Spectroscopic signatures of nonequilibrium pairing in atomic fermi gases

We determine the radio-frequency (rf) spectra for nonstationary states of a fermionic condensate produced by a rapid switch of the scattering length. The rf spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast with equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter, the rf-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where a rf photon in addition to breaking a pair emits or absorbs oscillation quanta.     

Dynamical vanishing of the order parameter in a fermionic condensate

We analyze the dynamics of a condensate of ultracold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a nonstationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid states -- the gap and the condensate fraction vanish, while the superfluid density is nonzero.     

N-particle Bogoliubov vacuum state

We consider the Bogoliubov vacuum state in the number-conserving Bogoliubov theory proposed by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We show that, in the particle representation, the vacuum can be written in a simple diagonal form. The vacuum state can describe the stationary N-particle ground state of a condensate in a trap, but it can also represent a dynamical state when, for example, a Bose-Einstein condensate initially prepared in the stationary ground state is subject to a time-dependent perturbation. In both cases the diagonal form of the Bogoliubov vacuum can be obtained by basically diagonalizing the reduced single-particle density matrix of the vacuum. We compare N-body states obtained within the Bogoliubov theory with the exact ground states in a 3-site Bose-Hubbard model. In this example, the Bogoliubov theory fails to accurately describe the stationary ground state in the limit when N → ∞ but a small fraction of depleted particles is kept constant.     

Fragmented and single condensate ground states of spin-1 bose Gas

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order N) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.     

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.     

谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的巨涡旋态

研究谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的基态。发现凝聚体形成巨涡旋时,其涡旋个数等于平均角动量,且凝聚体密度分布和角动量密度分布相同,进而得到凝聚体形成巨涡旋时所处基态是角动量的本征态。发现势阱从各向同性的环形势阱逐渐变为各向异性的环形势阱的过程中,凝聚体的平均角动量与涡旋个数之比先由1平缓下降,然后迅速下降,最后保持在0.5附近。同时给出凝聚体密度分布和角动量分布的特征,并作出相应解释。     

梯度磁场中自旋-轨道耦合旋转两分量玻色-爱因斯坦凝聚体的基态研究

利用准二维Gross-Pitaevskii方程,研究了在梯度磁场中具有自旋-轨道耦合的旋转两分量玻色-爱因斯坦凝聚体的基态结构.探索了自旋-轨道耦合作用和梯度磁场对基态的影响.结果发现,在梯度磁场下,随着自旋-轨道耦合强度增大,基态结构由skyrmion格子逐渐过渡为skyrmion列.对于弱自旋-轨道耦合和小旋转频率情况,增大磁场梯度强度可导致基态由平面波相转变为half-skyrmion;对于强自旋-轨道耦合和大旋转频率情况,梯度磁场可诱导hidden涡旋的产生.梯度磁场、自旋-轨道耦合和旋转作为体系的调控参数,可用于控制不同基态相间的转化.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Trapped Bose-Einstein condensate in the weakly interacting limit

We study the Bose-Einstein condensate in a harmonic trap in the weakly interacting limit well below the temperature for Bose-Einstein condensation transition. We show that the ground state is a canonical coherent state. The energy spectrum, the chemical potential, and the order parameter for the condensate are obtained analytically.     

Zero-energy bound states in superconductor/ferromagnet superlattices

Andreev bound states in monoatomic superconductor–ferromagnet (S/F) superlattices are studied theoretically, assuming tunneling between S and F layers in perpendicular direction. Andreev reflection at S/F interfaces is strongly affected by the exchange interaction h in F layers. In the ground state, only for h≠0 zero-energy states (ZES) are formed on S and F layers. For h=0, corresponding to superconductor–normal metal (S/N) superlattices, ZES may appear in the nonequilibrium phase, =π. This is found both for s-wave and d-wave symmetry of the order parameter in S. The conditions for ZES are obtained as a function of h, of the transfer integral t for movement of quasiparticles (QPs) between S and F layers, and of the corresponding ground state phase difference _eq between two neighboring S layers.     

A continuation BSOR-Lanczos–Galerkin method for positive bound states of a multi-component Bose–Einstein condensate

We develop a continuation block successive over-relaxation (BSOR)-Lanczos–Galerkin method for the computation of positive bound states of time-independent, coupled Gross–Pitaevskii equations (CGPEs) which describe a multi-component Bose–Einstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a single-component BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multi-component BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a two/three-component BEC are solved efficiently and reliably by the continuation BSOR-Lanczos–Galerkin method.     

Symmetry induced compression of discrete phase space

A compressed representation is described of the state space of discrete systems with some kind of symmetry of its states. An initial state space is represented as a network of states. Two states are linked if some single process leads from one state to another. The network can be compressed by a grouping of states into classes. States in the same class are represented by nodes of equal degree. Further, subclasses are defined: states belong to the same subclass if their neighbouring states belong to the same subclasses. The goal is that the equilibrium probability distribution of states in the initial network can be found from the probability of subclasses in the compressed network. The approach is applied to three exemplary systems: two pieces of a triangular lattice (25 and 36 nodes) with Ising spins at the lattice nodes, and a roundabout with three access roads and three exit roads. The compression is from 3630 ground states to 12 subclasses, from 263 640 ground states to 409 subclasses, and from 729 states to 55 subclasses, respectively.     

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.     

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations.     

Cosmological constant: a lesson from the effective gravity of topological weyl media

Topological matter with Weyl points, such as superfluid ³He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates (S. Finazzi, S. Liberati, and L. Sindoni, Phys. Rev. Lett. 108, 071101 (2012); arXiv:1103.4841). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in ³He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter ??, which in ³He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant ?? is huge, the cosmological term T _??? ^?? itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.     

Bound states of the Josephson degrees of freedom and trap oscillations

It is shown that the interaction of the Josephson degrees of freedom with states of condensate motion can produce their equilibrium bound states. As a result of the appearance of these states, first, the tunneling splitting is significantly increased in double-well trapped condensates. Second, the bound states can realize an absolute minimum of the thermodynamic energy for a sufficiently strong interaction. Transition to the new ground state is a second-order phase transition. The existence of the bound state leads to an equilibrium distortion of the condensate shape. This implies that the Josephson states can be detected by observing the change in the condensate shape.     

One Dimensional Models with a Singular Potential of the Type −<Emphasis Type="Italic">αδ</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)+<Emphasis Type="Italic">βδ</Emphasis>′(<Emphasis Type="Italic">x</Emphasis>)

We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique. Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy “quasibound states” appear. The harmonic oscillator demonstrates the general result that for a symmetric potential the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation is attractive or repulsive. No states are created or annihilated.     

Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flat-band Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property of the degeneracy is the same as the domain wall solutions in the XXZ Heisenberg–Ising model. We derive a useful recursion relation for the normalization of the domain wall ground state. Using this recursion relation, we discuss the convergence of the ground state expectation values of arbitrary local operators in the infinite-volume limit. In the ground state of the infinite-volume system, the translational symmetry is spontaneously broken by this structure. We prove that the cluster property holds for the domain wall ground state and excited states. We also estimate bounds of the ground state expectation values of several observables, such as one- and two-point functions of spin and electron number density.     

电荷量子比特与量子化光场之间的纠缠

研究了初态为混合态的电荷量子比特与量子化光场之间的纠缠.通过求解系统的concurrence下限, 研究初态的混合度λ和失谐量Δ对系统纠缠随时间演化的影响. 在弱场中, 电荷量子比特初始是激发态的系统, 其纠缠度远远大于电荷量子比特初始是基态的系统, 并且Δ对系统的纠缠有明显的抑制作用. 在强场中, 电荷量子比特初始分别为激发态和基态时系统的纠缠演化接近一致, 初态混合度最高时系统的纠缠度最小, 并且Δ对系统纠缠的影响变弱. 关键词： 约瑟夫森结 纠缠 混合态 concurrence下限     

量子激发态最陡下降微扰理论

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。 关键词：