by a factor of ∼3, allowing for an exponential suppression in the number of cycles. We use interleaved randomized benchmarking on the qubit subspace to show that this pumping procedure has negligible side effects on the qubit subspace, bounding the induced qubit memory error by ≤2.0(8)×10^{-5} per cycle, and qubit population decay to ≤1.4(3)×10^{-7} per cycle. These results clear a major obstacle for implementations of quantum error correction and error mitigation protocols.

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.

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.

Quantum criticality of hot random spin chains.

We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)_{k} anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses." We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit k→∞. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.

Skeletal muscle-specific expression of a utrophin transgene rescues utrophin-dystrophin deficient mice.

Duchenne muscular dystrophy (DMD) is a progressive muscle wasting disease usually resulting in death of patients by their early twenties. In contrast, mice lacking dystrophin (Dmd(mdx)), appear physically normal despite their underlying muscle pathology. Mice deficient for both dystrophin and the dystrophin-related protein, utrophin, (Dmd(mdx);Utrn-/- mice) die between 6 and 20 weeks of age suffering from severe muscle weakness with joint contractures, pronounced growth retardation and kyphosis, suggesting that dystrophin and utrophin play complementary roles. The exact cause of death in these mice was not determined. Here we show that expression of a truncated utrophin transgene solely within the skeletal muscle of these mutants prevents premature death and the development of any clinical phenotype. In the absence of full-length dystrophin and utrophin, the presence of truncated utrophin also decreases muscle fibre regeneration, relocalizes the dystrophin protein complex to the sarcolemma and re-establishes a normal expression pattern of developmental muscle proteins. These data suggest that Dmd(mdx);Utrn-/- mice succumb to a skeletal muscle defect and that their reduced lifespan is not due to cardiac or neurogenic components. The phenotypic rescue observed demonstrates that the Dmd(mdx);Utrn-/- mice are an ideal model for testing gene delivery protocols for the expression of utrophin or dystrophin in skeletal muscle. To determine the cause of death of the Dmd(mdx):Utrn-/- mice.

Postsynaptic abnormalities at the neuromuscular junctions of utrophin-deficient mice.

Utrophin is a dystrophin-related cytoskeletal protein expressed in many tissues. It is thought to link F-actin in the internal cytoskeleton to a transmembrane protein complex similar to the dystrophin protein complex (DPC). At the adult neuromuscular junction (NMJ), utrophin is precisely colocalized with acetylcholine receptors (AChRs) and recent studies have suggested a role for utrophin in AChR cluster formation or maintenance during NMJ differentiation. We have disrupted utrophin expression by gene targeting in the mouse. Such mice have no utrophin detectable by Western blotting or immunocytochemistry. Utrophin-deficient mice are healthy and show no signs of weakness. However, their NMJs have reduced numbers of AChRs (alpha-bungarotoxin [alpha-BgTx] binding reduced to approximately 60% normal) and decreased postsynaptic folding, though only minimal electrophysiological changes. Utrophin is thus not essential for AChR clustering at the NMJ but may act as a component of the postsynaptic cytoskeleton, contributing to the development or maintenance of the postsynaptic folds. Defects of utrophin could underlie some forms of congenital myasthenic syndrome in which a reduction of postsynaptic folds is observed.

Variation of erythroid and myeloid precursors in the marrow and peripheral blood of volunteer subjects infected with human parvovirus (B19).

Infection of normal individuals with human parvovirus (B19) results in a mild disease (erythema infectiosum) but gives rise to aplastic crises in patients with chronic hemolytic anemias. The effects of this disease on hemopoiesis were investigated following intranasal inoculation of the virus into three volunteers. A typical disease ensued with a viremia peaking at 9 d. Marrow morphology 6 d after inoculation appeared normal but at 10 d there was a severe loss of erythroid precursors followed by a 1-2-g drop in hemoglobin, and an increase in serum immunoreactive erythropoietin. Erythroid burst-forming units (BFU-E) from the peripheral blood were considerably reduced, starting at the time of viremia and persisting for 4-8 d depending on the individual. Granulocyte-macrophage colony-forming units (CFU-GM) were also affected but the loss started 2 d later. Both CFU-GM and BFU-E showed a sharp overshoot at recovery. In the marrow, BFU-E and CFU-E were reduced at 6 and 10 d in the individual having the longest period of peripheral progenitor loss. In contrast, there was an increase in BFU-E and CFU-E in the subject with least change in peripheral progenitors. In the third subject, with an intermediate picture, there was a loss at 6 d but an increase at 10 d of erythroid progenitors. It is suggested that the architecture of the marrow might partially isolate progenitors from high titers of virus in the serum and individual variation in this respect might give the results observed.

Erythroid differentiation in CGL cells from a patient with blast crisis.

A 60-year-old patient with Ph1 + ve CGL presented with blast crisis. The leukaemic blast cells resembled erythroblasts and had 51 chromosomes with two Ph1. Cells obtained from peripheral blood, marrow and a pleural effusion were cultured under a variety of conditions. After 2-3 weeks in culture, the model 51-chromosome line persisted but many of the cells displayed erythroid morphology and differentiated to resemble mature normoblasts, strongly positive on o-tolidine +ve staining. Haemoglobin analysis by starch gel and globin synthesis studies demonstrated only fetal haemoglobin (HbF) synthesis in the cultured cells whilst the patient's reticulocytes synthesized very little HbF. Restriction enzyme mapping of DNA from the cultured cells showed that beta-globin genes were still present in these cells even though they were not expressed.

Dystrophin and utrophin do not play crucial roles in nonmuscle tissues in mice.

The loss of full-length dystrophin from skeletal muscle leads to the clinical features of Duchenne muscular dystrophy. Both Dp71, a C-terminal dystrophin isoform, and the dystrophin-related protein, utrophin, are present at high levels in many nonmuscle tissues. To investigate the roles of these proteins in nonmuscle tissues, mice were generated null for utrophin, and deficient in all dystrophin isoforms. These mice reach adulthood and do not appear to have any devastating pathology in nonmuscle tissues.

Dystrophin and utrophin influence fiber type composition and post-synaptic membrane structure.

The X-linked muscle wasting disease Duchenne muscular dystrophy is caused by the lack of dystrophin in muscle. Protein structure predictions, patient mutations, in vitro binding studies and transgenic and knockout mice suggest that dystrophin plays a mechanical role in skeletal muscle, linking the subsarcolemmal cytoskeleton with the extracellular matrix through its direct interaction with the dystrophin-associated protein complex (DAPC). Although a signaling role for dystrophin has been postulated, definitive data have been lacking. To identify potential non-mechanical roles of dystrophin, we tested the ability of various truncated dystrophin transgenes to prevent any of the skeletal muscle abnormalities associated with the double knockout mouse deficient for both dystrophin and the dystrophin-related protein utrophin. We show that restoration of the DAPC with Dp71 does not prevent the structural abnormalities of the post-synaptic membrane or the abnormal oxidative properties of utrophin/dystrophin-deficient muscle. In marked contrast, a dystrophin protein lacking the cysteine-rich domain, which is unable to prevent dystrophy in the mdx mouse, is able to ameliorate these abnormalities in utrophin/dystrophin-deficient mice. These experiments provide the first direct evidence that in addition to a mechanical role and relocalization of the DAPC, dystrophin and utrophin are able to alter both structural and biochemical properties of skeletal muscle. In addition, these mice provide unique insights into skeletal muscle fiber type composition.

Amelioration of the dystrophic phenotype of mdx mice using a truncated utrophin transgene.

Duchenne muscular dystrophy (DMD) is a severe, progressive muscle-wasting disease that causes cardiac or respiratory failure and results in death at about 20 years of age. Replacement of the missing protein, dystrophin, using myoblast transfer in humans or viral/liposomal delivery in the mouse DMD model is inefficient and short-lived. One alternative approach to treatment would be to upregulate the closely related protein, utrophin, which might be able to compensate for the dystrophin deficiency in all relevant muscles. As a first step to this approach, we have expressed a utrophin transgene at high levels in the dystrophin-deficient mdx mouse. Our results indicate that high expression of the utrophin transgene in skeletal and diaphragm muscle can markedly reduce the dystrophic pathology. These data suggest that systemic upregulation of utrophin in DMD patients may lead to the development of an effective treatment for this devastating disorder.

Utrophin-dystrophin-deficient mice as a model for Duchenne muscular dystrophy.

The absence of dystrophin at the muscle membrane leads to Duchenne muscular dystrophy (DMD), a severe muscle-wasting disease that is inevitably fatal in early adulthood. In contrast, dystrophin-deficient mdx mice appear physically normal despite their underlying muscle pathology. We describe mice deficient for both dystrophin and the dystrophin-related protein utrophin. These mice show many signs typical of DMD in humans: they show severe progressive muscular dystrophy that results in premature death, they have ultrastructural neuromuscular and myotendinous junction abnormalities, and they aberrantly coexpress myosin heavy chain isoforms within a fiber. The data suggest that utrophin and dystrophin have complementing roles in normal functional or developmental pathways in muscle. Detailed study of these mice should provide novel insights into the pathogenesis of DMD and provide an improved model for rapid evaluation of gene therapy strategies.