Two-body correlation functions in nuclear matter with neutron-proton condensate

The density, spin, and isospin correlation functions in nuclear matter with a neutron-proton condensate are calculated to study the possible signatures of the BEC-BCS crossover in the low-density region. It is shown that the criterion of the crossover (Phys. Rev. Lett. 95, 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. The presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states can be used as an unambiguous signature of the BEC-BCS transition.     

Observation of the BEC-BCS crossover in a degenerate Fermi gas of lithium atoms

We observe characteristic atomic behaviors in the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer(BEC-BCS)crossover,by accurately tuning the magnetic field across the Feshbach resonance of lithium atoms.The magnetic field is calibrated by measuring the Zeeman shift of the optical transition.A non-monotonic anisotropic expansion is observed across the Feshbach resonance.The density distribution is explored in different interacting regimes,where a condensate of diatomic molecules forms in the BEC limit with the indication of a bimodal distribution.We also measure the three-body recombination atom loss in the BEC-BCS crossover,and find that the magnetic field of the maximum atom loss is in the BEC limit and gets closer to the Feshbach resonance when decreasing the atom temperature,which agrees with previous experiments and theoretical prediction.This work builds up a controllable platform for the study on the strongly interacting Fermi gas.     

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas--Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.     

Simultaneous effects of electron-hole correlation,hydrostatic pressure,and temperature on the third harmonic generation in parabolic GaAs quantum dots

The combined effects of electron-hole correlation, hydrostatic pressure, and temperature on the third harmonic generation in disk-shaped parabolic GaAs quantum dots are studied under the density matrix formalism and the effective mass approximation. Two well-defined regimes are discussed: (1) the strong-confinement regime, where the Coulomb interaction between the electron and hole is neglected and (2) the weak-confinement regime where the parabolic confinement term is neglected and the system reaches the limit of a hydrogenic problem. The results show that the third harmonic-generation coefficient is strongly dependent on the localization of the electron-hole pair. Also, that by using external perturbations like hydrostatic pressure or by considering the temperature effects it is possible to induce a blue-shift and/or red-shift on the resonant peaks of the third harmonic generation coefficient.     

Superfluid equation of state of dilute composite bosons

We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n(3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a(M), the composite nature of the dimers appearing only in the next order term proportional to n(2).     

Collective excitations of a degenerate gas at the BEC-BCS crossover

We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.     

Acoustic attenuation probe for Fermion superfluidity in ultracold-atom gases

Dilute gas Bose-Einstein condensates (BEC's), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter, and gives an estimate of the size of the Cooper pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasiparticle dispersion relation.     

Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length a(aa) displays a confinement-induced resonance. We compute the dimer-dimer scattering length a(dd) and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.     

Superfluid transition in a rotating fermi gas with resonant interactions

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial trap with frequencies Omega perpendicular, Omega z. We predict the upper-critical angular velocity, omega c2(delta,T), as a function of temperature T and detuning delta across the BEC-BCS crossover. The suppression of superfluidity at omega c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low T and Omega z < Omega perpendicular, in the BCS and crossover regimes of 0 less similar delta less similar delta c, omega c2 is implicitly given by [formula: see text], vanishing as omega c2 approximately Omega perpendicular(1 - delta/delta c)(1/2) near [formula: see text] (with Delta the BCS gap and gamma the resonance width), and extending the bulk result variant Planck's over 2pi omega c2 approximately 2Delta2/epsilonF to a trap. In the BEC regime of delta < 0 we find omega c2-->Omega perpendicular-, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.     

Coherence properties of a radiating electron-hole condensate

We analyze both the spatial as well as the temporal coherence of an electron-hole condensate and the radiation emitted from it. These coherences evolve from being full for the low density Bose-Einstein condensate to a chaotic behavior for a high density Bardeen-Cooper-Schrieffer-like state. Time coherence is transferred, to the emitted radiation in the ultrafast regime, in a damped oscillatory way.     

一维光晶格中超流Fermi气体基态性质的研究

研究了一维光晶格中超流Fermi气体基态解的性质.在平均场理论框架下,利用超流Fermi体系中原子间相互作用能与晶格势能相互平衡的条件,得到了一维光晶格中超流Fermi气体在整个BEC-BCS跨越区的一组基态解,给出了基态的原子数密度空间分布、总原子数和能量.进一步对系统从BEC端转变到BCS端时的基态解性质进行了深入分析和对比.结果表明,一维光晶格中超流Fermi气体基态分布具有一些特殊的性质,由于Fermi压力,相比而言超流Fermi气体在BCS端的基态原子数密度空间分布较为扩展,平均能量明显偏高.     

Viscous to inertial crossover in liquid drop coalescence

Using an electrical method and high-speed imaging, we probe drop coalescence down to 10?ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that, at a sufficiently low approach velocity where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argue that the late crossover, not accounted for in the theory, can be explained by an appropriate choice of length scales present in the flow geometry.     

Density inhomogeneity driven percolation metal-insulator transition and dimensional crossover in graphene nanoribbons

Transport in graphene nanoribbons with an energy gap in the spectrum is considered in the presence of random charged impurity centers. At low carrier density, we predict and establish that the system exhibits a density inhomogeneity driven two dimensional metal-insulator transition that is in the percolation universality class. For very narrow graphene nanoribbons (with widths smaller than the disorder induced length scale), we predict that there should be a dimensional crossover to the 1D percolation universality class with observable signatures in the transport gap. In addition, there should be a crossover to the Boltzmann transport regime at high carrier densities. The measured conductivity exponent and the critical density are consistent with this percolation transition scenario.     

Critical velocity for superfluid flow across the BEC-BCS crossover

Critical velocities have been observed in an ultracold superfluid Fermi gas throughout the BEC-BCS crossover. A pronounced peak of the critical velocity at unitarity demonstrates that superfluidity is most robust for resonant atomic interactions. Critical velocities were determined from the abrupt onset of dissipation when the velocity of a moving one-dimensional optical lattice was varied. The dependence of the critical velocity on lattice depth and on the inhomogeneous density profile was studied.     

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.     

由N-E-V分布及赝势法研究弱磁场中弱相互作用费米子气体的热力学性质

基于低温下量子系统的相关实验多是在体积、能量和粒子数都可变的外场束缚下进行的事实, 由体积、能量和粒子数可变的完全开放系统的统计分布(N-E-V分布)研究了弱磁场中弱相互作用费米系统的热力学性质. 首先求出了一般情况下由费米积分表示的内能和热容的解析表达式. 在此基础上, 又给出了在低温极限条件下内能与热容的解析表达式和数值计算结果, 并将N-E-V分布(粒子数密度变化)的结果与赝势法(粒子数密度不变)的结果进行了比较. 结果表明: N-E-V分布方法的计算结果总是补偿赝势法计算结果的过度偏差. 由N-E-V 分布方法所得结果最特异之处在于: 在低温条件下, 弱磁场中弱相互作用费米系统存在一相变温度t_c, 其正处于费米系统发生玻色-爱因斯坦凝聚(BEC)和费米原子形成库珀对的超流状态(BCS)相变及BEC-BCS跨越的温度范围内, 且不随反映弱相互作用大小和特征的散射长度a (a<0引力, a>0斥力)变化, 但随弱磁场的加强而降低, 即弱磁场可调节该相变温度. 磁场为零时, 相变温度最高, 为费米温度的0.184倍.     

Precision measurements of collective oscillations in the BEC-BCS crossover

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of (6)Li atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.     

Superfluid equation of state of dilute composite bosons or how to include 3- and 4-body problems in the many body problem

We show how the 3 and 4-body problems emerge in the BEC limit of the BEC-BCS crossover, where we treat explicitly dimers as made of two fermions. We give the argument leading, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n ^3/2, the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a _M , the composite nature of the dimers appearing only in the next order term proportional to n ².     

Quantum-to-classical crossover in full counting statistics

The reduction of quantum scattering leads to the suppression of shot noise. In this Letter, we analyze the crossover from the quantum transport regime with universal shot noise to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.