耦合腔系统中的三体纠缠演化

研究由耦合腔和四个全同的二能级原子构成的系统中三体纠缠态纠缠量的演化. 四个原子分别囚禁在单模耦合腔A和B中, 并且原子通过单光子跃迁与腔场发生共振相互作用. 采用纠缠张量方法, 通过数值计算研究了每个腔中三体纠缠的演化. 讨论了原子与腔场间的耦合强度对三体纠缠演化的影响. 研究结果表明: 原子与腔场间的两体纠缠强于原子间的两体纠缠, 每个腔中的三体纠缠是两体纠缠相干叠加的结果.     

Differential equations in momentum space for the three-body problem in the case of pointlike pair interactions

Corrects schemes for solving equations of three-body dynamics for systems governed by a zerorange two-body interaction are considered. Correlations between spectral features of a three-boson system are obtained. The results are compared with the results obtained by calculating the spectra and scattering lengths in the system of three helium atoms with realistic two-body interaction potentials.     

Dynamics of entanglement in one-dimensional Ising chains with two- and three-body interactions

The evolution of entanglement in a one-dimensional Ising chain with both two-body and three-body interactions, under two types of initial states, is numerically simulated. We analyse three problems concerning the dynamics of pairwise entanglement: (i) the possibility of generating large entanglement from an initial separable state by the use of a selective irradiation scheme; (ii) the effect of three-body interaction on the generation of entanglement from an initial separable state; (iii) the effect of three-body interaction on the decay of the entanglement from a state with only (m,n)-pair maximal entangled, and the rest in product form. It is shown that a large pairwise concurrence C_mn can be obtained when the resonant, transverse radio-frequency fields are selectively switched on from the mth to nth spins. Three-body interaction will decrease the oscillation amplitude of the nearest neighbour concurrence, while the oscillation amplitude of remote pairwise concurrence will be greatly increased with the consideration of three-body interactions. For an initial (m,n)-pair maximal entangled state, a slow decay of the pairwise concurrence C_mn is found with the introduction of three-body interactions.     

A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.     

耦合系数对Tavis-Cummings模型中三体纠缠态纠缠量的影响

研究了两个全同二能级原子与单模场相互作用的Tavis-Cummings模型中的量子纠缠.在两原子初始时处于基态,光场处于单光子状态下,得出体系状态演化为近似W纠缠态.结果表明:两原子耦合量越大,三体纠缠态中两两纠缠量和三体纠缠量越小,其中两原子间纠缠量和三体纠缠量减小的程度更大,并且三体纠缠态中两两纠缠量和三体纠缠量的振荡周期也相应减小.     

Quantum Entanglement in a System of Two Spatially Separated Atoms Coupled to the Thermal Reservoir

We study quantum entanglement between two spatially separated atoms coupled to the thermal reservoir. The influences of the initial state of the system, the atomic frequency difference and the mean number of the thermal field on the entanglement are examined. The results show that the maximum of the entanglement obtained with nonidentical atoms is greater than that obtained with identical atoms. The degree of entanglement is progressively decreased with the increase of the thermal noise. Interestingly, the two atoms can be easily entangled even when the two atoms are initially prepared in the most mixed states.     

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.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.     

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。     

两纠缠原子之一与腔场相互作用过程的纠缠研究

使一对纠缠的二能级原子之一与单模真空腔场发生共振相互作用,通过选择不同的演化时间,对这个三体系统的其中之一做选择性测量,可调节另外两体的纠缠状态。在不做测量时,研究了在不同的初始状态下,三体纠缠及三体中两两纠缠的演化特性。结果表明,该体系纠缠都呈现周期性的振荡,特别是,通过选择合适的初始状态和演化时间可生成强壮纠缠态———W纠缠态;在特定演化时刻,可使两纠缠原子的纠缠信息完全转化到腔外原子和腔场中去。     

Tavis-Cummings模型中三体纠缠态纠缠量的演化特性

研究两个全同二能级原子与单模场相互作用的Tavis-Cummings模型中的量子纠缠.在场和两原子初始分别为真空场和纠缠或非纠缠状态下，得出体系状态将演化为三体近似W纠缠态.通过对纠缠量的计算得出：该三体近似W纠缠态纠缠量的演化特性将随三体所处的初始状态、原子间及原子与场间的耦合系数、失谐程度、原子反转粒子数的变化而变化.值得一提的是可得出原子间耦合作用强度对纠缠量的非线性效应，并且纠缠量展现出与原子反转粒子数一致的周期振荡现象. 关键词： W纠缠态 纠缠量 反转粒子数     

Accumulation of three-body resonances above two-body thresholds

We calculate resonances in the three-body system with attractive Coulomb potential by solving homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved using the Coulomb-Sturmian separable expansion method. This approach allows us to study the exact behavior of the three-body Coulomb systems near the threshold. A negatively charged positronium ion is used as a test case. In addition to locating all previously known S-wave resonances of the positronium ion, we also find a large number of new resonant states that accumulate just slightly above the two-body thresholds. The pattern of accumulation of resonant states above the two-body thresholds suggests that probably they are infinite in number. We conjecture that this may be a general property of the three-body system with an attractive Coulomb potential.     

A low-energy physics of an extended Hubbard chain with additional three-body couplings

A low-energy physics of a one-dimensional interacting electron system at half filling is constructed. Beyond the usual two-body approximation, the two different types of three-body couplings are highlighted. The rich ground-state phase diagrams are obtained at weak coupling. In the case of two-body repulsions, the off-diagonal three-body coupling favors the bond-located density-wave insulating phases, while the diagonal three-body attraction favors the superconducting phases.     

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.     

Environment-Induced Entanglement for a Tripartite System in Non-Markovian Dissipation

We show that entanglement between three two-level atoms can be generated if the three atoms interact with a common structured reservoir, but do not interact directly with each other. Comparing with the results in Markovian case, we find that much higher values of bipartite and tripartite entanglement can be obtained for an initially factorized state of the tripartite system. The maximal value of entanglement depends on the detuning and the strength of relative coupling between the atoms and the reservoir.     

Manifestation of Three-Body Forces in Three-Body Bethe–Salpeter and Light-Front Equations

Bethe–Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe–Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.     

A simple coordinate space approach to three-body problems — Examples: Halo nucleus and double-λ hypernucleus

We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in simple coordinate space variational approach. The method is constructive and gives an efficient way of resolving a three-body system to an effective two-body system. It is illustrated by explaining the structural properties of some nuclei of current interest, namely halo nuclei and double-λ hypernuclei. The ansatz used here may be of value in a number of three particle problems of similar nature.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

Structure and Occurrence of Three-Body Halos in Two Dimensions

 The quantum-mechanical three-body problem is reformulated in two dimensions by use of hyperspherical coordinates and an adiabatic expansion of the Faddeev equations. The effective radial potentials are calculated and their large-distance asymptotic behavior is derived analytically for short-range two-body interactions. Energies and wave functions are computed numerically for various potentials. An infinite series of Efimov states does not exist in two dimensions. Borromean systems, i.e. bound three-body systems without bound binary subsystems, can only appear when a short-range repulsive barrier at finite distance is present in the two-body interaction. The corresponding Borromean state is never spatially extended. For a system of three weakly interacting identical bosons we find two bound states with both binding energies proportional to the two-body binding energy. In the limit of small binding these states are spatially located at the very large distances characterized by the scattering length. Their properties are universal and independent of the details of the potential. We compare throughout with the corresponding properties in three dimensions. Received September 25, 1998; accepted for publication January 30, 1999     

On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k⁰, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k², two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.