Nonlinear transport of Bose--Einstein condensates in a double barrier potential

The stable nonlinear transport of the Bose-Einstein condensates through a double barrier potential in a waveguide is studied. By using the direct perturbation method we have obtained a perturbed solution of Cross-Pitaevskii equation. Theoretical analysis reveals that this perturbed solution is a stable periodic solution, which shows that the transport of Bose-Einstein condensed atoms in this system is a stable nonlinear transport. The corresponding numerical results are in good agreement with the theoretical analytical results.     

Dynamics of vector solitons in two-component Bose--Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schr?dinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark--dark solitons.     

Exact periodic wave and soliton solutions in two-component Bose--Einstein condensates

We present several families of exact solutions to a system of coupled nonlinear Schr\"{o}dinger equations. The model describes a binary mixture of two Bose--Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.     

Hyperchaos of two coupled Bose--Einstein condensates with a three-body interaction

We investigate the dynamics of two tunnel-coupled Bose--Einstein condensates (BECs) in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.     

Effect of interaction strength on gap solitons of Bose--Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.     

Squeezing via coupling of Bose--Einstein condensates in a double-well potential with a cavity light field

Squeezing via the interaction between the cavity light field and the Bose Einstein Condensate （BEC） in a doublewell potential is considered within the context of the two-mode approximation. For the cavity light field initially in a coherent state, it is shown that by choosing appropriate parameters, quadrature squeezing of the cavity light field can be achieved and it exhibits periodic oscillation. We also study the case in which BEC is tuned to resonance by periodically modulating the trapping potentiaL and the quadrature squeezing of the cavity field exhibits periodic collapse and revival effect. Both analytic and numerical calculations are performed, and they are found to be in good agreement with each other. The result shows that the quantum statistical properties of the cavity light field can be manipulated by its coupling with the condensates in the double-well potential. On the other hand, dynamical properties of the condensates in the double-well potential will be reflected by the quadrature squeezing of the light field.     

The stability of Bose--Einstein condensates in a two-dimensional shallow trap

The stability of Bose--Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.     

Energy spectrum and entanglement of two tunnel- coupled Bose--Einstein condensates

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose--Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.     

Formation of combined solitons in two-component Bose—Einstein condensates

<正>We investigate the combined soliton solutions of two-component Bose—Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons.Our results show that the intraspecies(interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright,and dark-bright soliton solutions in different regions.Especially,we find that the bright-bright (dark-dark) soliton can exist in the case of both repulsive(attractive) intraspecies interaction strengths in the presence of external potential.This novel phenomenon is completely different from the formation of soliton solution of one-component Bose-Einstein condensates without external potential,and it will be useful for the study of two-component Bose-Einstein condensates.     

Stability properties of vector solitons in two-component Bose-Einstein condensates with tunable interactions

By using a unified theory of the formation of various types of vector-solitons in two-component Bose-Einstein condensates with tunable interactions,we obtain a family of exact vector-soliton solutions for the coupled nonlinear Schro¨dinger equations.Moreover,the Bogoliubov equation shows that there exists stable dark soliton in specific situations.Our results open up new ways in considerable experimental interest for the quantum control of multi-component Bose-Einstein condensates.     

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates.It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions.It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.     

Effects of junction parameters on the resonant macroscopic quantum tunnelling in small Josephson junctions

Summary Within the well-established quantum picture of a Josephson junction, it has been shown that the possibility of a resonant macroscopic quantum tunnelling can produce sharp voltage peaks in the current-voltage characteristics. We investigate the effects of the junction parametrs and bias conditions on the step amplitude, in view of an experimental check of the proposed phenomenon.     

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.     

Effect of a barrier potential on soliton dynamical characteristics in condensates

By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose--Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.     

Phase diffusion of a two-component Bose-Einstein condensates:exact and short-time solutions for arbitrary coherent spin state

We investigate phase diffusion of a two-component Bose--Einstein condensates prepared initially in arbitrary coherent spin state |θ₀,φ₀|. Analytical expression of the phase-diffusion time is presented for θ₀～π/2 case. In comparison with the symmetrical case (i.e., θ₀=π/2), we find that the diffusion process becomes slow due to the reduced atom number variance.     

Controlling the amplitude of soliton in agrowing Bose--Einstein condensate by means of Feshbach resonance

By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose-Einstein condensate （BEC）. It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases （increases） for the BEC growing coefficient Ω 〈 0 （Ω 〉 0）. Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.     

Electron-phonon interaction function by numerical analysis of superconducting tunnelling experimental data

Summary A new method of numerical analysis is presented which allows the determination of the electron-phonon interaction functionα ²(ω)F(α) using the experimental data obtained from a superconducting tunnel junction. This method utilizes the dispersion relation for Δ(ω) (complex energy gap function) proposed by Galkin, D'yachenko and Svistunov. The method and the hypotheses which allow the numerical solution of the first-kind integral equation derived from the Eliashberg equations are shown and discussed. Δ(ω) andα ²(ω)F(α) of Pb are obtained by applying this method to the tunnel data of an Al−Al₂O₃-Pb (superconducting electrode) junction. The results are discussed with particular reference to the stability and convergence of the method applied.

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Riassunto Si presenta un nuovo metodo di analisi numerica che, utilizzando la relazione di dispersione per Δ(ω), energy gap function, proposta da Galkin, D'yachenko and Svistunov, permette di determinare da dati sperimentali ottenuti su giunzioni tunnel superconduttive la funzione interazione elettrone-fononeα ²(ω)F(α) per l'elettrodo superconduttore. Il metodo stesso è discusso e si evidenziano le ipotesi che permettono la soluzione numerica dell'equazione integrale di prima specie derivata dalle equazioni di Eliashberg. Le Δ(ω) edα ²(ω)F(α) ottenute applicando tale metodo ai dati relativi ad una giunzione Al−Al₂O₃−Pb (elettrodo superconduttore) sono presentate e discusse con particolare riferimento alla stabilità e convergenza del metodo.

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Резюме Предлагается новый метод численного анализа, который позволяет определить функцию электрон-фононного взаимодействияα ²(ω)F(α), используя экспериментальные данные, полученные для сверхпроводяшего туннельного перехода. Этот метод использует дисперсионное соотнощение длл Д(щ), предложенное Галкиным, Яшенко и Свистуновым. Обсуждается предложенный метод и подтверждаются гипотезы, которые розволяют численно рещить интегральное уравнение первого рода, выведенное из уравнений Элиащберга. Испрльзуя этот метод для туннельных данных в Al−Al₂O₃−Pb переходе, получаются Δ(ω) иα ²(ω)F(α). Полученные результаты обсуждаются с точки зрения устойчивости и сходимости предложенного метода.

     

Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

Generation and control of chaos in a Bose--Einstein condensate

For a Bose--Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k₁\approx k₂ between the two laser wave vectors is kept, the adjustment from k₂1 to k₂\ge k₁ can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.