Sheng-Chang Li

The effects of Bohm potential on ion-acoustic solitary waves interaction in a nonplanar quantum plasma

The interaction of ion-acoustic solitary waves (IASWs) in a nonplanar unmagnetized quantum plasma consisting of electrons, positrons, and ions are studied by employing the quantum hydrodynamic model and the Korteweg-de Vries description. We provide the theoretical predictions about the phase shifts for the compressive IASWs and the rarefactive IASWs collisions, respectively. The effects of the positron to electron Fermi temperature ratio, the positron to ion number density ratio, and the quantum Bohm potential on phase shift are investigated. It is found that these factors can significantly modify the properties of the IASWs collisions. In particular, we find that the variations of phase shifts with quantum Bohm potential for two types of IASWs are apparently different. The validity of the results of present study is also pointed out.

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

We study localized wave on continuous wave background analytically in a nonlinear fiber with higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. We present an exact rational W-shaped soliton solutions, whose structural properties depend on the frequency of the background field. The hump value increase with the decrease of the background frequency in the certain regime. The highest value of the W-shaped soliton can be nine times the background’s, and the distribution shape is identical with the one of well-known eyes-shaped rogue wave with its maximum peak. The numerical stimulations indicate that the W-shaped soliton is stable with small perturbations.

Nonlinear Ramsey interferometry with Rosen-Zener pulses on a two-component Bose-Einstein condensate

We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.

W-shaped solitons generated from a weak modulation in the Sasa-Satsuma equation.

We study rational solutions of continuous wave backgrounds with the critical frequencies of the Sasa-Satsuma equation, which can be used to describe the evolution of the optical field in a nonlinear fiber with some high-order effects. We find a striking dynamical process that two W-shaped solitons are generated from a weak modulation signal on the continuous wave backgrounds. This provides a possible way to obtain stable high-intensity pulses from a low-intensity continuous wave background. The process involves both modulational instability and modulational stability regimes, in contrast to the rogue waves and W-shaped solitons reported before which involve modulational instability and stability, respectively. Furthermore, we present a phase diagram on a modulational instability spectrum plane for the fundamental nonlinear localized waves obtained already in the Sasa-Satsuma equation. The interactions between different types of nonlinear localized waves are discussed based on the phase diagram.

Composite nonlinear structure within the magnetosonic soliton interactions in a spin-1/2 degenerate quantum plasma

We study the basic physical properties of composite nonlinear structure induced by the head-on collision of magnetosonic solitons. Solitary waves are assumed to propagate in a quantum electron-ion magnetoplasma with spin-1/2 degenerate electrons. The main interest of the present work is to investigate the time evolution of the merged composite structure during a specific time interval of the wave interaction process. We consider three cases of colliding-situation, namely, compressive-rarefactive solitons interaction, compressive-compressive solitons interaction, and rarefactive-rarefactive solitons interaction, respectively. Compared with the last two colliding cases, the changing process of the composite structure is more complex for the first situation. Moreover, it is found that they are obviously different for the last two colliding cases.

Response to “Comment on ‘The effects of Bohm potential on ion-acoustic solitary waves interaction in a nonplanar quantum plasma’” [Phys. Plasmas 17, 114701 (2010)]

In a recent comment, M. Akbari-Moghanjoughi [Phys. Plasmas 17, 114701 (2010)] (whom we will refer to as A.M.) pointed out that in the quantum hydrodynamics plasma model the parameters p (the fractional positron to ion number density) and σ (the relative positron to electron Fermi temperature) are not independent quantum plasma parameters which has important consequences on the graphical interpretations presented in our article. We agree with A.M. that the phase shift cannot be plotted in a σ-p plane and the value of p=0.2 does not correspond to σ=0.02. However, the main results given by formulas and the conclusion in our paper [S.-C. Li, Phys. Plasmas 17, 082307 (2010)] are independent of the figures and remain valid. To understand and interpret the results obtained in our previous article correctly, in this response, we will show some new figures and make some discusses.

Dynamic stabilization of a coupled ultracold atom-molecule system.

We numerically demonstrate the dynamic stabilization of a strongly interacting many-body bosonic system which can be realized by coupled ultracold atom-molecule gases. The system is initialized to an unstable equilibrium state corresponding to a saddle point in the classical phase space, where subsequent free evolution gives rise to atom-molecule conversion. To control and stabilize the system, periodic modulation is applied that suddenly shifts the relative phase between the atomic and the molecular modes and limits their further interconversion. The stability diagram for the range of modulation amplitudes and periods that stabilize the dynamics is given. The validity of the phase diagram obtained from the time-average calculation is discussed by using the orbit tracking method, and the difference in contrast with the maximum absolute deviation analysis is shown as well. A brief quantum analysis shows that quantum fluctuations can put serious limitations on the applicability of the mean-field results.

Quantum phase transition in a three-level atom-molecule system

We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy level structure, fidelity, and adiabatical geometric phase, we confirm that the system exists a second-order phase transition from an atommolecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular we find that both the critical exponents and the behaviors of ground-state geometric phase change obviously in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to ?pi/3 at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.

Applications of Nonlinear Adiabatic Evolution

In this chapter, we show selected applications of nonlinear adiabatic evolution in the geometric phase, in tunneling dynamics, and in quantum interference. We introduce the adiabatic geometric phase in a nonlinear coherent coupler and illustrate the nonlinear adiabatic tunneling with four cases, namely, Landau-Zener tunneling, Rosen-Zener tunneling, atom-molecule conversion, and composite adiabatic passage. Adiabatic nonlinear Ramsey interferometry is also discussed.

Introduction to Adiabatic Evolution

In this chapter, we introduce the basic concepts of adiabatic theory in both classical and quantum systems. We discuss classical adiabatic motion, introduce the concepts of the classical adiabatic invariant and the Hannay angle, and give three examples: the one-dimensional harmonic oscillator, the celestial two-body problem, and the Foucault pendulum. We describe quantum adiabatic evolution, present the quantum adiabatic theorem, and describe the adiabatic geometric phase (specifically, the Berry phase) and the virtual magnetic monopole. Five examples of quantum adiabatic evolution are shown. We also discuss classical-quantum correspondence.