p-Wave interactions in low-dimensional fermionic gases

We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.     

Evolution from BCS to BEC superfluidity in p-wave Fermi gases

We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.     

Quasi-one-dimensional Bose gases with a large scattering length

Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).     

Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.     

Suppression of quantum scattering in strongly confined systems

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in "interacting" quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.     

The stability of a quantized vortex in a dilute Bose gas confined to a toroidal trap

We investigate the stability of a quantized vortex in a weakly interacting Bose gas, trapped in a toroidal container with hard walls. Calculating the excitation spectrum numerically and determining the stability condition by the Landau criterion, we examine the effect of reducing the confinement region of the condensate on the vortex stability. We find that tight confinement of the condensate increases the stabilization of the quantized vortex because an increase in the zero sound velocity due to tight confinement prevents the emergence of the elementary excitation which breaks superfluidity of the Bose system. We also discuss the experimental setup to observe such an effect.     

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated(cigar shaped)confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.     

Coherent Scattering of Light by Bose-Einstein Condensation in a Tight Confinement

We have observed strong scattering of a probe light by dilute Bose-Einstein condensate （BEC） ^87Rb gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.     

Released momentum distribution of a Fermi gas in the BCS-BEC crossover

We develop a time-dependent mean-field theory to investigate the released momentum distribution and the released energy of an ultracold Fermi gas in the BCS-BEC crossover after the scattering length has been set to zero by a fast magnetic-field ramp. For a homogeneous gas we analyze the nonequilibrium dynamics of the system as a function of the interaction strength and of the ramp speed. For a trapped gas the theoretical predictions are compared with experimental results.     

s-wave and p-wave scattering in a cold gas of Na and Rb atoms

Using improved experimentally based X¹Σ⁺ and a³Σ⁺ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of ²³Na atoms by ⁸⁵Rb atoms and ⁸⁷Rb atoms. These are the scattering lengths and volumes, numbers of bound states and effective ranges, which we use to obtain the low energy spin-change cross section as functions of the system temperature and the isotope masses. From an analysis of the contributions of s-wave and p-wave scatterings to the elastic cross section we estimate temperatures below which only s-wave scattering is dominant. We compare our quantal results to data obtained from the semiclassical approximation. We supply evidence for the existence of a near zero energy p-wave bound state supported by the singlet molecular potential.     

超冷钠原子弹性散射特性的精确计算

基于精确的原子之间相互作用势,系统研究了钠原子在超冷温度下的弹性散射特性,精确计算了钠原子间碰撞时的s波散射长度、有效力程、p波散射长度以及束缚态数目等散射参数.超冷温度下单重态和三重态原子间的弹性散射截面主要为s波贡献,随着碰撞能量的增加散射截面有丰富的形状共振出现,计算发现单重态和三重态散射截面分别存在显著的f波和i波形状共振.应用简并内态近似方法获得了超精细态相互作用时的s波散射长度,所得结果与精确值比较符合.     

Dynamics of an Ultracold Bose Gas in Funnel-Shaped Potential

In this paper we develop a variational theory to study the dynamicproperties of ultracold Bose gas in a funnel external potential. We obtain one-dimensional nonlinear equation which describes the dynamics of transverse tight confined bosonic gas from three-dimension to one-dimension, and find one-dimensional s-wave scattering length which depends on the shape oftransverse confining potential. If the funnel trapping potential is strong enough at zero temperature, all transverse excitations are frozen. We find the dynamic equation which describes the Tonks-Girardeau gas and present a qualitative analysis of the experimental accessibility of the Tonks-Girardeau gas with funnel-trapped alkalic atoms.     

有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.     

Spectral singularities and zero energy bound states

Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled.     

量子线/铁基超导隧道结中隧道谱的研究

考虑铁基超导中能带间的相互作用和界面对每一个能带的散射作用, 利用推广的Blonder-Tinkham-Klapwijk模型, 并通过求解Bogoliubov-de Gennes 方程研究了具有不同类型双能隙系统的量子线/铁基超导隧道结中准粒子的输运系数和隧道谱. 研究表明: 1)在弹道极限时, 随着带间相互作用的增大, s_± 波隧道谱中零偏压附近的平台演变成电导峰; s₊₊ 波的平台演变成凹陷; p波的零偏压电导峰被压低. 2)界面对两个能带的散射作用不为零时, 随着带间相互作用的增大, s_± 波和s₊₊ 波两能隙处的峰值将降低, 而两峰间的凹陷值将变大; p波的零偏压电导峰被压低, 非零偏压电导增大. 3)界面对每个能带的散射, 可使其产生的电导峰变得更加尖锐, 但可压低和抹平另一个带产生的电导峰值. 这些结果对于澄清铁基超导体的能隙结构和区别不同类型铁基超导体有所帮助.     

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.     

Realization of a resonant Fermi gas with a large effective range

We have measured the interaction energy and three-body recombination rate for a two-component Fermi gas near a narrow Feshbach resonance and found both to be strongly energy dependent. Even for de Broglie wavelengths greatly exceeding the van der Waals length scale, the behavior of the interaction energy as a function of temperature cannot be described by atoms interacting via a contact potential. Rather, energy-dependent corrections beyond the scattering length approximation are required, indicating a resonance with an anomalously large effective range. For fields where the molecular state is above threshold, the rate of three-body recombination is enhanced by a sharp, two-body resonance arising from the closed-channel molecular state which can be magnetically tuned through the continuum. This narrow resonance can be used to study strongly correlated Fermi gases that simultaneously have a sizable effective range and a large scattering length.     

Properties of pseudopotentials for higher partial waves

Contact psuedopotentials for relative angular momentum greater than zero are of interest for the study of cold atomic gases. For bosons, it is known that when the s-wave scattering length becomes infinite, an infinite number of three-body bound states, called Efimov states, are predicted by such potentials. Realistic potentials also exhibit the such states, thus a study of the Efimov effect for contact psuedopotentials for higher partial waves and fermions is important for the study of cold atoms. In this Letter we analyze three-body states of three particles interacting via psuedopotentials for higher partial waves and show that there is an Efimov effect for three fermions interacting via p-wave psuedopotentials.     

BEC transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount DeltaT(c) approximately equal to ca(sc)n(1/3)T(0) from the ideal gas result T(0), where a(sc) is the scattering length, n is the density, and c is a pure number. There have been several different theoretical estimates for c. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) straight phi(4) field theory in three dimensions-an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find c = 1.32+/-0.02.     

Four-body Efimov effect for three fermions and a lighter particle

We study three same-spin-state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384相似文献