Cooper instability of composite fermions

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture an even number of quantum vortices and transform into particles called 'composite fermions' (refs 1-3). The fractional quantum Hall effect occurs in such a system when the ratio (or 'filling factor, nu) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling nu = 1/2 corresponds to a metallic state in which the composite fermions form a gapless Fermi sea. But for nu = 5/2, a fractional quantum Hall effect is observed instead; this unexpected result is the subject of considerable debate and controversy. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at nu = 5/2, but not at nu = 1/2. In effect, the repulsive Coulomb interaction between electrons is overscreened in the nu = 5/2 state by the formation of composite fermions, resulting in a weak, attractive interaction.     

超声波加工工具对复合变幅杆谐振性能影响

基于变截面杆纵振动的波动方程，推导出安装简单工具双曲过渡形复合变幅杆频率方程和放大系数的一般公式，并讨论了超声波加工工具对复合变幅杆谐振性能的影响．随着工具长度和直径的增加，变幅杆谐振频率下降，应根据工具尺寸相应调整复合变幅杆末端长度，才能保证更好的谐振．推导出的一般公式为超声变幅杆及其工具的设计和使用提供了理论依据。     

费米子的弱荷

从标准模型的中性流出发引入费米子弱荷的新概念,并对它们的性质进行讨论．根据弱荷的对称性,提出所有的中微子都是有质量的,但右手中微子和左手反中微子的弱荷为零,因而不参与弱相互作用．根据弱荷的手征性,合理地解释了弱相互作用中宇称不守恒的原因．     

Cyclotron frequency shifts arising from polarization forces

The cyclotron frequency of a charged particle in a uniform magnetic field B is related to its mass m and charge q by the relationship omega(c) = qB/m. This simple relationship forms the basis for sensitive mass comparisons using ion cyclotron resonance mass spectroscopy, with applications ranging from the identification of biomolecules and the study of chemical reaction rates to determinations of the fine structure constant of atomic spectra. Here we report the observation of a deviation from the cyclotron frequency relationship for polarizable particles: in high-accuracy measurements of a single CO+ ion, a dipole induced in the orbiting ion shifts the measured cyclotron frequency. We use this cyclotron frequency shift to measure non-destructively the quantum state of the CO+ ion. The effect also provides a means to determine to a few per cent the body-frame dipole moment of CO+, thus establishing a method for measuring dipole moments of molecular ions for which few comparably accurate measurements exist. The general perturbation that we describe here affects the most precise mass comparisons attainable today, with applications including direct tests of Einstein's mass-energy relationship and charge-parity-time reversal symmetry, and possibly the weighing of chemical bonds.     

Two-dimensional gas of massless Dirac fermions in graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schr?dinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.     

电子回旋脉塞中相位俘获的数值分析

通过对柱型腔回旋管中电子与电磁波互作用自洽非线性方程组的数值计算,模拟出电子的相轨迹图,分析了与相位俘获有关的饱和现象,指出这种现象主要与波场幅值和互作用长度有关,可通过调整这些参数提高互作用效率。     

Evidence for superfluidity of ultracold fermions in an optical lattice

The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. By using cold atomic gases, various models of condensed matter can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the copper oxides. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in bulk atomic gases include the observation of fermion-pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported but have not yet addressed superfluid behaviour. Here we report the observation of distinct interference peaks when a condensate of fermionic atom pairs is released from an optical lattice, implying long-range order (a property of a superfluid). Conceptually, this means that s-wave pairing and coherence of fermion pairs have now been established in a lattice potential, in which the transport of atoms occurs by quantum mechanical tunnelling and not by simple propagation. These observations were made for interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly as a result of a transition from superfluid to insulator. Such strongly interacting fermions in an optical lattice can be used to study a new class of hamiltonians with interband and atom-molecule couplings.     

Comparison of the Hanbury Brown-Twiss effect for bosons and fermions

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.     

Designer Dirac fermions and topological phases in molecular graphene

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.     

一维费米原子系统中的拓扑超流和Majorana费米子

通过数值求解Bogoliubov de Gennes方程,研究了具有自旋轨道耦合作用的一维费米晶格系统的性质．结果表明：在有限的自旋轨道耦合下和一定的磁场强度时,系统具有零能,此时的准粒子即为Majorana费米子．准无序效应研究表明,Majorana费米子不会被弱准无序所破坏．     

离子回旋频段内热等离子体介电张量研究

给出了离子回旋频段内冷等离子体和热等离子体介电张量表达式,计算得到了其分布,并进行了对比.结果表明:热等离子体更能反映托卡马克等离子体的介电性质,在托卡马克离子回旋波电流驱动的相关研究中应尽量采用热等离子体模型.     

Visualizing heavy fermions emerging in a quantum critical Kondo lattice

In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to the appearance of unconventional superconductivity and non-Fermi-liquid behaviour observed in actinide- and lanthanide-based compounds. Here we use spectroscopic mapping with the scanning tunnelling microscope to detect the emergence of heavy excitations with lowering of temperature in a prototypical family of cerium-based heavy-fermion compounds. We demonstrate the sensitivity of the tunnelling process to the composite nature of these heavy quasiparticles, which arises from quantum entanglement of itinerant conduction and f electrons. Scattering and interference of the composite quasiparticles is used to resolve their energy-momentum structure and to extract their mass enhancement, which develops with decreasing temperature. The lifetime of the emergent heavy quasiparticles reveals signatures of enhanced scattering and their spectral lineshape shows evidence of energy-temperature scaling. These findings demonstrate that proximity to a quantum critical point results in critical damping of the emergent heavy excitation of our Kondo lattice system.     

Mathieu方程与4-度对称径向扇回旋加速器的动力学稳定性

在线性近似下,考虑到二次谐波梯度场的影响,把粒子的运动方程化为标准的Mathieu方程.数值分析表明,在参数δ-ε平面上,系统存在一系列稳定和不稳定区.指出了,当粒子穿越不稳定区(禁带)时,振幅将呈指数增长,从而导致系统不稳定.为了保证系统的稳定性,要求粒子尽量避免穿越或少穿越不稳定区,为加速器设计提供了理论分析.     

三元混晶AxB1—xC中极化子回旋质量

研究了三元混晶A_xB_(1-x)C中弱耦合磁性极化子问题,用微扰理论导出了极化子朗道(Landau)能级和回旋质量与外磁场B和混晶组分x的关系,并对结果进行了数值计算,与其它理论结果进行对比。当组分x=0(或1)时,得出的结果与相应的二元晶体BC(AC)的结果完全等价。     

跨膜离子回旋谐振运动的计算及分析

从离子在电磁场作用下的基本运动方程出发,对在不同频率和幅值的外场作用下跨膜离子的运动特性进行了数值分析,揭示了离子发生谐振的外场参数条件．指出离子谐振时动能随时间迅速增长,并且在离散的谐振点上,离子动能的增长速度随交变磁场幅值的增大而增大,离子由谐振运动能够获得很大的动能,通过能量转换,可能导致磁生物效应的发生．     

Structure of an antibody combining site by magnetic resonance.

The structure of the combining site of the DNP binding IgA mouse myeloma protein MOPC 315 has been determined by a combination of high resolution nuclear magnetic resonance, electron spin resonance, model building and chemical modifications. This approach yields that general dimensions of the site, its polarity and asymmetry features, the assignment of the DNP-contact residues and their three-dimensional coordinates.     

大跨钢-混凝土连续组合箱梁桥双重组合作用

为研究双重组合作用对大跨钢-混凝土连续组合箱梁桥受力性能的影响,通过对潍坊市跨济青高速立交桥现场静载试验研究,采用有限元方法对2种模型计算结果及现场实测结果进行比较分析,并对双重组合箱梁下层混凝土板的长度与主跨长度之比和混凝土板厚度与钢梁底板厚度之比2个变量进行参数分析。研究结果表明:双重组合箱梁下层混凝土板有效降低钢梁下翼缘的应力;考虑双重组合作用后,连续组合梁桥结构刚度及支点负弯矩略有增加,中跨跨中挠度及正弯矩略有减小,最大幅度不大于10%。     

Muscular fatigue investigated by phosphorus nuclear magnetic resonance.

Muscular fatigue has been studied using 31PNMR to measure the levels and rates of utilisation of several key metabolites and the free-energy change for ATP hydrolysis. Force development is closely correlated with metabolite levels and is proportional to the rate at which ATP is hydrolysed.