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1.
We investigate the coupled Gross-Pitaevskii equation describing the dynamics of two hyperfine states of Bose-Einstein condensates and deduce the integrability condition for the propagation of bright vector solitons. We show how the transient trap and scattering length can be suitably tailored to bring about fascinating collisional dynamics of vector solitons. 相似文献
2.
Controlling the collision between two solitons in the condensates by a double-barrier potential 下载免费PDF全文
We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential. 相似文献
3.
Alexandru I. Nicolin Mogens H. Jensen Jan W. Thomsen R. Carretero-Gonzlez 《Physica D: Nonlinear Phenomena》2008,237(19):2476-2481
We consider the dynamics of a dilute, magnetically-trapped one-dimensional Bose–Einstein condensate whose scattering length is periodically modulated with a frequency that linearly increases in time. We show that the response frequency of the condensate locks to its eigenfrequency for appropriate ranges of the parameters. The locking sets in at resonance, i.e., when the effective frequency of driving field is equal to the eigenfrequency, and is accompanied by a sudden increase of the oscillations amplitude due to resonant energy transfer. We show that the dynamics of the condensate is given, to leading order, by a driven harmonic oscillator on the time-dependent part of the width of the condensate. This equation captures accurately both the locking and the resonant energy transfer as it is evidenced by comparison with direct numerical simulations of original Gross–Pitaevskii equation. 相似文献
4.
In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented. 相似文献
5.
The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential. 相似文献
6.
7.
Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates 下载免费PDF全文
An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a time-space periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice. 相似文献
8.
9.
The ring dark solitons and their head-on collisions in a
Bose--Einstein condensates with thin disc-shaped potential
are studied. It is shown that the system admits a solution with
two concentric ring solitons, one moving inwards and the other
moving outwards, which in small-amplitude limit, are described by
the two cylindrical KdV equations in the respective reference
frames. By using the extended Poincar\'e--Lighthill--Kuo
perturbation method, the analytical phase shifts following
the head-on collisions between two ring dark solitary waves are
derived. It is shown that the phase shifts decrease with the
radial coordinate $r$ according to the $r^{-1/3}$ law and depend
on the initial soliton amplitude and radius. 相似文献
10.
Robert Graham 《Journal of statistical physics》2000,101(1-2):243-257
A quantum Langevin equation for the amplitudes of the collective modes in Bose–Einstein condensate is derived. The collective modes are coupled to a thermal reservoir of quasi-particles, whose elimination leads to the quantum Langevin equation. The dissipation rates are determined via the correlation function of the fluctuating force and are evaluated in the local-density approximation for the spectrum of quasi-particles and the Thomas–Fermi approximation for the condensate.I take great pleasure in dedicating this paper to Gregoire Nicolis on the occasion of his sixtieth birthday. 相似文献
11.
We investigate numerically the effects of higher-order space-charge field on the self-deflection of bright photovoltaic spatial solitons in two-photon photovoltaic photorefractive crystals under steady-state conditions. The expression for an induced space-charge electric field, including higher-order space-charge field terms is obtained. The dynamical evolution equation is built in which the effects that arise from these higher-order terms are considered. Numerical results indicate that bright photovoltaic solitons can bend towards both the same direction as the crystal's c-axis and the opposite direction, respectively. Specifically, self-deflection cannot occur for bright photovoltaic solitons if the strength of the photovoltaic field and the intensity of the input beam are appropriately selected. Relevant examples are provided. 相似文献
12.
We present Lax-pair corresponding to the coupled Gross-Pitaevskii equation (CGPE) which governs the evolution of the macroscopic wave function of two components Bose-Einstein condensates trapped in time-dependent harmonic potential. Kinds of soliton solutions can be derived from the Lax-pair through Darboux transformation conveniently. Furthermore, soliton management in two-component Bose-Einstein condensate would be realized base on that the shape and motion of soliton in both components are investigated analytically. Moreover, it is found that there is a transformation existed between the nonautonomous coupled system and Manakov model. 相似文献
13.
N. Vishnu Priya M. Senthilvelan Govindan Rangarajan M. Lakshmanan 《Physics letters. A》2019,383(1):15-26
We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schrödinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT) method. We present explicit one and two bright soliton solutions and show that they exhibit stable structures only when we combine the field and parity transformed complex conjugate field. Further, we derive two dark/antidark soliton solution with the help of DT method. Unlike the bright soliton case, dark/antidark soliton solution exhibits stable structure for the field and the parity transformed conjugate field separately. In the dark/antidark soliton solution case we observe a contrasting behaviour between the envelope of the field and parity transformed complex conjugate envelope of the field. For a particular parametric choice, we get dark (antidark) soliton for the field while the parity transformed complex conjugate field exhibits antidark (dark) soliton. Due to this surprising result, both the field and PT transformed complex conjugate field exhibit sixteen different combinations of collision scenario. We classify the parametric regions of dark and antidark solitons in both the field and parity transformed complex conjugate field by carrying out relevant asymptotic analysis. Further we present 2N-dark/antidark soliton solution formula and demonstrate that this solution may have combinations of collisions. 相似文献
14.
<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. 相似文献
15.
Luis Antonio Gonzlez-García Hctor Alva-Snchez Rosario Paredes 《Entropy (Basel, Switzerland)》2022,24(11)
We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for , while it occurs in the interval for octagonal and dodecagonal symmetries. 相似文献
16.
We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases. 相似文献
17.
Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates 下载免费PDF全文
We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length. 相似文献
18.
Zhi Lin 《Annalen der Physik》2021,533(1)
The phase boundaries of periodically driven spin–orbit coupled BECs with effective two‐body interactions are analytically calculated by using variational method. The phase diagrams of periodically driven and systems present distinguished features from undriven systems, respectively. For the BECs, the critical density (density at quantum tricritical point) will be dramatically reduced in some parameter regions, and the prospect of observing this intriguing quantum tricritical point is greatly enlarged. Moreover, a series of quantum tricritical points emerge quasi‐periodically when increasing the Raman coupling strength with fixed density. In the BECs, two hyperfine states of atoms can be miscible within the suitable regions of driving parameter space. As a result, systems will stay in the stripe phase with small Raman frequency at typical density, which expands the region of stripe phase in the phase diagram. In addition, an absence of quantum tricritical point in such system is observed, which is very unlike systems. 相似文献
19.
By developing multiple-scale method combined with
Wentzel--Kramer--Brillouin expansion, this paper analytically
studies the modulating effect of weakly periodic potential on the
dynamical properties of the Bose--Einstein condensates (BEC) trapped
in harmonic magnetic traps. A black--grey soliton transition is
observed in the BEC trapped in harmonic magnetic potential, due to
the weakly periodic potential modulating effect. Meanwhile, it finds
that with the slight increase of the weakly periodic potential
strength, the velocity of the soliton decreases, while its width
firstly decreases then increases, a minimum exists there. These
results show that the amplitude, velocity, and width of matter
solitons can be effectively managed by means of a weakly periodic
potential. 相似文献
20.
Stabilised bright solitons in Bose-Einstein condensates in an expulsive parabolic and complex potential 下载免费PDF全文
The exact solitonic solutions of the one-dimensional nonlinear Schr?dinger equation, which describes the dynamics of bright soliton in Bose—Einstein condensates with the time-dependent
interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave
density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially,when parameters satisfy the relation λ=2γ, the
soliton is stable with time evolution without changing its shape and amplitude. 相似文献