Mott-Hubbard transition of bosons in optical lattices with two-body interactions

In this paper, based on the Bose-Hubbard model with two-body on-site interactions, we study the quantum phase transition between the superfluid state and the Mott-insulator state. With the decoupling approximation, we get the relation between the weak superfluidity and dimensionless chemical potential with different particle number and different dimensionless interaction strength, and the relation between the weak superfluidity and the reciprocal of dimensionless interaction strength with different particle number. We also calculate the corresponding experimental parameters.     

玻色-爱因斯坦凝聚体中的超流现象

在玻色－爱因斯坦凝聚（BEC）的超流现象的研究中，人们通常采用平均场近似下求解Gross-Pitaveskii方程的方法，我们采用更严格的准确对角化的方法对弱排斥相互作用下两维旋转N－Boson体系的凝聚状态进行了研究，研究表明，弱相互作用下的基态并不是人们通常认为的单一凝聚态，而是一个碎裂凝聚态，通过碎裂态能谱与平均场方法给出的能谱之间的比较以及条件几率分布函数的计算，我们指出这种碎裂凝聚态有着内在的不稳定性，很容易破缺到一个单一凝聚状态；计算给出的条件几率分布可以用来揭示破缺石的状态，其分布图案与平均场近似下得到的涡旋图形相类似，我们进一步注意到过去研究工作主要集中在弱相互作用极限下和强相互作用Thomas-Fermi近似极限下这两种极端情况，为考察两种极限间的中间过渡区域，我们研究了中等相互作用强度下体系的基态性质。     

Rearrangements of interacting Fermi liquids

The stability condition of the Landau Fermi liquid theory may be broken when the interaction between particles is strong enough. In this case, the ground state is reconstructed to have a particle distribution different from the Fermi-step function. For specific instances, one case with the vector boson exchange and another with the relativistic heavy-ion collision are taken into consideration. With the vector boson exchange, we find that the relative weak interaction strength can lead to the ground-state rearrangement as long as the fermion mass is large enough. It is found that the relativistic heavy-ion collision may also cause the ground-state rearrangement, affecting the statistics of the collision system.     

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Using a universal relation between electron filling factor and ground state energy,this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime,and demonstrates that in contrast to the usual Hubbard model(gc = 1/2),the dimensionless coupling strength parameter g c heavily depends on the electron filling,and it has a "particle-hole" symmetry about electron quarter filling point.As increasing the nearest neighbouring repulsive interaction,the single particle spectral weight is transferred from low energy to high energy regimes.Moreover,at electron quarter filling,there is a metal-Mott insulator transition at the strong coupling point gc = 1/4,and this transition is a continuous phase transition.     

Phase separation in asymmetrical fermion superfluids

Motivated by recent developments on cold atom traps and high density QCD we consider fermionic systems composed of two particle species with different densities. We argue that a mixed phase composed of normal and superfluid components is the energetically favored ground state. We suggest how this phase separation can be used as a probe of fermion superfluidity in atomic traps.     

非线性两能级系统中的Landau-Zener-Coulomb跃迁

非线性跃迁动力学的研究是量子操控中的一个重要课题,在原子分子光物理、量子信息以及固体物理等领域都有着重要的应用.本文研究了具有粒子间相互作用两能级系统中的Landau-Zener-Coulomb跃迁动力学.结果表明,对于能级的斜率正负不同的情况,粒子间相互作用对系统跃迁动力学的影响完全不同.为正时,粒子间相互作用总是抑制能级间的非绝热跃迁,且相互作用强度越大,两能级间的非绝热跃迁越难发生.而为负时,弱相互作用会促进能级间的非绝热跃迁,在强相互作用情况下,跃迁概率会出现振荡.随着相互作用强度的增大,振荡幅度逐渐减小,能级间的非绝热跃迁受到抑制.     

Opposite effect of spin-orbit coupling on condensation and superfluidity

We investigate the effects of Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we find that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction), and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonically for all interaction parameters, while the superfluid density has a minimum when the interaction parameter is below a critical value. We also discuss the isotropic two-dimensional case where analytical expressions for the gap and number equations are obtained and the same phenomena are found as that of the 3D case.     

Alpha clusters in nuclei with 41 ≦ A ≦ 45

The effect of pairing and surface α-clustering structure was studied by means of a Hamiltonian with pairing and four-body interaction terms in a simple two-level model in odd nuclei with 41 ≦ A ≦ 45. It was shown that the dynamical α-structures can be induced by the pairing correlation alone, but with an unusually large value of the strength G of the pairing interaction. The addition of a small four-body interaction term allowed us to diminish the G-value to a physically reasonable one and, at the same time, to get meaningful α-clustering. The four-body term added to the Hamiltonian is a simplified way to improve, in this respect, the two-body pairing interaction (itself a simplified model interaction). For example, in the ground state of ⁴⁵Ti the “α-clusters” appeared with larger probability than that for separate nucleons, while in ⁴⁵Ca both probabilities are approximately equal. The calculated binding energy was also applied to reproduce the experimental difference of the masses of neighbouring nuclei. With the eigenstates of the Hamiltonian, schematic spectroscopic factors for two-nucleon transfer, α-transfer, and elastic scattering of α-particles were also calculated. Spectroscopic factors for the transitions from ground state to ground state and from ground state to excited state were then used to distinguish between superfluid or normal behaviour of these nuclei. In addition to the superfluidity induced by pairing forces, a superfluidity due to four-body correlations was also predicted.     

声子之间的相互作用对量子线中磁极化子性质的影响

研究了量子线中弱耦合磁极化子的性质.采用线性组合算符和微扰法导出量子线中弱耦合磁极化子的基态能量.在计及电子在反冲效应中发射和吸收不同波矢的声子之间的相互作用时,讨论了量子线的受限强度、电子-LO声子耦合强度和声子之间相互作用对量子线中弱耦合磁极化子的基态能量的影响.数值计算结果表明:量子线中弱耦合磁极化子的基态能量随量子线的受限强度ω₀的增大而迅速增大.当受限强度ω₀取相同值时,电子-声子耦合强度α越大基态能量E₀越小,磁场的回旋频率ω_e越大基态能量E₀越大.在弱磁场情况下,当ω₀<0.5时,随着量子线的受限强度ω₀的减少p值迅速增大,即对于弱磁场声子之间相互作用的影响不能忽略.     

中子物质中超流性的自能色散效应

利用扩展的 Brueckner- Hartree- Fock理论与推广的 BCS方法研究了自能的色散效应和基态关联对中子物质中超流性和能隙的影响 .研究结果表明 ,自能的色散效应使中子物质中能隙减小;考虑基态关联后 ,超流性将进一步减弱. The effects of the dispersion and ground state correlation of the single particle self-energy on neutron matter superfluidity have been investigated in the framework of the Extended Brueckner-Hartree-Fock and the generalized BCS approaches. A sizable reduction of the energy gap is found due to the energy dependence of the self-energy. And the inclusion of the ground state correlations in the self-energy suppresses further the neutron matter superfluidity.     

BCS-BEC crossover in a two-dimensional Fermi gas

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte?Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.     

A variational approach to superfluidity

A variational approach to problems in quantum statistical mechanics is described and it is shown how to determine the best quasi-free approximation to the equilibrium state. The relation between this approximation and the Bogoliubov approximation in superfluidity is discussed.     

Novel superfluidity in a trapped gas of Fermi atoms with repulsive interaction loaded on an optical lattice

We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes negative below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a "Mott insulating core" appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left- and right-hand sides of this core.     

Direct coupling between magnetism and superconducting current in the Josephson phi0 junction

We study the proximity effect between conventional superconductor and magnetic normal metal with a spin-orbit interaction of the Rashba type. Using the phenomenological Ginzburg-Landau theory and the quasiclassical Eilenberger approach it is demonstrated that the Josephson junction with such a metal as a weak link has a special nonsinusoidal current-phase relation. The ground state of this junction is characterized by the finite phase difference phi{0}, which is proportional to the strength of the spin-orbit interaction and the exchange field in the normal metal. The proposed mechanism of the phi{0} junction formation gives a direct coupling between the superconducting current and the magnetic moment in the weak link. Therefore the phi{0} junctions open interesting perspectives for the superconducting spintronics.     

Extraction of spectroscopic factors using R-matrix theory

The relation of the dimensionless reduced width of a state to its spectroscopic strength is discussed and the spectroscopic factor is calculated as the ratio of the reduced width to that of an optical potential analyzed with the same channel radius and boundary condition number. From a model square well problem, the reduced width is shown to be sensitive to these parameters. Neutron scattering to the 5.08 MeV state of ¹⁷O is analyzed with R-matrix theory and the value obtained for its spectroscopic factor is 0.80. This value is shown to be moderately independent of the parameters of the optical potential, a fact which greatly simplifies analysis by eliminating the strong dependence upon the location of the pure single particle state.     

Josephson effect in a Coulomb-blockaded SINIS junction

The problem of a Josephson current through a Coulomb-blocked nanoscale superconductor-normal-superconductor structure with tunnel contacts is reconsidered. Two different contributions to the phase-biased supercurrent I(?) are identified, which are dominant in the limits of weak and strong Coulomb interaction. Full expression for the free energy valid at arbitrary Coulomb strength is found. The current derived from this free energy interpolates between known results for weak and strong Coulomb interaction as the phase bias changes from 0 to π. In the broad range of Coulomb strength, the current-phase relation is substantially nonsinusoidal and qualitatively different from the case of semiballistic SNS junctions. The Coulomb interaction leads to the appearance of a local minimum in the current at some intermediate value of the phase difference applied to the junction.     

激光空泡在近自由液面运动特性的实验研究

采用激光技术聚焦击穿液体产生空泡,利用高速摄像系统开展激光空泡与自由液面的相互作用的实验研究。实验研究发现,空泡与自由液面之间的无量纲距离对水下空泡的脉动特性和自由液面的水冢现象存在影响。通过大量实验总结了无量纲距离与空泡半径、空泡脉动周期、自由液面水柱的最大高度和产生水冢时间的相互关系。实验表明无量纲距离越小,空泡脉动周期越短,自由面的水冢现象越明显。同时统计出了在不同无量纲距离范围内所出现的5种不同水冢现象的规律。研究内容为空泡与自由液面相互作用的理论提供了实验依据。     

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron-molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.     

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.