The 'Higgs' amplitude mode at the two-dimensional superfluid/Mott insulator transition

Spontaneous symmetry breaking plays a key role in our understanding of nature. In relativistic quantum field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitation: massless Nambu-Goldstone modes and a massive 'Higgs' amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particle physics, and also appears as a fundamental collective mode in quantum many-body systems. Whether such a mode exists in low-dimensional systems as a resonance-like feature, or whether it becomes overdamped through coupling to Nambu-Goldstone modes, has been a subject of debate. Here we experimentally find and study a Higgs mode in a two-dimensional neutral superfluid close to a quantum phase transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected reduction in frequency of the onset of spectral response when approaching the transition point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum field, which constitutes a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations that also addresses the consequences of the reduced dimensionality and confinement of the system. Our work constitutes a step towards exploring emergent relativistic models with ultracold atomic gases.     

Creation of ultracold molecules from a Fermi gas of atoms

Following the realization of Bose-Einstein condensates in atomic gases, an experimental challenge is the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation or a magnetic field Feshbach resonance. The availability of atomic Fermi gases offers the prospect of coupling fermionic atoms to bosonic molecules, thus altering the quantum statistics of the system. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of ultracold 40K2 molecules. Starting with a quantum degenerate Fermi gas of atoms at a temperature of less than 150 nK, we scan the system over a Feshbach resonance to create adiabatically more than 250,000 trapped molecules; these can be converted back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning the magnetic field away from the Feshbach resonance, and can be varied over a wide range. We directly detect these weakly bound molecules through their radio-frequency photodissociation spectra; these probe the molecular wavefunction, and yield binding energies that are consistent with theory.     

A Mott insulator of fermionic atoms in an optical lattice

Strong interactions between electrons in a solid material can lead to surprising properties. A prime example is the Mott insulator, in which suppression of conductivity occurs as a result of interactions rather than a filled Bloch band. Proximity to the Mott insulating phase in fermionic systems is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. The Hubbard model, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice. It is therefore now possible to access this regime with tools developed in atomic physics. However, an atomic Mott insulator has so far been realized only with a gas of bosons, which lack the rich and peculiar nature of fermions. Here we report the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is identified by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to an increase in atom number, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating regime and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin-ordering and ultimately the question of d-wave superfluidity.     

Tonks-Girardeau gas of ultracold atoms in an optical lattice

Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks-Girardeau gas, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution. Here we report the preparation of a Tonks-Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks-Girardeau regime by increasing the atoms' effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.     

Quantum coherence and entanglement with ultracold atoms in optical lattices

At nanokelvin temperatures, ultracold quantum gases can be stored in optical lattices, which are arrays of microscopic trapping potentials formed by laser light. Such large arrays of atoms provide opportunities for investigating quantum coherence and generating large-scale entanglement, ultimately leading to quantum information processing in these artificial crystal structures. These arrays can also function as versatile model systems for the study of strongly interacting many-body systems on a lattice.     

光晶格中自旋3/2超冷费米原子的Mott绝缘态及其量子相变

我们首先简要介绍了超冷原子和光晶格,然后利用推广的单带Hubbard模型讨论了二维正方光晶格中自旋3/2费米型超冷原子体系中的几种Mott绝缘态,其中该系统的自旋自由度具有较大SO(5)对称性.对于对称性破缺的自旋四极矩有序态和自旋偶极-八极矩共存有序态,我们详细研究了系统的低能集体激发模式-Goldstone玻色激发的具体行为.在SU(4)对称点附近,我们发现强烈的量子涨落可能会演生出一个SU(4)π通量的自旋液体态.对此,我们还分析了这两种奇异量子态之间可能存在的量子相变.     

A superconductor to superfluid phase transition in liquid metallic hydrogen

Although hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical properties, including spatial order. To date, the structure of dense hydrogen remains experimentally elusive. Recent studies of the melting curve of hydrogen indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report a topological analysis of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a superconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids.     

Evidence for Efimov quantum states in an ultracold gas of caesium atoms

Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.     

Quantum phase transition in a single-molecule quantum dot

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.     

Quantum phase transition in a resonant level coupled to interacting leads

A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.     

Quantum metallicity in a two-dimensional insulator

One of the most far-reaching problems in condensed-matter physics is to understand how interactions between electrons, and the resulting correlations, affect the electronic properties of disordered two-dimensional systems. Extensive experimental and theoretical studies have shown that interaction effects are enhanced by disorder, and that this generally results in a depletion of the density of electronic states. In the limit of strong disorder, this depletion takes the form of a complete gap in the density of states. It is known that this 'Coulomb gap' can turn a pure metal film that is highly disordered into a poorly conducting insulator, but the properties of these insulators are not well understood. Here we investigate the electronic properties of disordered beryllium films, with the aim of disentangling the effects of the Coulomb gap and the underlying disorder. We show that the gap is suppressed by a magnetic field and that this drives the strongly insulating beryllium films into a low-temperature 'quantum metal' phase with resistance near the quantum resistance RQ = h/e2, where h is Planck's constant and e is the electron charge.     

Quantum interference of superfluid 3He.

Celebrated interference experiments have demonstrated the wave nature of light and electrons, quantum interference being the manifestation of wave-particle duality. More recently, double-path interference experiments have also demonstrated the quantum-wave nature of beams of neutrons, atoms and Bose-Einstein condensates. In condensed matter systems, double-path quantum interference is observed in the d.c. superconducting quantum interference device (d.c. SQUID). Here we report a double-path quantum interference experiment involving a liquid: superfluid 3He. Using a geometry analogous to the superconducting d.c. SQUID, we control a quantum phase shift by using the rotation of the Earth, and find the classic interference pattern with periodicity determined by the 3He quantum of circulation.     

Fluctuating superconductivity in organic molecular metals close to the Mott transition

On cooling through the transition temperature T(c) of a conventional superconductor, an energy gap develops as the normal-state charge carriers form Cooper pairs; these pairs form a phase-coherent condensate that exhibits the well-known signatures of superconductivity: zero resistivity and the expulsion of magnetic flux (the Meissner effect). However, in many unconventional superconductors, the formation of the energy gap is not coincident with the formation of the phase-coherent superfluid. Instead, at temperatures above the critical temperature a range of unusual properties, collectively known as 'pseudogap phenomena', are observed. Here we argue that a key pseudogap phenomenon-fluctuating superconductivity occurring substantially above the transition temperature-could be induced by the proximity of a Mott-insulating state. The Mott-insulating state in the kappa-(BEDT-TTF)2X organic molecular metals can be tuned, without doping, through superconductivity into a normal metallic state as a function of the parameter t/U, where t is the tight-binding transfer integral characterizing the metallic bandwidth and U is the on-site Coulomb repulsion. By exploiting a particularly sensitive probe of superconducting fluctuations, the vortex-Nernst effect, we find that a fluctuating regime develops as t/U decreases and the role of Coulomb correlations increases.     

Pressure-induced insulator conductor transition in a photoconducting organic liquid-crystal film

Intermolecular separation determines the extent of orbital overlap and thus the rate of electron transfer between neighbouring molecules in an organic crystal. If such a crystal is compressed, the resistivity decreases owing to a diminishing intermolecular distance. Metal insulator transitions have been observed by applying hydrostatic pressure to, for example, Langmuir films of metal nanoparticles. But previous attempts to observe a clear transition point in organic crystals, such as anthracene and tetracene, were not successful owing to difficulties with electrically insulating the high-pressure cell. Here we report a different approach by using a sample that is photoconductive and forms an organized film. A cylindrical tip (approximately 100 microm in diameter) was used to compress the sample instead of a piston/cylinder structure, entirely eliminating the problem of electrical insulation. Furthermore, by illuminating the sample with a laser, the conductivity of the sample is increased by several orders of magnitude. By monitoring the photocurrent with sensitivity at the 10(-13) A level, changes in resistivity at very low pressure could be monitored. We observe a sharp increase in current that could indicate a transition from hopping to delocalized conduction.     

Energetic neutral atoms from a trans-Europa gas torus at Jupiter

The space environments--or magnetospheres--of magnetized planets emit copious quantities of energetic neutral atoms (ENAs) at energies between tens of electron volts to hundreds of kiloelectron volts (keV). These energetic atoms result from charge exchange between magnetically trapped energetic ions and cold neutral atoms, and they carry significant amounts of energy and mass from the magnetospheres. Imaging their distribution allows us to investigate the structure of planetary magnetospheres. Here we report the analysis of 50-80 keV ENA images of Jupiter's magnetosphere, where two distinct emission regions dominate: the upper atmosphere of Jupiter itself, and a torus of emission residing just outside the orbit of Jupiter's satellite Europa. The trans-Europa component shows that, unexpectedly, Europa generates a gas cloud comparable in gas content to that associated with the volcanic moon Io. The quantity of gas found indicates that Europa has a much greater impact than hitherto believed on the structure of, and the energy flow within, Jupiter's magnetosphere.     

A topological Dirac insulator in a quantum spin Hall phase

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields. Bulk Bi(1-x)Sb(x) single crystals are predicted to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi(1-x)Sb(x) is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest following the new findings in two-dimensional graphene and charge quantum Hall fractionalization observed in pure bismuth. However, despite numerous transport and magnetic measurements on the Bi(1-x)Sb(x) family since the 1960s, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi(0.9)Sb(0.1), locate the Kramers points at the sample's boundary and provide a comprehensive mapping of the Dirac insulator's gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the 'topological metal'. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate 'light-like' bulk carriers and spin-textured surface currents.     

光晶格中多体极化子在Mott绝缘体区域的量子相

极化子是在玻色-爱因斯坦凝聚(BEC)背景下,光晶格中的玻色子与BEC声子库耦合形成的一种准粒子。通过Lang-Firsov变换得到极化子体系的有效哈密顿量,其形式为拓展的玻色-哈伯德模型。在Mott绝缘体区域,通过直接求解体系的哈密顿量得到了单组份极化子在填充数分别为1/2和1/4时的量子相;通过Hartree-Fock近似,进一步得到了双组份极化子在填充数分别为1/2和1/4时体系的量子相。研究预测了单组份和双组份极化子体系可能存在的非平庸量子相。