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Physical Review A

Regular and irregular spin-mixing dynamics in coupled spin-1 atomic and molecular Bose-Einstein condensates

Jing Cheng

Published Aug 17, 2009• 8 citations
Publisher

Abstract

Regular and irregular spin-mixing dynamics are studied in a spin-1 atomic Bose-Einstein condensate coupled with a molecular condensate. Based on the experimental photoassociation spectroscopy of $^{87}\text{R}\text{b}$ spin-1 atoms, a two-channel model is proposed, in which two zero-spin atoms can be associated with a molecular state via a laser field, and a pair of $+1$- and $\ensuremath{-}1$-spin atoms can also be associated with the same molecular state via the same laser field. We find that the spin-mixing dynamics can be manipulated by the laser field and a magnetic field. Both regular and irregular oscillations can be observed under different parameters. Using the Fourier transform analysis, the spin-mixing dynamics may be changed from the regular oscillation with localized spectral distributions to irregular oscillation with a broad spectral distribution.

DOI
10.1103/physreva.80.023608

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Regular and irregular spin-mixing dynamics are studied in a spin-1 atomic Bose-Einstein condensate coupled with a molecular condensate. Based on the experimental photoassociation spectroscopy of 87Rb^{87}\text{R}\text{b}87Rb spin-1 atoms, a two-channel model is proposed, in which two zero-spin atoms can be associated with a molecular state via a laser field, and a pair of +1+1+1- and \ensuremath−1\ensuremath{-}1\ensuremath−1-spin atoms can also be associated with the same molecular state via the same laser field. We find that the spin-mixing dynamics can be manipulated by the laser field and a magnetic field. Both regular and irregular oscillations can be observed under different parameters. Using the Fourier transform analysis, the spin-mixing dynamics may be changed from the regular oscillation with localized spectral distributions to irregular oscillation with a broad spectral distribution.
We study the coherent spin-mixing dynamics in a spin-1 atomic condensate coupled with a molecular condensate. A model is proposed to include the photoassociation (PA) interaction in a spinor condensate. If only the ${m}_{F}=\ensuremath{-}1$ spin component can be converted into molecules, the combined dynamics of spin-mixing and PA can be described by nonlinearly coupled pendulums. We performed detailed numerical calculations on the antiferromagnetic spin-1 systems. We find the spin-mixing dynamics can be greatly controlled by the PA field. The PA field can enhance or suppress the period and amplitude of the spin oscillations, which provide more degrees of freedom to control the spin-mixing dynamics.
We study the spin mixing dynamics of a spin-orbit coupled spin-1 Bose–Einstein condensate. Using mean-field theory and adopting plane wave solutions, the spin mixing dynamics can be well described by an internal Josephson equation. In order to establish the role of the different terms in spin mixing dynamics clearly, we consider the equilibrium state firstly, which shows that the spin-orbit coupling can significantly modify the dispersion relation and change the property of ground state of the condensate. For the non-equilibrium state, the spin-orbit coupling plays an important role in the spin mixing dynamics. Moreover, the oscillation period of spin mixing dynamics is determined by the coupled effects of momentum, magnetization, spin-dependent atomic interaction and spin-orbit coupling. When spin-orbit coupling is less than a critical value, it can prolong the oscillation period of spin mixing dynamics. Conversely, when the spin-orbit coupling is larger than the critical value, it can shorten the oscillation period of spin mixing dynamics. Particularly, when spin-orbit coupling is equal to the critical value, the period tends to infinity. Our study provides a complete spin mixing dynamics of spin-orbit coupled spin-1 BEC, which can be used to explore the spin mixing dynamics experimentally.
We report on the high resolution photoassociation spectroscopy of a 87Rb^{87}\mathrm{Rb}87Rb spin-1 Bose-Einstein condensate to the 1g(P3∕2){1}_{g}({P}_{3∕2})1g​(P3∕2​) v=152v=152v=152 excited molecular states. We demonstrate the use of spin dependent photoassociation to experimentally identify the molecular states and their corresponding initial scattering channel. These identifications are in excellent agreement with the eigenvalues of a hyperfine-rotational Hamiltonian. Using the observed spectra we estimate the change in scattering length and identify photoassociation laser light frequency ranges that maximize the change in the spin-dependent mean-field interaction energy.
We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of 87Rb^{87}\text{R}\text{b}87Rb in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of 85Rb^{85}\text{R}\text{b}85Rb. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.
The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in an optical lattice, where light-induced and static magnetic dipole-dipole interactions originate the interplay of the condensate at each site, are investigated. Classical-quantum correspondence in the large-spin limit is studied. Quantum chaotic features are studied through analysis of the irregular spectrum and time evolution of the Shannon entropy of wave packets. We show how the optical lattice strength influences the system dynamics, and is responsible for a transition from regular to irregular bahavior.