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.     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

Spin-imbalance in a one-dimensional Fermi gas

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold (6)Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.     

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.     

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen-Cooper-Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose-Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose-Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS-BEC continuum.     

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.     

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.     

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.     

囚禁有限unitary费米气体的压强与状态方程

目的研究非对称与球对称简谐势阱中有限unitary费米气体的压强与状态方程。方法运用分数不相容统计法。结果求出了非对称与球对称简谐势阱中有限unitary费米气体的压强张量以及压强与内能的关系,导出了球对称势阱中的状态方程并给出了低温强简并近似和高温弱简并近似。结论揭示了有限unitary费米气体系统压强的有限尺度效应,给出了有限尺度效应判据。指出了球对称简谐势阱中有限unitary费米气体的压强在空间3个方向上各向同性与非对称势阱中压强张量在空间3个方向各向异性的特征,阐明了非对称势阱中沿着势阱圆频率低的方向压强张量高,沿着势阱圆频率高的方向压强张量低的规律,揭示了压强张量在空间3个方向各向异性的物理本质。     

准二维谐振势阱中有限尺度的非理想玻色气体

研究了准二维谐振势阱中粒子数有限的非理想玻色气体的热力学性质。利用巨正则系综的求和方法与平均场理论,给出了有限粒子数与原子间相互作用对系统势力学性质的共同修正;并将所得结果与三维时的情况进行了比较。结果表明：降低维数不能提高系统的临界温度;在准二维谐振系统中,有限粒子数对系统的影响随着粒子数的增大而减小直至消失,而相互作用的影响与粒子数无关,因此可以通过增大粒子数来提高准二维谐振系统的临界温度。     

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantum-by-quantum control of light fields, including single-photon switching, all-optical deterministic quantum logic and the realization of strongly correlated many-body states of light.     

克尔非线性黑体中光超流态的研究

研究了克尔非线性黑体中一种新的光超流态.研究表明:非线性黑体中具有相反波矢和旋量的裸光子结合成对,未成对的裸光子则转换成一种新的准粒子--非极化激元;光子对系统是一个超流态,而非极化激元系统是一个正常流态.正常流态的光谱能量密度和辐射压强都比普通黑体大并且随温度单调增加.在理论上证明了克尔非线性黑体中光超流态的存在并给出了测量这种光超流态的方法.     

非广延统计下二维费米气体的热力学性质

目的在非广延统计物理框架下,探讨了二维费米气体在非广延参数q的影响下的热力学性质,计算出了总粒子数、总能量、自由能、热容量等热力学量。方法采用分解近似的方法。结果和结论在低温区域,q→1时,所有的结果可以回到传统的Fermi—Dirac分布,二维费米子气体的粒子数不受非广延参数q的影响。     

Speckle无序对一维谐振势中自旋极化费米气体的影响

基于局域密度近似的Bethe-ansatz方法,研究了谐振势中两组分一维自旋极化费米气体的基态性质,以及无序对其影响.对于无外势的干净系统,基态是完全配对的Bardeen-Cooper-Schrieffer(BCS)相,或部分极化的Fulde-Ferrell-Larkin-Ovchinnikov(FFLO)相,或完全极化的正常相.当系统中存在谐振势但仍干净时,系统成为两相混合的状态:中间部分是FFLO相;边缘部分或为BCS相,或为正常相.这之间存在一个临界相,即纯的FFLO相.发现当外势和无序共同存在,总极化强度固定时,随着无序振幅的增强,系统能从FFLO-BCS相变为FFLO-N(FFLO-Normal)相.     

低维电子气的费密能量与温度的关系

在探索新型材料的过程中 ,人们发现金属材料的一系列实验现象不能由三维电子气的费密能量与温度的关系来解释 ,但它们具有明显的低维特征 ,为此 ,该文研究了低维电子气的费密能量与温度之间的关系。研究结果表明 ,在低温情况下 ,低维电子气费密能量随着温度的变化关系与三维电子气是不相同的 ,尤其在一维情况下 ,电子气费密能量的变化量随着温度的变化规律与三维时恰恰相反。     

理想多自由度无相互作用费米气体系统的量子纠缠

对理想的具有自旋1/2和赝旋1/2两自由度费米气体系统的两体纠缠进行研究.结果表明:态空间的扩大,导致系统不超过4个费米子间的两体纠缠表现出类似于自旋1/2自由度的费米气体系统中两费米子间的纠缠分布,而完全不同于其对应的多个费米子间的约化两体纠缠分布;系统两费米子间纠缠存在的相对距离比单个自旋1/2自由度系统时增加了约1.7倍,并且由于两费米子间任一自由度的子纠缠始终为零,因此其中一个自由度的两费米子的子纠缠或量子关联来自于系统的相互作用.     

有限重力场中理想Fermi气体的弱简并特性

研究有限重力场中弱简并理想费米气体的热力学性质.采用Thomas-Fermi半经典近似方法,从有限重力场中理想费米气体的状态密度出发,给出系统的化学势、内能和压强解析表达式,分析重力场对弱简并理想费米气体热力学性质的影响.结果表明,有限重力场的存在使弱简并理想费米气体热力学量出现一个附加的修正项.