Observation of a pairing pseudogap in a two-dimensional Fermi gas

Pairing of fermions is ubiquitous in nature, underlying many phenomena. Examples include superconductivity, superfluidity of (3)He, the anomalous rotation of neutron stars, and the crossover between Bose-Einstein condensation of dimers and the BCS (Bardeen, Cooper and Schrieffer) regime in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems show even more subtle effects, many of which are not understood at a fundamental level. Most striking is the (as yet unexplained) phenomenon of high-temperature superconductivity in copper oxides, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, it is not understood how the many-body pairing is established at high temperature, and whether it precedes superconductivity. Here we report the observation of a many-body pairing gap above the superfluid transition temperature in a harmonically trapped, two-dimensional atomic Fermi gas in the regime of strong coupling. Our measurements of the spectral function of the gas are performed using momentum-resolved photoemission spectroscopy, analogous to angle-resolved photoemission spectroscopy in the solid state. Our observations mark a significant step in the emulation of layered two-dimensional strongly correlated superconductors using ultracold atomic gases.     

Attractive and repulsive Fermi polarons in two dimensions

The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well known case is an impurity coupled to a bosonic bath (such as lattice vibrations); the impurity and its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-transition-temperature superconductors, as well as in colossal magnetoresistance in manganites. For impurities in a fermionic bath, studies have considered heavy or immobile impurities which exhibit Anderson's orthogonality catastrophe and the Kondo effect. More recently, mobile impurities have moved into the focus of research, and they have been found to form new quasiparticles known as Fermi polarons. The Fermi polaron problem constitutes the extreme, but conceptually simple, limit of two important quantum many-body problems: the crossover between a molecular Bose-Einstein condensate and a superfluid with BCS (Bardeen-Cooper-Schrieffer) pairing with spin-imbalance for attractive interactions, and Stoner's itinerant ferromagnetism for repulsive interactions. It has been proposed that such quantum phases (and other elusive exotic states) might become realizable in Fermi gases confined to two dimensions. Their stability and observability are intimately related to the theoretically debated properties of the Fermi polaron in a two-dimensional Fermi gas. Here we create and investigate Fermi polarons in a two-dimensional, spin-imbalanced Fermi gas, measuring their spectral function using momentum-resolved photoemission spectroscopy. For attractive interactions, we find evidence for a disputed pairing transition between polarons and tightly bound dimers, which provides insight into the elementary pairing mechanism of imbalanced, strongly coupled two-dimensional Fermi gases. Additionally, for repulsive interactions, we study novel quasiparticles--repulsive polarons--the lifetime of which determines the possibility of stabilizing repulsively interacting Fermi systems.     

Observation of a roton collective mode in a two-dimensional Fermi liquid

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, (4)He (bosons) and (3)He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon-roton mode in liquid (4)He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as 'zero-sound' in (3)He, and 'plasmons' in charged systems) and incoherent particle-hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle-hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid (3)He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.     

Universal spin transport in a strongly interacting Fermi gas

Transport of fermions, particles with half-integer spin, is central to many fields of physics. Electron transport runs modern technology, defining states of matter such as superconductors and insulators, and electron spin is being explored as a new carrier of information. Neutrino transport energizes supernova explosions following the collapse of a dying star, and hydrodynamic transport of the quark-gluon plasma governed the expansion of the early Universe. However, our understanding of non-equilibrium dynamics in such strongly interacting fermionic matter is still limited. Ultracold gases of fermionic atoms realize a pristine model for such systems and can be studied in real time with the precision of atomic physics. Even above the superfluid transition, such gases flow as an almost perfect fluid with very low viscosity when interactions are tuned to a scattering resonance. In this hydrodynamic regime, collective density excitations are weakly damped. Here we experimentally investigate spin excitations in a Fermi gas of (6)Li atoms, finding that, in contrast, they are maximally damped. A spin current is induced by spatially separating two spin components and observing their evolution in an external trapping potential. We demonstrate that interactions can be strong enough to reverse spin currents, with components of opposite spin reflecting off each other. Near equilibrium, we obtain the spin drag coefficient, the spin diffusivity and the spin susceptibility as a function of temperature on resonance and show that they obey universal laws at high temperatures. In the degenerate regime, the spin diffusivity approaches a value set by [planck]/m, the quantum limit of diffusion, where [planck]/m is Planck's constant divided by 2π and m the atomic mass. For repulsive interactions, our measurements seem to exclude a metastable ferromagnetic state.     

High-resolution spectroscopy of two-dimensional electron systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunnelling, yield measurements of the 'single-particle' density of states spectrum of a system. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proved difficult to probe spectroscopically. Here we present an improved version of time-domain capacitance spectroscopy that allows us to measure the single-particle density of states of a 2DES with unprecedented fidelity and resolution. Using the method, we perform measurements of a cold 2DES, providing direct measurements of interesting correlated electronic effects at energies that are difficult to reach with other techniques; these effects include the single-particle exchange-enhanced spin gap, single-particle lifetimes in the quantum Hall system, and exchange splitting of Landau levels not at the Fermi surface.     

The birth of a quasiparticle in silicon observed in time-frequency space

The concept of quasiparticles in solid-state physics is an extremely powerful tool for describing complex many-body phenomena in terms of single-particle excitations. Introducing a simple particle, such as an electron, hole or phonon, deforms a many-body system through its interactions with other particles. In this way, the added particle is 'dressed' or 'renormalized' by a self-energy cloud that describes the response of the many-body system, so forming a new entity--the quasiparticle. Using ultrafast laser techniques, it is possible to impulsively generate bare particles and observe their subsequent dressing by the many-body interactions (that is, quasiparticle formation) on the time and energy scales governed by the Heisenberg uncertainty principle. Here we describe the coherent response of silicon to excitation with a 10-femtosecond (10(-14) s) laser pulse. The optical pulse interacts with the sample by way of the complex second-order nonlinear susceptibility to generate a force on the lattice driving coherent phonon excitation. Transforming the transient reflectivity signal into frequency-time space reveals interference effects leading to the coherent phonon generation and subsequent dressing of the phonon by electron-hole pair excitations.     

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.     

Bose-Einstein condensation of atomic gases

The early experiments on Bose-Einstein condensation in dilute atomic gases accomplished three long-standing goals. First, cooling of neutral atoms into their motional ground state, thus subjecting them to ultimate control, limited only by Heisenberg's uncertainty relation. Second, creation of a coherent sample of atoms, in which all occupy the same quantum state, and the realization of atom lasers - devices that output coherent matter waves. And third, creation of a gaseous quantum fluid, with properties that are different from the quantum liquids helium-3 and helium-4. The field of Bose-Einstein condensation of atomic gases has continued to progress rapidly, driven by the combination of new experimental techniques and theoretical advances. The family of quantum-degenerate gases has grown, and now includes metastable and fermionic atoms. Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.     

非简谐势中两组分简并费米气体的集体激发

研究了在一个扭曲的谐振势中两组分简并费米气体的集体激发.运用变分法导出了1组描述两组分简并费米气体质心运动与宽度变化的耦合方程,获得了2个低能激发模.在不同的有效s波相互作用和有效p波相互作用下,分别讨论了由于势的非简谐改变引起的集体激发的频移和集体激发的塌缩与恢复.     

人工自旋轨道耦合玻色-爱因斯坦凝聚体的元激发

文章研究了准一维人工自旋轨道耦合玻色-爱因斯坦凝聚体中的元激发. 利用平均场理论和波戈留波夫近似方法,分别计算了此原子凝聚体在依赖于拉曼耦合强度的零动量相和平面波相的激发谱. 结果表明,在零动量相时体系激发谱的2个分支都呈现出对称结构;相反地,在较小拉曼耦合强度时的平面波相,激发谱呈现出旋子最低结构,从而预示了体系从平面波相到条纹相的相变. 文中证明了在平面波相和零动量相的相变附近,低频元激发的声速急剧下降并消失于相变点. 文章全面分析了人工自旋轨道耦合原子凝聚体的元激发特性,为实验研究该类崭新的多体系统提供理论支持.     

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.     

Electron-plasmon interaction induced plasmonic-polaron band replication in epitaxial perovskite SrIrO3 films

Electron-boson interaction is fundamental to a thorough understanding of various exotic properties emerging in many-body physics.In photoemission spectroscopy,p...     

Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.     

Vortices and superfluidity in a strongly interacting Fermi gas

Quantum degenerate Fermi gases provide a remarkable opportunity to study strongly interacting fermions. In contrast to other Fermi systems, such as superconductors, neutron stars or the quark-gluon plasma of the early Universe, these gases have low densities and their interactions can be precisely controlled over an enormous range. Previous experiments with Fermi gases have revealed condensation of fermion pairs. Although these and other studies were consistent with predictions assuming superfluidity, proof of superfluid behaviour has been elusive. Here we report observations of vortex lattices in a strongly interacting, rotating Fermi gas that provide definitive evidence for superfluidity. The interaction and therefore the pairing strength between two 6Li fermions near a Feshbach resonance can be controlled by an external magnetic field. This allows us to explore the crossover from a Bose-Einstein condensate of molecules to a Bardeen-Cooper-Schrieffer superfluid of loosely bound pairs. The crossover is associated with a new form of superfluidity that may provide insights into high-transition-temperature superconductors.     

Observation of scale invariance and universality in two-dimensional Bose gases

The collective behaviour of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics; for example, thermodynamic observables follow generalized scaling laws near the phase transition. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry result in a broad fluctuation regime and an extended range of universal scaling behaviour. Studies of the BKT transition in cold atoms have stimulated great interest in recent years, but a clear demonstration of critical behaviour near the phase transition has remained elusive. Here we report in situ density and density-fluctuation measurements of two-dimensional Bose gases of caesium at different temperatures and interaction strengths, observing scale-invariant, universal behaviours. The extracted thermodynamic functions confirm the existence of a wide universal region near the BKT phase transition, and provide a sensitive test of the universality predicted by classical-field theory and quantum Monte Carlo calculations. Our experimental results provide evidence for growing density-density correlations in the fluctuation region, and call for further explorations of universal phenomena in classical and quantum critical physics.     

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.     

Determination of the fermion pair size in a resonantly interacting superfluid

Fermionic superfluidity requires the formation of particle pairs, the size of which varies from the femtometre scale in neutron stars and nuclei to the micrometre scale in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in 'BCS-BEC crossover' theories, describing the crossover from a Bardeen-Cooper-Schrieffer (BCS)-type superfluid of loosely bound, large Cooper pairs to Bose-Einstein condensates (BECs) of tightly bound molecules. Such a crossover superfluid has been realized in ultracold atomic gases where high-temperature superfluidity has been observed. The microscopic properties of the fermion pairs can be probed using radio-frequency spectroscopy. However, previous work was difficult to interpret owing to strong final-state interactions that were not well understood. Here we realize a superfluid spin mixture in which such interactions have negligible influence and present fermion pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine that the spectroscopic pair size in the resonantly interacting gas is 20 per cent smaller than the interparticle spacing. These are the smallest pairs so far observed in fermionic superfluids, highlighting the importance of small fermion pairs for superfluidity at high critical temperatures. We have also identified transitions from fermion pairs to bound molecular states and to many-body bound states in the case of strong final-state interactions.     

Phase diagram of a two-component Fermi gas with resonant interactions

The pairing of fermions lies at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state, and the quest for superconductors with high critical temperature equates to a search for systems with strong pairing mechanisms. Ultracold atomic Fermi gases present a highly controllable model system for studying strongly interacting fermions. Tunable interactions (through Feshbach collisional resonances) and the control of population or mass imbalance among the spin components provide unique opportunities to investigate the stability of pairing-and possibly to search for exotic forms of superfluidity. A major controversy has surrounded the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly (that is, at unitarity). Here we present the phase diagram of a spin-polarized Fermi gas of (6)Li atoms at unitarity, experimentally mapping out the superfluid phases versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization; this is the signature of a first-order superfluid-to-normal phase transition, and disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully paired superfluid to a partially polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.