Anderson localization of a non-interacting Bose-Einstein condensate

Anderson localization of waves in disordered media was originally predicted fifty years ago, in the context of transport of electrons in crystals. The phenomenon is much more general and has been observed in a variety of systems, including light waves. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice-a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases.     

Transport and Anderson localization in disordered two-dimensional photonic lattices

One of the most interesting phenomena in solid-state physics is Anderson localization, which predicts that an electron may become immobile when placed in a disordered lattice. The origin of localization is interference between multiple scatterings of the electron by random defects in the potential, altering the eigenmodes from being extended (Bloch waves) to exponentially localized. As a result, the material is transformed from a conductor to an insulator. Anderson's work dates back to 1958, yet strong localization has never been observed in atomic crystals, because localization occurs only if the potential (the periodic lattice and the fluctuations superimposed on it) is time-independent. However, in atomic crystals important deviations from the Anderson model always occur, because of thermally excited phonons and electron-electron interactions. Realizing that Anderson localization is a wave phenomenon relying on interference, these concepts were extended to optics. Indeed, both weak and strong localization effects were experimentally demonstrated, traditionally by studying the transmission properties of randomly distributed optical scatterers (typically suspensions or powders of dielectric materials). However, in these studies the potential was fully random, rather than being 'frozen' fluctuations on a periodic potential, as the Anderson model assumes. Here we report the experimental observation of Anderson localization in a perturbed periodic potential: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice. We demonstrate how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder. Finally, we study how nonlinearities affect Anderson localization. As Anderson localization is a universal phenomenon, the ideas presented here could also be implemented in other systems (for example, matter waves), thereby making it feasible to explore experimentally long-sought fundamental concepts, and bringing up a variety of intriguing questions related to the interplay between disorder and nonlinearity.     

Direct measurement of intra-cochlear pressure waves

The cochlear travelling wave is fundamental to the ability of the mammalian auditory system to resolve frequency. The seashell-shaped outer bone of the cochlea (the auditory inner ear) contains a spiral of cochlear fluid and the sensory tissue known as the cochlear partition. Sound travels down the ear canal to the eardrum, causing its flexible tympanic membrane to vibrate. This vibration is transmitted to the cochlea via the ossides. Motion of the stapes (the stirrup ossicle) sets the cochlear fluid in motion, which in turn sets the cochlear partition near the states in motion. The motion of the cochlear partition ripples down the cochlear spiral as a travelling wave, stimulating the cochlea's sensory hair cells. The wave peaks near the base (the stapes end) of the cochlea for high frequency tones and near the apex for low frequencies. The fundamental elements of the cochlear travelling wave are fluid pressure and motion and partition forces and motion. However, the wave's direct experimental study has to date relied almost solely on measurements of the partition motion. Here I report finely spaced measurements of intracochlear pressure close to the partition, which reveal the fluid component of the cochlear wave. The penetration depth of the wave is very limited, approximately 15 microm. Over a range of frequencies at least an octave wide, the depth is independent of frequency.     

Direct observation of second-order atom tunnelling

Tunnelling of material particles through a classically impenetrable barrier constitutes one of the hallmark effects of quantum physics. When interactions between the particles compete with their mobility through a tunnel junction, intriguing dynamical behaviour can arise because the particles do not tunnel independently. In single-electron or Bloch transistors, for example, the tunnelling of an electron or Cooper pair can be enabled or suppressed by the presence of a second charge carrier due to Coulomb blockade. Here we report direct, time-resolved observations of the correlated tunnelling of two interacting ultracold atoms through a barrier in a double-well potential. For the regime in which the interactions between the atoms are weak and tunnel coupling dominates, individual atoms can tunnel independently, similar to the case of a normal Josephson junction. However, when strong repulsive interactions are present, two atoms located on one side of the barrier cannot separate, but are observed to tunnel together as a pair in a second-order co-tunnelling process. By recording both the atom position and phase coherence over time, we fully characterize the tunnelling process for a single atom as well as the correlated dynamics of a pair of atoms for weak and strong interactions. In addition, we identify a conditional tunnelling regime in which a single atom can only tunnel in the presence of a second particle, acting as a single atom switch. Such second-order tunnelling events, which are the dominating dynamical effect in the strongly interacting regime, have not been previously observed with ultracold atoms. Similar second-order processes form the basis of superexchange interactions between atoms on neighbouring lattice sites of a periodic potential, a central component of proposals for realizing quantum magnetism.     

Direct observation of attosecond light bunching

Temporal probing of a number of fundamental dynamical processes requires intense pulses at femtosecond or even attosecond (1 as = 10(-18) s) timescales. A frequency 'comb' of extreme-ultraviolet odd harmonics can easily be generated in the interaction of subpicosecond laser pulses with rare gases: if the spectral components within this comb possess an appropriate phase relationship to one another, their Fourier synthesis results in an attosecond pulse train. Laser pulses spanning many optical cycles have been used for the production of such light bunching, but in the limit of few-cycle pulses the same process produces isolated attosecond bursts. If these bursts are intense enough to induce a nonlinear process in a target system, they can be used for subfemtosecond pump-probe studies of ultrafast processes. To date, all methods for the quantitative investigation of attosecond light localization and ultrafast dynamics rely on modelling of the cross-correlation process between the extreme-ultraviolet pulses and the fundamental laser field used in their generation. Here we report the direct determination of the temporal characteristics of pulses in the subfemtosecond regime, by measuring the second-order autocorrelation trace of a train of attosecond pulses. The method exhibits distinct capabilities for the characterization and utilization of attosecond pulses for a host of applications in attoscience.     

Direct observation of microtubule dynamics in living cells

The study of cell locomotion is fundamental to such diverse processes as embryonic development, wound healing and metastasis. Since microtubules play a role in establishing the leading lamellum and maintaining cell polarity, it is important to understand their dynamic behaviour. In vitro, subunits exchange with polymer by treadmilling and by dynamic instability. Disassembly events can be complete (catastrophic) or incomplete (tempered). In vivo, microtubules are in dynamic equilibrium with subunits with a half-time for turnover of 4-20 min. Microtubules grow by elongation of their ends and are replaced one by one with turnover being most rapid at the periphery. Although previous results are consistent with dynamic instability, we sought to directly test the mechanism of turnover. Direct observations of fluorescent microtubules in the fibroblast lamellum show that individual microtubules undergo rounds of assembly and disassembly from the same end. Reorganization of the microtubule network occurs by a tempered mode of dynamic instability.     

Decoherence of matter waves by thermal emission of radiation

Emergent quantum technologies have led to increasing interest in decoherence--the processes that limit the appearance of quantum effects and turn them into classical phenomena. One important cause of decoherence is the interaction of a quantum system with its environment, which 'entangles' the two and distributes the quantum coherence over so many degrees of freedom as to render it unobservable. Decoherence theory has been complemented by experiments using matter waves coupled to external photons or molecules, and by investigations using coherent photon states, trapped ions and electron interferometers. Large molecules are particularly suitable for the investigation of the quantum-classical transition because they can store much energy in numerous internal degrees of freedom; the internal energy can be converted into thermal radiation and thus induce decoherence. Here we report matter wave interferometer experiments in which C70 molecules lose their quantum behaviour by thermal emission of radiation. We find good quantitative agreement between our experimental observations and microscopic decoherence theory. Decoherence by emission of thermal radiation is a general mechanism that should be relevant to all macroscopic bodies.     

Direct Urca processes involving hyperons in neutron star matter

The presence of the isovector scalar interaction in neutron star matter is considered by exchangingδmeson;we study the effects ofδmesons on the direct Urca processes involving hyperons.The calculation is based on the framework of the relativistic mean field theory.By our analysis,the hyperon direct Urca processes under beta equilibrium are open at lower densities due toδmesons,which create a larger energy gap between two baryons in the reactions.Theδmeson leads to an obvious enhancement of the neutrino emissivity for the hyperon direct Urca processes.In particular,the relativistic neutrino emissivity is found to be substantially larger than predicted in the nonrelativistic approach whetherδmesons appear in an neutron star or not.In our results,δmesons not only change the baryons properties,but also result in more rapid cooling rate of neutron stars by hyperon direct Urca processes.     

Direct observation of a submarine volcanic eruption from a sea-floor instrument caught in a lava flow

Our understanding of submarine volcanic eruptions has improved substantially in the past decade owing to the recent ability to remotely detect such events and to then respond rapidly with synoptic surveys and sampling at the eruption site. But these data are necessarily limited to observations after the event. In contrast, the 1998 eruption of Axial volcano on the Juan de Fuca ridge was monitored by in situ sea-floor instruments. One of these instruments, which measured bottom pressure as a proxy for vertical deformation of the sea floor, was overrun and entrapped by the 1998 lava flow. The instrument survived-being insulated from the molten lava by the solidified crust-and was later recovered. The data serendipitously recorded by this instrument reveal the duration, character and effusion rate of a sheet flow eruption on a mid-ocean ridge, and document over three metres of lava-flow inflation and subsequent drain-back. After the brief two-hour eruption, the instrument also measured gradual subsidence of 1.4 metres over the next several days, reflecting deflation of the entire volcano summit as magma moved into the adjacent rift zone. These findings are consistent with our understanding of submarine lava effusion, as previously inferred from seafloor observations, terrestrial analogues, and laboratory simulations.     

Direct observation of electron dynamics in the attosecond domain

Dynamical processes are commonly investigated using laser pump-probe experiments, with a pump pulse exciting the system of interest and a second probe pulse tracking its temporal evolution as a function of the delay between the pulses. Because the time resolution attainable in such experiments depends on the temporal definition of the laser pulses, pulse compression to 200 attoseconds (1 as = 10(-18) s) is a promising recent development. These ultrafast pulses have been fully characterized, and used to directly measure light waves and electronic relaxation in free atoms. But attosecond pulses can only be realized in the extreme ultraviolet and X-ray regime; in contrast, the optical laser pulses typically used for experiments on complex systems last several femtoseconds (1 fs = 10(-15) s). Here we monitor the dynamics of ultrafast electron transfer--a process important in photo- and electrochemistry and used in solid-state solar cells, molecular electronics and single-electron devices--on attosecond timescales using core-hole spectroscopy. We push the method, which uses the lifetime of a core electron hole as an internal reference clock for following dynamic processes, into the attosecond regime by focusing on short-lived holes with initial and final states in the same electronic shell. This allows us to show that electron transfer from an adsorbed sulphur atom to a ruthenium surface proceeds in about 320 as.     

Direct observation of catch bonds involving cell-adhesion molecules

Bonds between adhesion molecules are often mechanically stressed. A striking example is the tensile force applied to selectin-ligand bonds, which mediate the tethering and rolling of flowing leukocytes on vascular surfaces. It has been suggested that force could either shorten bond lifetimes, because work done by the force could lower the energy barrier between the bound and free states ('slip'), or prolong bond lifetimes by deforming the molecules such that they lock more tightly ('catch'). Whereas slip bonds have been widely observed, catch bonds have not been demonstrated experimentally. Here, using atomic force microscopy and flow-chamber experiments, we show that increasing force first prolonged and then shortened the lifetimes of P-selectin complexes with P-selectin glycoprotein ligand-1, revealing both catch and slip bond behaviour. Transitions between catch and slip bonds might explain why leukocyte rolling on selectins first increases and then decreases as wall shear stress increases. This dual response to force provides a mechanism for regulating cell adhesion under conditions of variable mechanical stress.     

Direct observation of ligand recognition by T cells

The activation of T cells through interaction of their T-cell receptors with antigenic peptide bound to major histocompatibility complex (MHC) on the surface of antigen presenting cells (APCs) is a crucial step in adaptive immunity. Here we use three-dimensional fluorescence microscopy to visualize individual peptide-I-E(k) class II MHC complexes labelled with the phycobiliprotein phycoerythrin in an effort to characterize T-cell sensitivity and the requirements for forming an immunological synapse in single cells. We show that T cells expressing the CD4 antigen respond with transient calcium signalling to even a single agonist peptide-MHC ligand, and that the organization of molecules in the contact zone of the T cell and APC takes on the characteristics of an immunological synapse when only about ten agonists are present. This sensitivity is highly dependent on CD4, because blocking this molecule with antibodies renders T cells unable to detect less than about 30 ligands.     

Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions

Quantum theory predicts that Bose-Einstein condensation of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form, provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between the self-attractive forces and a repulsion that arises from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate is therefore punctuated by intermittent collapses that are triggered by either macroscopic quantum tunnelling or thermal fluctuation. Previous observations of growth and collapse dynamics have been hampered by the stochastic nature of these mechanisms. Here we report direct observations of the growth and subsequent collapse of a 7Li condensate with attractive interactions, using phase-contrast imaging. The success of the measurement lies in our ability to reduce the stochasticity in the dynamics by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state.     

Direct observation of steps in rotation of the bacterial flagellar motor

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H+-driven and Na+-driven motors, respectively. Here we demonstrate a stepping motion of a Na+-driven chimaeric flagellar motor in Escherichia coli at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.     

Direct observation of monomer film structure of bacteriochlorophyll c

The adsorption and assembling of bacteriochlorophyll c (BChl c) on a highly oriented pyrolytic graphite (HOPG) surface have been investigated by the scanning tunneling microscopy (STM). BChl c molecules are found to self-organize a well-defined adlayer on HOPG surface with a monomeric structure different from the dimer association seen on adlayers of Chls a, c and BChlide c, d. A structural model is proposed for the adlayer.     

Direct observation of Tomonaga-Luttinger-liquid state in carbon nanotubes at low temperatures

The electronic transport properties of conventional three-dimensional metals are successfully described by Fermi-liquid theory. But when the dimensionality of such a system is reduced to one, the Fermi-liquid state becomes unstable to Coulomb interactions, and the conduction electrons should instead behave according to Tomonaga-Luttinger-liquid (TLL) theory. Such a state reveals itself through interaction-dependent anomalous exponents in the correlation functions, density of states and momentum distribution of the electrons. Metallic single-walled carbon nanotubes (SWNTs) are considered to be ideal one-dimensional systems for realizing TLL states. Indeed, the results of transport measurements on metal-SWNT and SWNT-SWNT junctions have been attributed to the effects of tunnelling into or between TLLs, although there remains some ambiguity in these interpretations. Direct observations of the electronic states in SWNTs are therefore needed to resolve these uncertainties. Here we report angle-integrated photoemission measurements of SWNTs. Our results reveal an oscillation in the pi-electron density of states owing to one-dimensional van Hove singularities, confirming the one-dimensional nature of the valence band. The spectral function and intensities at the Fermi level both exhibit power-law behaviour (with almost identical exponents) in good agreement with theoretical predictions for the TLL state in SWNTs.     

Direct observation of molecular cooperativity near the glass transition

The increasingly sluggish response of a supercooled liquid as it nears its glass transition (for example, refrigerated honey) is prototypical of glassy dynamics found in proteins, neural networks and superconductors. The notion that molecules rearrange cooperatively has long been postulated to explain diverging relaxation times and broadened (non-exponential) response functions near the glass transition. Recently, cooperativity was observed and analysed in colloid glasses and in simulations of binary liquids well above the glass transition. But nanometre-scale studies of cooperativity at the molecular glass transition are lacking. Important issues to be resolved include the precise form of the cooperativity and its length scale, and whether the broadened response is intrinsic to individual cooperative regions, or arises only from heterogeneity in an ensemble of such regions. Here we describe direct observations of molecular cooperativity near the glass transition in polyvinylacetate (PVAc), using nanometre-scale probing of dielectric fluctuations. Molecular clusters switched spontaneously among two to four distinct configurations, producing random telegraph noise. Our analysis of these noise signals and their power spectra reveals that individual clusters exhibit transient dynamical heterogeneity and non-exponential kinetics.