Propagation, breathing and transition of matter-wave packet trains

Abstract

We find a set of new exact solutions of a quantum harmonic oscillator, which describes some wave-packet trains with average energy being proportional to both the quantum level and classical energy of the oscillator. Center of the wave-packet trains may oscillate like a classical harmonic oscillator of frequency $\omega$. Width and highness of the trains may change simultaneously with frequency $2\omega$ as an array of breathers. Under some perturbations the wave-packet trains could transit between the states of different quantum numbers. We demonstrate analytically and numerically that the wave-packet trains can be strictly fitted to the matter-wave soliton trains observed by Strecher et al. and reported in Nature 417, 150(2002). When the wave-packets breathe with greater amplitudes, they show periodic collapse and revival of the matter-wave.

15 pages, 7 figures

References in corpus (11)

• Theory of Bose-Einstein condensation in trapped gases
• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Modulational Instability and Complex Dynamics of Confined Matter-Wave Solitons
• Spontaneous soliton formation and modulational instability in Bose-Einstein condensates
• Intermittent implosion and pattern formation of trapped Bose-Einstein condensates with attractive interaction
• Squeezed States for General Systems
• Nonlinear Matter Wave Dynamics with a Chaotic Potential
• Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates
• Classical chaos with Bose-Einstein condensates in tilted optical lattices
• Transition radiation by matter-wave solitons in optical lattices

Cited by in corpus (7)

• Enhanced Quantum Reflection of Matter-Wave Solitons
• Modulated amplitude waves with nonzero phases in Bose-Einstein condensates
• From short-time diffusive to long-time ballistic dynamics: the unusual center-of-mass motion of quantum bright solitons
• Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions
• Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space
• Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms
• Wave Packet Dynamics in the Majorana Equation