Expulsive Parabolic Potential Research Articles

Reflection, Localization, Transmission, and Oscillation Behaviors of Solitons in Ultracold Bose Gases with Spatiotemporally Modulated Interactions in an Expulsive Parabolic Potential

Reflection, Localization, Transmission, and Oscillation Behaviors of Solitons in Ultracold Bose Gases with Spatiotemporally Modulated Interactions in an Expulsive Parabolic Potential

Engineering bright solitons to enhance the stability of two-component Bose–Einstein condensates

We consider a system of coupled Gross–Pitaevskii (GP) equations describing a binary quasi-one-dimensional Bose–Einstein condensate (BEC) with intrinsic time-dependent attractive interactions, placed in a time-dependent expulsive parabolic potential, in a special case when the system is integrable (a deformed Manakov's system). Since the nonlinearity in the integrable system which represents binary attractive interactions exponentially decays with time, solitons are also subject to decay. Nevertheless, it is shown that the robustness of bright solitons can be enhanced in this system, making their respective lifetime longer, by matching the time dependence of the interaction strength (adjusted with the help of the Feshbach-resonance management) to the time modulation of the strength of the parabolic potential. The analytical results, and their stability, are corroborated by numerical simulations. In particular, we demonstrate that the addition of random noise does not impact the stability of the solitons.

Compression of bright bound soliton trains in the Bose–Einstein condensates with exponentially time-dependent atomic scattering length in an expulsive parabolic potential

Three types of two bright bound solitons with increasing coherence are investigated in the Bose–Einstein condensates (BECs) with the exponentially time-dependent interparticle interaction in an expulsive parabolic potential. Two methods are provided with symbolic computation to improve the number of matter density peaks within the given temporal range before the collapse of the solitons under the one-dimensional approximation: (i) enhancing the axial harmonic oscillator frequency; (ii) increasing the initial coherence of the bound solitons. Compression of the three- and four-bright-bound-soliton trains is presented. Estimation of the net binding forces among the bound solitons gives an explanation for the interaction patterns if the coherence of the bound state is limited. Our investigation theoretically reveals the existence of the bright bound solitons in the BECs and analyzes their complex interactions.

Frictionless atom cooling in harmonic traps: A time-optimal approach

In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for trasient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has "bang-bang" form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.

Stabilised bright solitons in Bose–Einstein condensates in an expulsive parabolic and complex potential

The exact solitonic solutions of the one-dimensional nonlinear Schrödinger 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.

Nonautonomous bright and dark solitons of Bose–Einstein condensates with Feshbach-managed time-dependent scattering length

We present a family of nonautonomous bright and dark soliton solutions of Bose–Einstein condensates with the time-dependent scattering length in an expulsive parabolic potential. These solutions show that the amplitude, width, and velocity of soliton can be manipulated by adjusting the atomic scattering length via Feshbach resonance. For the cases of both attractive and repulsive interactions, the total particle number is a conservation quantity, but the peak (dip) density can be controlled by the Feshbach resonance parameter. Especially, we investigate the modulation instability process in uniform Bose–Einstein condensates with attractive interaction and nonvanishing background, and clarify that the procedure of pattern formation is in fact the superposition of the perturbed dark and bright solitary waves. At last, we give the analytical expressions of nonautonomous dark one- and two-soliton solutions for repulsive interaction, and investigate their properties analytically.

Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity

A method is proposed to cool down atoms in a harmonic trap without phase-space compression as in a perfectly slow adiabatic expansion, i.e., keeping the same populations of instantaneous levels in the initial and final traps, but in a much shorter time. This may require that the harmonic trap become transiently an expulsive parabolic potential. The cooling times achieved are shorter than those obtained using optimal-control bang-bang methods and real frequencies.

EXACT BRIGHT SELF-SIMILAR SOLITARY WAVES IN AN EXPULSIVE PARABOLIC POTENTIAL

Exact bright self-similar solitary waves are analytically derived in a cigar-shaped condensate with time-dependent atomic scattering length as(t) in an expulsive parabolic potential. The straightforward relation between the Gross–Pitaevskii equation and the standard nonlinear Schrödinger equation is presented for as(t)=a0exp (γt) at the growing or decaying coefficient γ=±|ωz|/ωtwith ωz(ω⊥) the axial (transverse) frequency. In the expulsive parabolic potential, in particular, it is found that the bright self-similar solitary wave is accelerated and set into motion due to the expulsive force. The results tally with the experimental observations by Khaykovich et al. [Science296 (2002) 1290].

Analyzing Dynamics of a Bright Soliton in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length

We analyze the dynamics of a bright soliton in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross–Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.

Gain/loss effect on a bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential

Taking into account both gain/loss and time-dependent atomic scattering length, this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss, the bright solitary wave is shown to have constant amplitude. Especially, it is found that the bright solitary wave is accelerated by expulsive force, whose velocity can be modulated by changing the axial and transverse angular frequencies. The results are in good agreement with the experimental observations by Khaykovich et al (2002 Science 296 1290).

Solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic and complex potential

We present two families of analytical solutions of the one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.

Integrability of the Gross–Pitaevskii equation with Feshbach resonance management

In this Letter we study the integrability of a class of Gross–Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross–Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98 (2007) 074102]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross–Pitaevskii equation into the well-known standard nonlinear Schrödinger equation. By this transformation, each exact solution of the standard nonlinear Schrödinger equation can be converted into that of the Gross–Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitons and the dynamics of the Bose–Einstein condensates by using the Feshbach resonance technique.

A Generalized Method and Exact Solutions in Bose–EinsteinCondensates in an Expulsive Parabolic Potential

In the paper, a generalized sub-equation method ispresented to construct some exact analytical solutions of nonlinearpartial differential equations. Making use of the method, we presentrich exact analytical solutions of the one-dimensional nonlinearSchrödinger equation which describes the dynamics of solitons inBose–Einstein condensates with time-dependent atomic scatteringlength in an expulsive parabolic potential. The solutions obtainedinclude not only non-traveling wave and coefficient function'ssoliton solutions, but also Jacobi elliptic function solutions andWeierstrass elliptic function solutions. Some plots are given todemonstrate the properties of some exact solutions under theFeshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.

Dark and bright solitons in a Bose–Einstein condensate with a Feshbach resonance

Both dark and bright solitons are constructed exactly for a Bose–Einstein condensation with a time-dependent scattering length in an expulsive parabolic potential. It is shown analytically how the size of the cloud and the sharp peak of the condensate changes via the Feshbach resonance. It is also found that the atom loss due to three-body recombination can be controlled with the help of Feshbach resonance. The exact calculation is performed to compare the rate of the atom loss between the system with time-dependent scattering length in an expulsive parabolic potential and the system with constant scattering length.

Dynamics of solitons in Bose–Einstein condensate with time-dependent atomic scattering length

The evolution of solitons in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature (Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Lett. 22 (2005) 1855).

Dynamics of bright matter wave solitons in Bose–Einstein condensates in an expulsive parabolic and complex potential

We present a new family of analytic solutions of the nonlinear Schrödinger equation with an imaginary potential that describes the dynamics of a bright soliton in a Bose–Einstein condensate with an expulsive parabolic and complex potential. We found that under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the value of the feeding parameter.

Controllable compression of bright soliton matter waves

An analytical study on the dynamics of bright solitons of Bose–Einstein condensates (BEC) with a time-varying atomic scattering length in a time-varying expulsive parabolic potential is presented. Exact solutions of the one-dimensional Gross–Pitaevskii equation are obtained. The results show that the bright soliton (including the higher-order bright soliton) can be compressed into a desired width and amplitude in a controllable manner by changing the scattering length and external potential. Furthermore, it is shown numerically that the present method is also efficient for the two-dimensional BEC's compression.

Soliton Solutions in Bose–Einstein Condensates withTime-Dependent Atomic Scattering Length in an Expulsive ParabolicPotential

We present both the bright and dark solitons of Bose–Einsteincondensates with a time-dependent atomic scattering length in anexpulsive parabolic potential. As a discussed example, we select theexperimental parameter, i.e. the Feshbach-managed nonlinear coefficientreading a(t) = g0exp(λt), and obtain the results which can berecovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.