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.     

Extracting the condensate density from projection experiments with Fermi gases

A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the Bose-Einstein condensation (BEC) sides, thus "projecting" the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of the mean field.     

Self-trapping and Macroscopic Tunnelling of Superfluid Fermi Gases in Multi-well Potentials

We study the tunnelling dynamics of superfluid Fermi gases trapped in multi-well system along the BEC-BCS crossover. Within the hydrodynamical model and by using the multi-mode approximation, the self-trapping dynamics of superfluid Fermi gases in multi-well system are obtained numerically. We find that the self-trapping to diffusion transition strongly depends on the well number. When the well number is less than three, the self-trapped state takes place easier on the BEC side than that on the BCS side. However, when the well number is larger than three, the self-trapped state takes place easier on the BCS side instead of the BEC side. Furthermore, by considering a superfluid of ⁴⁰K atoms, we obtain the zero-mode and π-mode Josephson frequencies of coherent atomic oscillations in double-well system. It is noteworthy that the Josephson mode, especially, the existence of π-mode frequency strongly depends on the atoms number on the BCS side.     

Dynamics of dark solitons in a trapped superfluid fermi gas

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation for the oscillation period in terms of observable quantities, which we confirm by solving the time-dependent Bogoliubov-de Gennes equations. Hence we reveal the appearance and dynamics of solitons across the crossover, and show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.     

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.     

Superconductivity of the FeSe/SrTiO_3 Interface in View of BCS–BEC Crossover

In paired Fermi systems,strong many-body effects exhibit in the crossover regime between the Bardeen-CooperSchrieffer(BCS)and the Bose-Einstein condensation(BEC)limits.The concept of the BCS-BEC crossover,which is studied intensively in the research field of cold atoms,has been extended to condensed matters.Here by anal.yzing the typical superconductors within the BCS-BEC phase diagram,we find that FeSe-based superconductors are prone to shift their positions in the BCS-BEC crossover regime by charge doping or substrate substitution,since their Fermi energies and the superconducting gap sizes are comparable.Especiall.y at the interface of single-layer FeSe on SrTiO_3 substrate,the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials,indicating that the pairing interaction is effectively modulated.We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons,demonstrating its flexible tunability within the BCS-BEC crossover regime.     

Finite-temperature collective dynamics of a Fermi gas in the BEC-BCS crossover

We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of the quantum gas in terms of hydrodynamic or near-collisionless behavior. We obtain a crossover phase diagram for collisional properties, showing a large region where a nonsuperfluid strongly interacting gas shows hydrodynamic behavior. In a narrow interaction regime on the BCS side of the crossover, we find a novel temperature-dependent damping peak, suggesting a relation to the superfluid phase transition.     

Negative echo in the density evolution of ultracold fermionic gases

We predict a nonequilibrium critical phenomenon in the space-time density evolution of a fermionic gas above the temperature of transition into the superfluid phase. On the BCS side of the Bose-Einstein condensation-BCS crossover, the evolution of a localized density disturbance exhibits a negative echo at the point of the initial inhomogeneity. Approaching the Bose-Einstein condensation side, this effect competes with the slow spreading of the density of bosonic molecules. However, even here the echo dominates for large enough times. This effect may be used as an experimental tool to locate the position of the transition.     

Unitarity Schrödinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross-Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.     

Universal correlations, pseudo‐gaps and condensation mechanisms in high‐Tc superconductors

We combine universal correlations between T_c and n_s/m^* (superconducting carrier density/effective mass) found by μSR with the pseudo gap behavior found in the underdoped region by various techniques to develop a picture for explaining doping dependence of high‐T_c superconductivity in terms of a crossover from Bose–Einstein to BCS condensation. μSR results in overdoped and Zn‐substituted systems suggest that behavior on the high‐density side is more complicated than expected in a simple BCS model. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optical soliton solutions of the generalized higher-order nonlinear Schrödinger equations and their applications

The propagation of the optical solitons is usually governed by the higher order nonlinear Schrödinger equations (NLSE). In optics, the NLSE modelizes light-wave propagation in an optical fiber. In this article, modified extended direct algebraic method with add of symbolic computation is employed to construct bright soliton, dark soliton, periodic solitary wave and elliptic function solutions of two higher order NLSEs such as the resonant NLSE and NLSE with the dual-power law nonlinearity. Realizing the properties of static and dynamic for these kinds of solutions are very important in various many aspects and have important applications. The obtaining results confirm that the current method is powerful and effectiveness which can be employed to other complex problems that arising in mathematical physics.     

Superconductivity in ultrasmall metallic grains

We review recent experimental and theoretical work on superconductivity in ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an individual grain can be measured by the technique of single‐electron tunneling spectroscopy, and reveals parity effects indicative of pairing correlations in the grain. After introducing the discrete BCS model that has been used to model such grains, we review a phenomenological, grand‐canonical, variational BCS theory describing the paramagnetic breakdown of these pairing correlations with increasing magnetic field. We also review recent canonical theories that have been developed to describe how pairing correlations change during the crossover, with decreasing grain size, from the bulk limit to the limit of few electrons, and compare their results to those obtained using Richardson's exact solution of the discrete BCS model.     

Extreme waves that appear from nowhere: On the nature of rogue waves

We have numerically calculated chaotic waves of the focusing nonlinear Schrr?odinger equation (NLSE), starting with a plane wave modulated by relatively weak random waves. We show that the peaks with highest amplitude of the resulting wave composition (rogue waves) can be described in terms of exact solutions of the NLSE in the form of the collision of Akhmediev breathers.     

BCS–BEC crossover in one-dimensional integrable model

The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.     

Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the
tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.     

Waves that appear from nowhere and disappear without a trace

The title (WANDT) can be applied to two objects: rogue waves in the ocean and rational solutions of the nonlinear Schrödinger equation (NLSE). There is a hierarchy of rational solutions of ‘focussing’ NLSE with increasing order and with progressively increasing amplitude. As the equation can be applied to waves in the deep ocean, the solutions can describe “rogue waves” with virtually infinite amplitude. They can appear from smooth initial conditions that are only slightly perturbed in a special way, and are given by our exact solutions. Thus, a slight perturbation on the ocean surface can dramatically increase the amplitude of the singular wave event that appears as a result.     

BEC-BCS crossover in "magnetized" Feshbach-resonantly paired superfluids

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.     

BCS wave-function approach to the BEC-BCS crossover of exciton-polariton condensates

The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.     

Solving forward and inverse problems of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via PINN deep learning

In this paper, based on physics-informed neural networks (PINNs), a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations (PDEs) and other types of nonlinear physical models, we study the nonlinear Schrödinger equation (NLSE) with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential, which is an important physical model in many fields of nonlinear physics. Firstly, we choose three different initial values and the same Dirichlet boundary conditions to solve the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via the PINN deep learning method, and the obtained results are compared with those derived by the traditional numerical methods. Then, we investigate the effects of two factors (optimization steps and activation functions) on the performance of the PINN deep learning method in the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential. Ultimately, the data-driven coefficient discovery of the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential or the dispersion and nonlinear items of the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential can be approximately ascertained by using the PINN deep learning method. Our results may be meaningful for further investigation of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential in the deep learning.     

Energy Spectrum of a Degenerate Fermi Gas at the BEC-BCS Crossover

A theoretical study of the BCS-BEC crossover is presented. Starting from a two-channel Boson-Fermion resonance model, the BCS-Bogoiubov mean-field method and the Green＇s function method are adopted. The result shows that we can end up with a BCS-type theory but with a composite order parameter. Calculation shows that the Bose condensate of BCS Cooper pairs is proportional to the molecular BEC of Bose molecules. The resonance superfluid phase is indicated by the energy spectrum with an obvious interpretation of the transition mechanism.