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arXiv:0811.3157 · Europhysics Letters (EPL)

Spin mixing in colliding spinor condensates: Formation of an effective barrier

M. Guilleumas, Bruno Juliá-Díaz, Jordi Mur-Petit, A. Polls

Published Dec 1, 2008• 4 citations
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Abstract

The dynamics of F =1 spinor condensates initially prepared in a double-well potential is studied in the mean-field approach. It is shown that a small seed of m =0 atoms on a system with initially well-separated m =1 and m =-1 condensates has a dramatic effect on their mixing dynamics, acting as an effective barrier for a remarkably long time. We show that this effect is due to the spinor character of the system, and provides an observable example of the interplay between the internal spin dynamics and the macroscopic evolution of the magnetization in a spinor Bose-Einstein condensate.

DOI
10.1209/0295-5075/84/60005

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The dynamics of F =1 spinor condensates initially prepared in a double-well potential is studied in the mean-field approach. It is shown that a small seed of m =0 atoms on a system with initially well-separated m =1 and m =-1 condensates has a dramatic effect on their mixing dynamics, acting as an effective barrier for a remarkably long time. We show that this effect is due to the spinor character of the system, and provides an observable example of the interplay between the internal spin dynamics and the macroscopic evolution of the magnetization in a spinor Bose-Einstein condensate.
Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.
We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1F=1F=1 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.
Decoherence and Recurrences in a Large Ferromagnetic F=1F = 1F=1 Spinor Bose-Einstein Condensate
Decoherence with recurrences appear in the dynamics of the one-body density matrix of an F=1F = 1F=1 spinor Bose-Einstein condensate, initially prepared in coherent states, in the presence of an external uniform magnetic field and within the single mode approximation. The phenomenon emerges as a many-body effect of the interplay of the quadratic Zeeman effect, that breaks the rotational symmetry, and the spin-spin interactions. By performing full quantum diagonalizations very accurate time evolution of large condensates are analyzed, leading to heuristic analytic expressions for the time dependence of the density matrix, in the weak and strong interacting regimes. We are able to find accurate analytical expressions for both the decoherence and the recurrence times, in terms of the number of atoms and strength parameters, that show remarkable differences depending on the strength of the spin-spin interactions. We discuss the nature of these limits in the light of the thermodynamic limit.
We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.