Tunneling dynamics of a few bosons with both two-and three-body interactions in a double-well potential

We investigate the tunneling dynamics of a few bosons with both two-and three-body interactions in a doublewell potential. Uncorrelated tunneling of Rabi oscillation with the minimum period can happen only when the two-and three-body interactions satisfy a critical condition, i.e., the effective interaction energy is minimized. When the atomic interactions are slightly away from the critical condition in the weak interaction regime, the uncorrelated tunneling exhibits collapse-revival character. When the atomic interactions are strong and far away from the critical condition, the correlated tunneling with Rabi oscillation occurs. The tunneling period(the period of collapse-revival) increases(decreases) when the rate between the two-body and three-body interactions is away from the corresponding critical condition or when the number of bosons increases. Further, the tunneling properties are understood with the help of the energy spectrum of the system. Eventually, the effect of the initial configuration on the tunneling dynamics of a few bosons for both odd and even numbers of bosons is studied, which results in intriguing consequences.     

Three-body model for neutron-halo nuclei

The neutron-halo nuclei,11Li,14Be,and 17B,are studied in the three-body model.The Yukawa interaction is used to describe the interaction of the two-body subsystem.For given parameters of the two-body interaction,the properties of these neutron-halo nuclei are calculated with the Faddeev equations and the results are compared with those in the variational method.It is shown that the method of the Faddeev equations is more accurate.Then the dependencies of the two-and three-body energies on the parameters are studied. We find numerically that two-and three-body correlations differ greatly from each other with the variation of the intrinsic force range.     

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.     

Three-body model for neutron-halo nuclei

The neutron-halo nuclei, ¹¹Li, ¹⁴Be, and ¹⁷B, are studied in the three-body model. The Yukawa interaction is used to describe the interaction of the two-body subsystem. For given parameters of the two-body interaction, the properties of these neutron-halo nuclei are calculated with the Faddeev equations and the results are compared with those in the variational method. It is shown that the method of the Faddeev equations is more accurate. Then the dependencies of the two- and three-body energies on the parameters are studied. We find numerically that two- and three-body correlations differ greatly from each other with the variation of the intrinsic force range.     

Coherent Destruction of Tunneling of Bosons with Effective Three-Body Interactions

The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically.In our findings,when the system is with only repulsive twobody interactions or only three-body interactions,the tunneling will be suppressed;while in the case of the coupling between two- and three-body interactions,the tunneling can be either suppressed or enhanced.Particularly,when attractive three-body interactions are twice large as repulsive two-body interactions,CDT occurs at isolated points of driving force,which is similar to the linear case.Considering different interaction,the system can experience different transformation from coherent tunneling to coherent destruction of tunneling(CDT).The quasi-energy of the system as the function of the periodically driving force shows a triangular structure,which provides a deep insight into the tunneling dynamics of the system.     

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interacting and that an impurity and a boson have a resonant zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.     

Phase separation in one-dimensional hard-core boson system with two- and three-body interactions

We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optical lattice. When these two interactions are comparable and increasing the hopping rate, physically intuitive analysis indicates that there exists a phase separation region between the solid phase with charge density wave order and superfluid phase. We identify these phases and phase transitions by numerically analyzing the density distribution, structure factor of density-density correlation function, three-body correlation function and von Neumann entropy estimator obtained by density matrix renormalization group method. These phases and phase transitions are expected to be observed in the ultra-cold polar molecule experiments by properly tuning interaction parameters as suggested in Methods by Büchler et al. [Nat. Phys. 3, 726 (2007)], which is constructive to understand the physics of ubiquitous insulating-superconducting phase transitions in condensed matter systems.     

计及两体和三体作用下的二维凝聚体中的孤子特性

使用多重尺度法,解析地研究计及粒子间两体和三体同时作用下二维凝聚体中孤子的特性. 结果发现,当凝聚体粒子间两体作用为排斥、三体作用为吸引时,凝聚体内会产生暗孤子环,且随着三体吸引作用的减弱,暗孤子环中心峰的高度逐渐降低,并当三体吸引作用消失时暗孤子环演化为一个完美的二维暗孤子. 当两体和三体作用均为排斥时,凝聚体中的暗孤子的宽度和幅度随着三体排斥作用的加强而减小,且当三体作用强度增加到与两体作用同一数量级时,凝聚体产生坍塌现象. 关键词： 玻色-爱因斯坦凝聚体 两体和三体作用 暗孤子     

Effects of three-body interactions in the parametric and modulational instabilities of Bose-Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic-quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.     

Effects of three-body interaction on collective excitation and stability of Bose--Einstein condensate

This paper investigates the collective excitation and stability of low-dimensional Bose--Einstein condensates with two- and three-body interactions by the variational analysis of the time-dependent Gross--Pitaevskii--Ginzburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate are obtained. The results show that: (i) the repulsive two-body interaction among atoms makes the frequency red-shifted for the internal excitation and the repulsive or attractive three-body interaction always makes it blue-shifted; (ii) the region for the existence of the stable bound states is obtained by identifying the critical value of the two- and three-body interactions.     

Ground States of Lattice Gases with “Almost” Convex Repulsive Interactions

To the best of our knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex interactions. Its ground-state particle configurations do not depend on any other details of the interactions and are known as the generalized Wigner lattices or the most homogeneous particle configurations. The question of the stability of this beautiful and universal result against certain perturbations of the repulsive and convex interactions is interesting in itself. Additional motivations for studying such perturbations come from surface physics (adsorption on crystal surfaces) and theories of correlated fermion systems (recent results on ground-state particle configurations of the one-dimensional spinless Falicov–Kimball model). As a first step, we studied a one-dimensional lattice gas whose two-body interactions are repulsive and strictly convex only from distance 2 on, while its value at distance 1 can be positive or negative, but close to zero. We showed that such a modification makes the ground-state particle configurations sensitive to the tail of the interactions; if the sum of the strengths of the interactions from the distance 3 on is small with respect to the strength of the interaction at distance 2, then particles form two-particle lattice-connected aggregates that are distributed in the most homogeneous way. Consequently, despite breaking of the convexity property, the ground state exhibits the feature known as the complete devil's staircase.     

Global phase diagram of the fractional quantum Hall effect arising from repulsive three-body interactions

The model of fermions in a magnetic field interacting via a purely three-body repulsive interaction has attracted interest because it produces, in the limit of short range interaction, the Pfaffian state with non-Abelian excitations. We show that this is part of a rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion. Recent breakthroughs in ultracold atoms have facilitated the realization of such a system, where this physics can be tested.     

Stabilization of trapless Bose-Einstein condensates without any management

In higher dimensions, so far, both attractive and repulsive trapless Bose-Einstein condensates (BECs) have been stabilized with the help of temporal or spatial management of the two-body contact interaction. However, in the absence of nonlinear management, up to now, there is no model to stabilize the repulsive, trapless BECs at higher dimensions. Hence, in the present study, we tried to stabilize the same and achieved with help of the interplay between three-body and higher-order interactions. In addition, we show that there is an enhancement of the stability of attractive, trapless BECs due to the inclusion of the higher-order interaction along with the two- and three-body interactions. Further, our analytical predictions are corroborated with 4th order Runge-Kutta and split-step Crank-Nicholson numerical results.     

Temperature effects on superfluid phase transition in Bose–Hubbard model with three-body interaction

We theoretically investigate the effect of the three-body on-site interactions on the Mott-insulator–superfluid transition for ultracold bosonic atoms in the framework of the Bose–Hubbard model. In particular, we explore the combined effects of three-body interaction and finite temperature on the phase diagram in detail. In order to handle system with strong local interactions a resolvent expansion technique based on the contour integral representation of the partition function has been devised. Subsequently, we derive the Landau-type expansion for the free energy in terms of the superfluid order parameter and find the phase diagrams depicting the relationships between various physical quantities of interest.     

Measurements of Tan's contact in an atomic Bose-Einstein condensate

A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with zero-range interactions. We report on measurements of the contact, using rf spectroscopy, for an (85)Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short time scales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In investigating this issue, we have located an Efimov resonance for (85)Rb atoms with loss measurements and thus determined the three-body interaction parameter. In our contact spectroscopy, in a region of observable beyond-mean-field effects, we find no measurable contribution from three-body physics.     

Three-body correlation functions and recombination rates for bosons in three dimensions and one dimension

We investigate local three-body correlations for bosonic particles in three dimensions and one dimension as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.     

Ultracold bosons with 3-body attractive interactions in an optical lattice

We study the effect of an optical lattice (OL) on the ground-state properties of one-dimensional ultracold bosons with three-body attractive interactions and two-body repulsive interactions, which are described by a cubic-quintic Gross-Pitaevskii equation with a periodic potential. Without the optical lattice and with a vanishing two-body interaction term, normalizable soliton solutions of the Townes type are possible only at a critical value of the interaction strength, at which an infinite degeneracy of the ground state occurs; a repulsive two-body interaction makes such localized solutions unstable. We show that the OL opens a stability window around the critical point when the strength of the periodic potential is above a critical threshold. We also consider the effect of an external parabolic trap, studying how the stability properties depend on the matching between minima of the periodic potential and the minimum of the parabolic trap.     

压缩氦原子团簇Hen（n＝3，4，5）排斥势及其多体展开分量计算

 采用Lowdin方法计算了处于压缩状态的氦原子团簇He_n（n＝3，4，5）的排斥势及其多体展开分量。发现随原子数目或压缩度增大，多体展开式的收敛性变差。多体展开式中两体势分量、四体势分量为正值，三体势分量和五体势分量为负值。因此，在进行近似处理时，两体近似法计算的排斥势偏高。经三体修正后的排斥势必然偏低。该计算结果与最新的实验结果定性符合。发现四体势和五体势分量对高密度氦状态方程仍然具有重要贡献。     

Quasi-two-dimensional Bose–Einstein condensates with spatially modulated cubic–quintic nonlinearities

We investigate exact nonlinear matter wave functions with odd and even parities in the framework of quasi-two-dimensional Bose–Einstein condensates (BECs) with spatially modulated cubic–quintic nonlinearities and harmonic potential. The existence condition for these exact solutions requires that the minimum energy eigenvalue of the corresponding linear Schrödinger equation with harmonic potential is the cutoff value of the chemical potential λ. The competition between two-body and three-body interactions influences the energy of the localized state. For attractive two-body and three-body interactions, the larger the matter wave order number n, the larger the energy of the corresponding localized state. A linear stability analysis and direct simulations with initial white noise demonstrate that, for the same state (fixed n), increasing the number of atoms can add stability. A quasi-stable ground-state matter wave is also found for repulsive two-body and three-body interactions. We also discuss the experimental realization of these results in future experiments. These results are of particular significance to matter wave management in higher-dimensional BECs.     

A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices

We classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for the other the interaction is two-body.