幺正极限附近费米气体反常激发模式的涡旋

在幺正极限附近研究了处于旋转外势中费米气体的量子化涡旋动力学. 选取适当的试探波函数并利用含时变分法, 得到了小振幅涡旋运动方程及描述其反常激发模式的解. 详细讨论了在幺正极限附近的反常模式产生的条件. 结果显示系统囚禁外势的临界转动频率在幺正极限附近随粒子间相互作用参数的增加而变大, 而涡旋进动的周期则随着粒子间相互作用参数的增加而减小. 关键词： 费米气体 涡旋 幺正极限     

磁阱中超冷玻色气体临界行为的观测

超冷玻色气体为研究量子临界现象提供了一个非常干净的实验系统. 弱相互作用下的三维玻色气体的临界行为与⁴He发生超流相变时的临界行为类似, 都属于三维XY型普适类. 从正常流体到超流的量子相变过程中, 系统会经历一个从无序相到长程有序相的转变; 而在相变点附近, 系统参量会表现出一些奇点的特征. 本文从实验上观测到了静磁阱中超冷⁸⁷Rb玻色气体在凝聚体相变温度T_c附近的临界行为. 原子气体从静磁阱中释放, 经过30 ms的自由飞行后, 通过吸收成像得到原子气体的动量分布; 然后从中扣除热原子气体的动量分布, 提取出空间上处于临界区域内的原子气体动量分布, 并对不同温度下的动量分布半高宽进行统计. 统计结果显示: 在非常接近相变温度T_c时, 动量分布的半高宽突然减小, 表现出十分明显的奇点行为.     

Superfluid phase transition in trapped atomic Fermi gas

Superfluid phase transition in an atomic Fermi gas confined to a harmonic trap is studied. The critical transition temperature and the temperature dependence and spatial shape of the order parameter are determined. The spectrum and wave functions of single-particle and collective excitations are obtained for a gas in the superfluid phase. The excitation eigenfrequencies exhibit a pronounced temperature dependence, allowing, e.g., identification of the superfluid phase.     

Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.     

Phase diagram and deformed phase separation for a trapped Fermi gas with population imbalance and BCS pairing interaction

We study the phase separated state of an ultracold atomic Fermi gas confined in a three-dimensional quantum harmonic trap with a BCS pairing interaction. Examining various finite-temperature phase diagrams, we investigate the interplay between the filling of the quantum trap energy levels and the pairing energy. We find that a low (high) filling leads to a large (small) critical population imbalance for the superfluid/normal transition, together with a fully (partially) polarized normal part. We also show that the decrease of the density leads to a changeover of the shape of the superfluid core from an equipotential form to a deformed one. Moreover, we clarify the intrinsic mechanisms that lead to the deformation, providing a unified scenario for phase separation and deformation in a trapped Fermi gas, allowing for a possible interpretation of the apparently controversial experimental findings.     

Superfluid expansion of a rotating Fermi gas

We study the expansion of a rotating, superfluid Fermi gas. The presence and absence of vortices in the rotating gas are used to distinguish the superfluid and normal parts of the expanding cloud. We find that the superfluid pairs survive during the expansion until the density decreases below a critical value. Our observation of superfluid flow in the expanding gas at 1/kFa=0 extends the range where fermionic superfluidity has been studied to densities of 1.2x10(11) cm(-3), about an order of magnitude lower than any previous study.     

Phase separation in a polarized Fermi gas at zero temperature

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Single-particle excitations and the order parameter for a trapped superfluid Fermi gas

It is found that the character of single-particle excitations of a trapped neutral-atom Fermi gas is strongly influenced by a superfluid phase transition. Below the transition temperature the presence of a spatially inhomogeneous order parameter (gap) shifts the excitation eigenenergies upward and leads to the appearance of in-gap excitations localized in the outer part of the gas sample. The eigenenergies become sensitive to the gas temperature and are no longer multiples of the trap frequencies. These features should manifest themselves in a strong change of the density oscillations induced by modulations of the trap frequencies and can be used for identifying the superfluid phase transition. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 392–397 (25 September 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Superfluidity and phase transitions in a resonant Bose gas

The atomic Bose gas is studied across a Feshbach resonance, mapping out its phase diagram, and computing its thermodynamics and excitation spectra. It is shown that such a degenerate gas admits two distinct atomic and molecular superfluid phases, with the latter distinguished by the absence of atomic off-diagonal long-range order, gapped atomic excitations, and deconfined atomic π-vortices. The properties of the molecular superfluid are explored, and it is shown that across a Feshbach resonance it undergoes a quantum Ising transition to the atomic superfluid, where both atoms and molecules are condensed. In addition to its distinct thermodynamic signatures and deconfined half-vortices, in a trap a molecular superfluid should be identifiable by the absence of an atomic condensate peak and the presence of a molecular one.     

Observation of nearly perfect irrotational flow in normal and superfluid strongly interacting Fermi gases

We study the hydrodynamic expansion of a rotating strongly interacting Fermi gas by releasing a cigar-shaped cloud with a known angular momentum from an optical trap. As the aspect ratio of the expanding cloud approaches unity, the angular velocity increases, indicating quenching of the moment of inertia I to as low as 0.05 of the rigid body value I(rig). Remarkably, we observe this behavior in both the superfluid and collisional normal fluid regimes, which obey nearly identical zero-viscosity irrotational hydrodynamics. We attribute irrotational flow in the normal fluid to a decay of the rotational part of the stream velocity during expansion, which occurs when the shear viscosity is negligible. Using conservation of angular momentum, we directly observe a fundamental result of irrotational hydrodynamics, I/I(rig) = delta2, where delta is the deformation parameter of the cloud.     

Observation of phase separation in a strongly interacting imbalanced fermi gas

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.     

Superfluidity-insulator phase transition in ensemble of Fermi atoms in optical lattice

An ultracold Fermi gas in an optical lattice with a parabolic potential is modeled by the quantum Monte Carlo method. The gas density profile is calculated in the Hubbard model; it is shown that a domain with a density of one atom per site is formed in the trap that corresponds to the Mott insulator state. The insulator phase is surrounded by a superfluid region occupying the center of the trap, as well as its periphery.     

Expansion of an interacting fermi gas

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.     

Metastability in spin-polarized Fermi gases

We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2?s.     

Rotating Fermi gases in an anharmonic trap

Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency Ω_DO leads to a ‘donut’-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein condensates. The free expansion of the gas after suddenly turning off the trap is considered and characterized by the time and rotation frequency dependence of the aspect ratio. Temperature effects are also taken into account and both low- and high-temperature expansions are presented for the relevant thermodynamical quantities. In the high-temperature regime a virial theorem approach is used to study the delicate interplay between rotation and anharmonicity.     

Direct observation of irrotational flow and evidence of superfluidity in a rotating Bose-Einstein condensate

We have observed the expansion of vortex-free, rotating Bose condensates after their sudden release from a slowly rotating anisotropic trap. Conservation of angular momentum, combined with the constraint of irrotational flow, cause the rotating condensate to expand in a distinctively different way to one released from a static (nonrotating) trap. This difference provides clear experimental evidence of the purely irrotational velocity field associated with a superfluid. We observed this behavior in absorption images taken along the rotation axis.     

Signatures of resonance superfluidity in a quantum Fermi gas

We predict a direct and observable signature of the superfluid phase in a quantum Fermi gas, in a temperature regime already accessible in current experiments. We apply the theory of resonance superfluidity to a gas confined in a harmonic potential and demonstrate that a significant increase in density will be observed in the vicinity of the trap center.