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arXiv:0705.3205 · Physical Review A

Quantum dynamics of two bosons in an anharmonic trap: Collective versus internal excitations

Christian Matthies, Sascha Zöllner, Hans‐Dieter Meyer, Peter Schmelcher

Published Aug 8, 2007• 16 citations
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Abstract

We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.

DOI
10.1103/physreva.76.023602

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We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.
We investigate the quantum dynamics of two interacting bosonic atoms confined in a one-dimensional anharmonic trap. The tunneling rate, an experimentally measurable parameter of the system, is calculated as a function of the effective coupling interatomic constant ggg from the ground (n=N=0n=N=0n=N=0) and first excited atomic states in the trap with respect to relative (n=2,N=0n=2,N=0n=2,N=0) and center-of-mass (n=0,N=2n=0,N=2n=0,N=2) atomic motion. This allows us to investigate the initial population and pair correlation, as well as the effective coupling constant ggg, of the system by comparing the calculated tunneling rate with the experimental one. We observe that the only possible tunneling scenario is a sequential particle tunneling in the cases we consider. We also analyze a rearrangement $(0,2)\ensuremath{\rightleftarrows}(2,0)$ of the spectrum in the limit $g\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}0$ of noninteracting atoms.
We investigate the collective excitations of a one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes, are discussed.
We investigate the low-energy excitations of a dilute atomic Bose gas confined in a anharmonic trap interacting with repulsive forces. The dispersion law of both surface and compression modes is derived and analyzed for large numbers of atoms in the trap, which show two branches of excitation and appear two critical values, where one of them indicates collective excitation which would be unstable dynamically, and the other one indicates the existing collective mode with lower frequency under anharmonic influence than that in harmonic trapping case. Our work reveals the key role played by the anharmonicity and interatomic forces which introduce a rich structure in the dynamic behavior of these new many-body systems.
We study the rotational properties of an attractively interacting Bose gas in an anharmonic potential. Low-energy excitations for the two possible rotational ground-state configurations (vortex and the center-of-mass rotating state) are analyzed. The vortex excitation spectrum is all positive for weak couplings, but as the interactions become stronger, the energy of the lowest mode decreases rapidly to a negative value. The broken rotational symmetry involved in the center-of-mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center-of-mass rotational state also demonstrate the coupling between the center of mass and relative motions.
The collective excitations of a one-dimensional dipolar Bose—Einstein condensate trapped in an anharmonic potential are investigated theoretically. Using the variational approach, we obtain the coupled equations of motion for the center-of-mass coordinate of the condensate and its width. In particular, analytical expressions for the low-lying excitation modes are given. The results show that dipole-dipole interactions reduce the frequency shift induced by quartic distortion. The interplay between dipole-dipole interactions and anharmonic distortion for the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes are also discussed.
We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.