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Journal of Sichuan Normal University

Study on Q Function and Quantum Dynamics in a Atom-molecule Bose-Einstein Condensed System

Zhengwei Xie

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Using direct numerical diagonalization method and the phase-space quasiprobability distribution function,Q function,the time evolution behaviour of the atom-molecule Bose-Einstein condensation system for two different initial states,Fock state and coherent state,is studied.Through the comparasion of the quasiprobability distribution of atoms and molecule at different evolution time,the influence of the nonlinear interaction on population and quantum fluctuation of the atom-molecular Bose-Einstein condensation system is also analyzed.

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Using direct numerical diagonalization method and the phase-space quasiprobability distribution function,Q function,the time evolution behaviour of the atom-molecule Bose-Einstein condensation system for two different initial states,Fock state and coherent state,is studied.Through the comparasion of the quasiprobability distribution of atoms and molecule at different evolution time,the influence of the nonlinear interaction on population and quantum fluctuation of the atom-molecular Bose-Einstein condensation system is also analyzed.
Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
Based on a two-mode boson model, we study nonclassical properties of the atom-molecule Bose-Einstein condensate. The effects of nonlinear collisions on the dynamics of the molecular formation is studied both in classical and quantum treatments. We find that the conversion from atoms to molecules can be suppressed strongly due to nonlinearity induced localization of the atomic population. In addition, we study statistical properties of the atom-molecule condensed system by calculating the intensity correlation functions numerically. We find that the effect of nonlinearity leads to the appearance of superchaotic molecular pulses, while maintaining the atomic field sub-Poissonian. The joint quantum statistical properties of the atoms and the molecules always show antibunching.
The dynamics of coherent Rabi oscillations in coupled atomic and molecular Bose-Einstein condensates is considered taking into account the atom-atom, atom-molecule, and molecule-molecule elastic interactions. The exact solution for the molecule formation probability is derived in terms of the elliptic functions. The two-dimensional space of the involved parameters intensity and detuning is analyzed and divided into two regions where the Rabi oscillations show different characteristics. A resonance curve is found, on which the molecular formation probability monotonically increases as a function of time. The maximum value of the final transition probability on this curve is 1∕21∕21∕2 (i.e., total transition to the molecular state) and it is achieved at high field intensities starting from a minimal threshold defined by the interspecies interaction scattering lights. The explicit form of the resonance curve is determined, and it is shown that the resonance frequency position reveals a nonlinear dependence on the Rabi frequency of the applied field. A singular point is found on the resonance curve, where a power-law time evolution of the system is observed.
Tunneling dynamics of multi-atomic molecules between atomic and multi-atomic molecular Bose–Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose–Einstein condensates depends on not only the inter-atomic-molecular nonlinear interactions and the initial number of atoms in these condensates, but also the tunneling coupling between the atomic condensate and the multi-atomic molecular condensate. It is discovered that besides oscillating tunneling current between the atomic condensate and the multi-atomic molecular condensate, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling. Moreover, the conception of the molecular Bose–Einstein condensate, which is different from the conventional single-atomic Bose–Einstein condensate, is specially emphasized in this paper.
A study of coherent photoassociation is presented for the case of an atomic Bose-Einstein condensate. It is shown that the phenomenon is analogous to coherent optical transient in a few-level system, with a difference that the participating levels have Bose enhanced populations. A second-quantized Hamiltonian in momentum and position representation is developed to describe photoassociation. A classical version of the field theory for atoms and molecules is used to demonstrate that in the presence of photoassociating light, a joint atom-molecule condensate is unstable against the growth of the density fluctuations. ^ A simple mean-field model of atom-molecule Bose-Einstein condensate is constructed and it is shown that in the model there is no collapse, irrespective of the sign of the effective atom-atom scattering length. The properties of the two most important eigenstates, the ground state and the twin state, are determined for different values of the system parameters δ and K, the detuning and the atom-molecule coupling, respectively. It is shown that in a coupled atom-molecule system a collapse is replaced by a dynamical instability. The lines in the parameter space where these instabilities occur are in fact fractures where the underlying eigenstates discontinuously change. The features of instability are in good qualitative agreement with the experimental observations of collapse. ^