超冷原子中拓扑超流的发展现状

拓扑超流态是一种奇异物质态,它的内部受能隙保护,而在其系统边缘却可以容纳无能隙的Majorana 费米子。由于该粒子满足非阿贝尔统计,并且受拓扑保护具有良好的稳定性,用它 们携带量子化的信息,可以用于拓扑量子计算的研究。近年来,理论工作预测了各类系统中可能 存在的拓扑超流态。我们首先介绍了在各类光晶格模型中的拓扑超流, 光晶格的超冷原子具有良 好的可控性与普适性,是实现拓扑超流的理想模型系统。接下来我们介绍了自旋轨道耦合调控下 的拓扑超流,自旋轨道耦合效应是诱导拓扑相的重要条件,并且人们已经在实验上合成了人工自 旋轨道耦合,这为实验上观测拓扑超流取得了突破性的进展。随着近年来实验技术的提高,曾经 难以在实验中观测的,被人们所忽略的拓扑Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) 超流相也 成为了人们研究的热点,因此我们接下来介绍了拓扑的FFLO 超流。此外,我们还介绍了拓扑超 流其他方面的进展,包括孤子引诱的拓扑超流、三组分的拓扑超流、大陈数的拓扑超流以及拓扑 超流临界温度的提高。在实验中,如何检测与实现拓扑超流,是其研究的目的及意义所在,因 此我们在文章的最后介绍了拓扑超流的识别与实现。     

Swallowtail band structure of the superfluid Fermi gas in an optical lattice

We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.     

Textural critical velocity of 3He-A in the limit of large magnetic fields

A path linking any uniform, current carrying state to the true equilibrium one is proposed, which becomes monotonically decreasing in energy if the superfluid velocity exceeds a critical value. This critical velocity as a function of the orientation is calculated.     

Generalized Landau superfluidity criterion

An analysis of experimental data shows that, in addition to phonon-roton excitations in superfluid helium, there necessarily exist at least one branch of elementary excitations whose energy spectrum strongly depends on temperature. On this basis, the Landau superfluidity criterion is generalized for several branches of elementary excitations, taking into account that the critical velocity should vanish during the phase transition of liquid helium from the superfluid state to the normal state.     

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.     

Phase diagram of a strongly interacting polarized Fermi gas in one dimension

Based on the integrable Gaudin model and local density approximation, we discuss the ground state of a one-dimensional trapped Fermi gas with imbalanced spin population, for an arbitrary attractive interaction. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an Fulde-Ferrell-Larkin-Ovchinnikov structure, and predict the resulting mode frequency as a function of the spin polarization.     

Holographic p-wave superfluid with Weyl corrections

In this work,we study the effects of the Weyl corrections on the p-wave superfluid phase transition in terms of an EinsteinMaxwell theory coupled to a complex vector field.In the probe limit,it is observed that the phase structure is significantly modified owing to the presence of the higher order Weyl corrections.The latter,in general,facilitates the emergence of the superfluid phase as the condensate increases with the Weyl coupling measured byγ.Moreover,several features about the phase structure of the holographic superfluid are carefully investigated.In a specific region,the phase transition from the normal phase to the superfluid phase is identified to be the first order,instead of being the second order,as in the cases for many holographic superconductors.By carrying out a numerical scan of model parameters,the boundary dividing these two types of transitions is located and shown to be rather sensitive to the strength of Weyl coupling.Also,a feature known as"Cave of Winds",associated with the emergence of a second superfluid phase,is observed for specific choices of model parameters.However,it becomes less prominent and eventually disappears asγincreases.Furthermore,for temperature in the vicinity of the critical one for vanishing superfluid velocity,denoted by T0,the supercurrent is found to be independent of the Weyl coupling.The calculated ratio,of the condensate with vanishing superfluid velocity to that with maximal superfluid velocity,is in good agreement with that predicted by Ginzburg-Landau theory.While compared with the impact on the phase structure owing to the higher curvature corrections,the findings in our present study demonstrate entirely different characteristics.Further implications are discussed.     

Superfluid to Normal Fluid Phase Transition in the Bose Gas Trapped in Two-Dimensional Optical Lattices at Finite Temperature

We develop the Hartree-Fock-Bogoliubov theory at finite temperature for Bose gas trapped in the two-dimensional optical lattice with the on-site energy low enough that the gas presents superfluid properties. We obtain the condensate density as function of the temperature neglecting the anomalous density in the thermodynamics equation. The condensate fraction provides two critical temperature. Below the temperature \(T_{C1}\), there is one condensate fraction. Above two condensate fractions merger up to the critical temperature \(T_{C2}\). At temperatures larger than \(T_{C2}\), the condensate fraction is null and, therefore, the gas is normal fluid. We resume by a finite-temperature phase diagram where three domains can be identified: the normal fluid, the superfluid with one stable condensate fraction and the superfluid with two condensate fractions being unstable one of them.     

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We find that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.     

Equilibrium shape of rotating helium crystals

We have studied theoretically the effects of rotation on the equilibrium shape of the interface between superfluid and solid helium. Surface structures in the shape of hillocks and ridges appear in the presence of a vortex lattice in the superfluid. These structures are very sensitive to the orientation of the interface boundary with respect to the crystal planes when surface stiffness is very anisotropic, as occurs well below the roughening transition. We predict the appearance of ring shaped facets for fast rotation speeds. These effects should be observable by using optical techniques.     

Crystalline order in superfluid (3)He films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).     

Symmetry-breaking vortex-lattice of a binary superfluid in a rotating bucket

We study spontaneous-symmetry-broken phase-separated vortex lattice in a weakly interacting uniform rapidly rotating binary Bose superfluid contained in a quasi-two-dimensional circular or square bucket. For the inter-species repulsion above a critical value, the two superfluid components separate and form a demixed phase with practically no overlap in the vortex lattices of the two components, which will permit an efficient experimental observation of such vortices and study their properties. In case of a circular bucket with equal intra-species energies of the two components, the two components separate into two non-overlapping semicircular domains for all frequencies of rotation Ω generating distinct demixed vortex lattices. In case of a binary Bose superfluid in both circular and square buckets, (a) the number of vortices increases linearly with Ω in agreement with a suggestion by Feynman, and (b) the rotational energy in the rotating frame decreases quadratically with Ω in agreement with a suggestion by Fetter.     

Effective area and expansion energy of trapped Bose gas in a combined magnetic-optical potential

In this Letter a conventional method of statistical physics and quantum mechanics is used to calculate the effective area and the expansion energy for trapped Bose gas in a combined optical-magnetic potential. Correction due to the finite number of particles, interatomic interaction and the deepness of the lattice potential are given simultaneously. It is found that the system possess two different phases which are superfluid phase and Mott insulator phase. The critical temperature which separate these two phases is calculated. In the superfluid phase both the effective area and expansion energy is sensitive to the variation of temperature and lattice depth. Mott insulator phase is characterized by vanishing of the condensed fraction and freezing of the effective area at the value which corresponding to BEC transition temperature. So these parameters can serve as a practical thermometer for such system. The expansion energy shows that the lack of expansion in any direction is due to the strong anisotropy of the trapping potential in this direction. The obtained results provide a solid theoretical foundation for the current experiments.     

自旋-轨道耦合作用下玻色-爱因斯坦凝聚在量子相变附近的朗道临界速度

各向异性超流体中的朗道临界速度并非简单地由运动方向的元激发能谱决定.在自旋-轨道耦合作用下的双分量玻色-爱因斯坦凝聚中,当系统跨过平面波相与零动量相之间的量子相变时,尽管超流声速连续变化,但垂直于自旋-轨道耦合方向的朗道临界速度会出现跳变,跳变幅度随自旋相互作用强度单调增加.根据线性响应理论,计算了凝聚体中运动杂质在不同速度下的能量耗散率,提出可以通过能量耗散观测临界速度在量子相变处的不连续性.     

Dynamical effects in superfluid helium 4

The close structural similarity between the commutation relations of harmonic oscillator operators and the operators for Bose fields is exploited to study the excitation spectrum in superfluid helium 4. By applying ‘broken symmetry’ condition it is shown how the creation of phonon gives rise to superfluid behaviour of liquid He 4. The energy gap needed for roton excitation is derived.     

Condensate formation and vortex generation in Bose gas upon cooling

The mechanism of transition of a Bose gas to the superfluid state via thermal fluctuations under the condition of external cooling at a temperature above the transition point is considered. The probability of formation of such critical fluctuations (instantons) is calculated; it is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.     

Measurements of the critical initiation radius and unsteady propagation of n-decane/air premixed flames

Unsteady flame propagation, the critical radius for flame initiation, and multiple flame regimes of n-decane/air mixtures are studied experimentally and computationally using outwardly propagating spherical flames at various equivalence ratios and pressures. The transient flame speeds, trajectories, and critical radius are measured. The experimental results are compared with direct numerical simulations using detailed high temperature kinetic models. Both experimental and numerical results show that there exist multiple flame regimes in the unsteady spherical flame initiation process. The transition between the flame regimes depends strongly on the mixture equivalence ratio (or Lewis number). It is found that there is a critical flame radius and that it increases dramatically as the mixture equivalence ratio and pressure decrease. The large increase of critical flame radius leads to a dramatic increase of the minimum ignition energy. Furthermore, the flame thickness and the radical pool concentration change significantly during the transition from the ignition flame regime to the self-sustained propagating flame regime. For the same steady state flame speeds, the predicted unsteady flame speeds and the critical flame radius differ significantly from the experimental results. Moreover, different chemical kinetic mechanisms predict different unsteady flame speeds. The existence of multiple flame regimes and the large critical radius of lean liquid fuel mixtures make the ignition of lean mixtures at low pressure and the development of a validated kinetic model more challenging. The unsteady flame regimes, speeds, and critical flame radius should be included as targets of future kinetic model development for turbulent combustion modeling.     

光格子中玻色-爱因斯坦凝聚体的超流相

本文采用Bogliubov方法分析了光格子中玻色-爱因斯坦凝聚体的能谱,得到超流-Mott相变条件,指出光格子中BEC是一种典型的超流态,最后给出了超流速度.     

Repetitive single vortex-loop creation by a vibrating wire in superfluid 3He-B

Spectacular features are observed on the velocity-force characteristics of a vibrating wire resonator in superfluid 3He-B at ultralow temperatures. Both plateaus and discontinuities are seen in the characteristics. The plateaus seem to have two separate critical velocities where first some "event" occurs, which causes the wire to lose energy and slow down, followed by a second lower critical velocity where the event decouples. It is suggested that these events are due to vortex-loop creation at protuberances on the vibrating wire. This opens up the possibility of controlling the creation of vorticity through specially prepared protuberances.