Deconfined quantum critical points

The theory of second-order phase transitions is one of the foundations of modern statistical mechanics and condensed-matter theory. A central concept is the observable order parameter, whose nonzero average value characterizes one or more phases. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. We show that near second-order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm, and we present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional "confining" order parameters. Nevertheless, the critical theory contains an emergent gauge field and "deconfined" degrees of freedom associated with fractionalization of the order parameters. We propose that this paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems and offer a new perspective on the properties of complex materials.     

Quantum criticality: competing ground states in low dimensions

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial emergent excitations that control the physics over a significant portion of the phase diagram. Nonzero temperature dynamic properties near quantum critical points are described, using simple theoretical models. Possible quantum phases and transitions in the two-dimensional electron gas on a square lattice are discussed.     

Evidence of soft-mode quantum phase transitions in electron double layers

Inelastic light scattering by low-energy spin-excitations reveals three distinct configurations of spin of electron double layers in gallium arsenide quantum wells at even-integer quantum Hall states. The transformations among these spin states appear as quantum phase transitions driven by the interplay between Coulomb interactions and Zeeman splittings. One of the transformations correlates with the emergence of a spin-flip intersubband excitation at vanishingly low energy and provides direct evidence of a link between quantum phase transitions and soft collective excitations in a two-dimensional electron system.     

Squeezed states in a Bose-Einstein condensate

We report manipulation of the atom number statistics associated with Bose-Einstein condensed atoms confined in an array of weakly linked mesoscopic traps. We used the interference of atoms released from the traps as a sensitive probe of these statistics. By controlling relative strengths of the tunneling rate between traps and atom-atom interactions within each trap, we observed trap states characterized by sub-Poissonian number fluctuations and adiabatic transitions between these number-squeezed states and coherent states of the atom field. The quantum states produced in this work may enable substantial gains in sensitivity for atom interference-based instruments as well as fundamental studies of quantum phase transitions.     

Dimensionality control of electronic phase transitions in nickel-oxide superlattices

The competition between collective quantum phases in materials with strongly correlated electrons depends sensitively on the dimensionality of the electron system, which is difficult to control by standard solid-state chemistry. We have fabricated superlattices of the paramagnetic metal lanthanum nickelate (LaNiO(3)) and the wide-gap insulator lanthanum aluminate (LaAlO(3)) with atomically precise layer sequences. We used optical ellipsometry and low-energy muon spin rotation to show that superlattices with LaNiO(3) as thin as two unit cells undergo a sequence of collective metal-insulator and antiferromagnetic transitions as a function of decreasing temperature, whereas samples with thicker LaNiO(3) layers remain metallic and paramagnetic at all temperatures. Metal-oxide superlattices thus allow control of the dimensionality and collective phase behavior of correlated-electron systems.     

Mach-Zehnder interferometry in a strongly driven superconducting qubit

We demonstrate Mach-Zehnder-type interferometry in a superconducting flux qubit. The qubit is a tunable artificial atom, the ground and excited states of which exhibit an avoided crossing. Strongly driving the qubit with harmonic excitation sweeps it through the avoided crossing two times per period. Because the induced Landau-Zener transitions act as coherent beamsplitters, the accumulated phase between transitions, which varies with microwave amplitude, results in quantum interference fringes for n = 1 to 20 photon transitions. The generalization of optical Mach-Zehnder interferometry, performed in qubit phase space, provides an alternative means to manipulate and characterize the qubit in the strongly driven regime.     

Bistability in atomic-scale antiferromagnets

Control of magnetism on the atomic scale is becoming essential as data storage devices are miniaturized. We show that antiferromagnetic nanostructures, composed of just a few Fe atoms on a surface, exhibit two magnetic states, the Néel states, that are stable for hours at low temperature. For the smallest structures, we observed transitions between Néel states due to quantum tunneling of magnetization. We sensed the magnetic states of the designed structures using spin-polarized tunneling and switched between them electrically with nanosecond speed. Tailoring the properties of neighboring antiferromagnetic nanostructures enables a low-temperature demonstration of dense nonvolatile storage of information.     

Spontaneous emission spectrum in double quantum dot devices

A double quantum dot device is a tunable two-level system for electronic energy states. A dc electron current was used to directly measure the rates for elastic and inelastic transitions between the two levels. For inelastic transitions, energy is exchanged with bosonic degrees of freedom in the environment. The inelastic transition rates are well described by the Einstein coefficients, relating absorption with stimulated and spontaneous emission. The most effectively coupled bosons in the specific environment of the semiconductor device used here were acoustic phonons. The experiments demonstrate the importance of vacuum fluctuations in the environment for quantum dot devices and potential design constraints for their use for preparing long-lived quantum states.     

Phase diagram of degenerate exciton systems

Degenerate exciton systems have been produced in quasi-two-dimensional confined areas in semiconductor coupled quantum well structures. We observed contractions of clouds containing tens of thousands of excitons within areas as small as (10 micron)2 near 10 kelvin. The spatial and energy distributions of optically active excitons were determined by measuring photoluminescence as a function of temperature and laser excitation and were used as thermodynamic quantities to construct the phase diagram of the exciton system, which demonstrates the existence of distinct phases. Understanding the formation mechanisms of these degenerate exciton systems can open new opportunities for the realization of Bose-Einstein condensation in the solid state.     

Implementing the quantum von Neumann architecture with superconducting circuits

The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory integrated on a chip, with instructions stored on a classical computer. We test our quantum machine by executing codes that involve seven quantum elements: Two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. Two vital algorithms for quantum computing are demonstrated, the quantum Fourier transform, with 66% process fidelity, and the three-qubit Toffoli-class OR phase gate, with 98% phase fidelity. Our results, in combination especially with longer qubit coherence, illustrate a potentially viable approach to factoring numbers and implementing simple quantum error correction codes.     

Size Dependence of Structural Metastability in Semiconductor Nanocrystals

The kinetics of a first-order, solid-solid phase transition were investigated in the prototypical nanocrystal system CdSe as a function of crystallite size. In contrast to extended solids, nanocrystals convert from one structure to another by single nucleation events, and the transformations obey simple unimolecular kinetics. Barrier heights were observed to increase with increasing nanocrystal size, although they also depend on the nature of the nanocrystal surface. These results are analogous to magnetic phase transitions in nanocrystals and suggest general rules that may be of use in the discovery of new metastable phases.     

Dipolar antiferromagnetism and quantum criticality in LiErF₄

Magnetism has been predicted to occur in systems in which dipolar interactions dominate exchange. We present neutron scattering, specific heat, and magnetic susceptibility data for LiErF(4), establishing it as a model dipolar-coupled antiferromagnet with planar spin-anisotropy and a quantum phase transition in applied field H(c|| = 4.0 ± 0.1 kilo-oersteds. We discovered non-mean-field critical scaling for the classical phase transition at the antiferromagnetic transition temperature that is consistent with the two-dimensional XY/h(4) universality class; in accord with this, the quantum phase transition at H(c) exhibits three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic frustrated nature of the dipolar interaction, which strengthens the role of fluctuations.     

Non-Fermi liquid metal without quantum criticality

A key question in condensed matter physics concerns whether pure three-dimensional metals can always be described as Fermi liquids. Using neutron Larmor diffraction to overcome the traditional resolution limit of diffraction experiments, we studied the lattice constants of the cubic itinerant-electron magnet manganese silicide (MnSi) at low temperatures and high pressures. We were able to resolve the nature of the phase diagram of MnSi and to establish that a stable, extended non-Fermi liquid state emerges under applied pressure without quantum criticality. This suggests that new forms of quantum order may be expected even far from quantum phase transitions.     

Grain size--dependent alteration and the magnetization of oceanic basalts

Unblocking temperatures of natural remanent magnetization were found to extend well above the dominant Curie points in samples of oceanic basalts from the axis of the East Pacific Rise. This phenomenon is attributed to the natural presence in the basalts of three related magnetic phases: an abundant fine-grained and preferentially oxidized titanomagnetite that carries most of the natural remanent magnetism, a few coarser and less oxidized grains of titanomagnetite that account for most of the high-field magnetic properties, and a small contribution to both the natural remanent magnetism and high-field magnetic properties from magnetite that may be due to the disproportionation of the oxidized titanomagnetite under sea-floor conditions. This model is consistent with evidence from the Central Anomaly magnetic high that the original magnetization acquired by oceanic basalts upon cooling is rapidly altered and accounts for the lack of sensitivity of bulk rock magnetic parameters to the degree of alteration of the remanence carrier in oceanic basalts.     

Theory of quantum annealing of an Ising spin glass

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power that makes it faster.     

Heralded entanglement between widely separated atoms

Entanglement is the essential feature of quantum mechanics. Notably, observers of two or more entangled particles will find correlations in their measurement results that cannot be explained by classical statistics. To make it a useful resource, particularly for scalable long-distance quantum communication, the heralded generation of entanglement between distant massive quantum systems is necessary. We report on the creation and analysis of heralded entanglement between spins of two single rubidium-87 atoms trapped independently 20 meters apart. Our results illustrate the viability of an integral resource for quantum information science, as well as for fundamental tests of quantum mechanics.     

Phase transitions of Dirac electrons in bismuth

The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy.     

Disorder-sensitive phase formation linked to metamagnetic quantum criticality

Condensed systems of strongly interacting electrons are ideal for the study of quantum complexity. It has become possible to promote the formation of new quantum phases by explicitly tuning systems toward special low-temperature quantum critical points. So far, the clearest examples have been appearances of superconductivity near pressure-tuned antiferromagnetic quantum critical points. We present experimental evidence for the formation of a nonsuperconducting phase in the vicinity of a magnetic field-tuned quantum critical point in ultrapure crystals of the ruthenate metal Sr3Ru2O7, and we discuss the possibility that the observed phase is due to a spin-dependent symmetry-breaking Fermi surface distortion.     

Mesoscopic phase coherence in a quantum spin fluid

Mesoscopic quantum phase coherence is important because it improves the prospects for handling quantum degrees of freedom in technology. Here we show that the development of such coherence can be monitored using magnetic neutron scattering from a one-dimensional spin chain of an oxide of nickel (Y2BaNiO5), a quantum spin fluid in which no classical static magnetic order is present. In the cleanest samples, the quantum coherence length is 20 nanometers, which is almost an order of magnitude larger than the classical antiferromagnetic correlation length of 3 nanometers. We also demonstrate that the coherence length can be modified by static and thermally activated defects in a quantitatively predictable manner.