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arXiv:cond-mat/0308259

Eigenstates and excitations of the simple atom-molecule Bose-Einstein condensate

Marijan Koštrun, Juha Javanainen

Published Aug 13, 2003• 0 citations
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Abstract

We model an atom-molecule Bose-Einstein condensate (AMBEC) using simplified set of coupled Gross-Pitaevskii equations (GPE), where we neglect the background (elastic) scattering length of the atoms. We analyze the ground state numerically and analytically, and construct its twin state through transformation $δ\rightarrow-δ, K\rightarrow-K$. We find that the ground state is a collection of three local eigenstates: all-atom state, mixed (atom-molecule) state, and all-molecule state, while the twin state comprises of mixed state with tunable fraction of atoms including unity but excluding all-molecules. We find the analytic boundaries of the local eigenstates from the stability analysis of the underlying all-molecule and all-atom eigenstate. In the ground state we find either regular oscillations in size and fraction of both condensates, or shrinking of the atomic condensate that resembles the collapse. In the twin state we find rapid irregular disintegration of both condensates. We contrast the properties of the mean-field parametric excitations found in AMBEC with the experimentally observed excitations of the BEC. We discuss some enticing possibilities for creation of atomic BEC of controllable half-width by performing the parameter sweep around the boundary.

DOI
10.48550/arxiv.cond-mat/0308259

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The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.
We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation and check these results against numerical simulations of the coupled Gross-Pitaevskii equations (GPEs). We find that they can be divided into two general categories. The first class contains solutions with a region of overlap between the components. The other class consists of non-overlapping wavefunctions and also contains solutions that do not possess the symmetry of the trap. The chemical potential and average energy can be found for both classes within the TF approximation by solving a set of coupled algebraic equations representing the normalization conditions for each component. A ground state minimizing the energy (within both classes of states) is found for a given set of parameters characterizing the scattering length and confining potential. In the TF approximation, the ground state always shares the symmetry of the trap. However, a full numerical solution of the coupled GPEs, incorporating the kinetic energy of the BEC atoms, can sometimes select a broken-symmetry state as the ground state of the system. We also investigate effects of finite-range interactions on the structure of the ground state.
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This is a theoretical study of a many-body system of spin-zero atoms and their diatomic bound states (molecules) which form a single Bose-Einstein condensate at zero temperature. The Gross-Pitaevskii approach is used to analyze the equilibrium states and dynamics of this system. It is shown that, depending on the binding energy of the system, the system can exist in two phases: an atom-molecule condensate and a molecular condensate. The basic thermodynamic characteristics and the criteria for their stability are found. Both phases have two branches of collective excitations, one of which is acoustic, while the other has an activation energy.
Summary form only given. We present a quantum and semiclassical analysis of the dynamics of three coupled atomic Bose-Einstein condensates (BEC). The quantum description is most conveniently analyzed in terms of the operator algebra of SU(3). The space of pure states corresponds to a real manifold of five dimensions corresponding to the parameters of the coset SU(3)/U(2). This is the higher dimensional analogue of the Bloch sphere which has been used to describe the dynamics of two coupled BECs. The equations of motion in the Heisenberg picture can be mapped onto equations in this real manifold. The semiclassical description also involves five real parameters, and corresponds to the mean values of the Heisenberg equations with a factorisation assumption for higher order moments. The symmetries of the problem may be used to construct the ground states of the quantum system for both positive and negative scattering lengths. The structure of the ground states change as the elastic scattering strength changes with respect to the linear tunnelling coupling between the condensate components.