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arXiv:cond-mat/0611734

Irregular Spin Tunnelling for Spin-1 Bose-Einstein Condensates in a Sweeping Magnetic Field

Guanfang Wang, Libin Fu, Jie Liu

Published Nov 29, 2006• 0 citations
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Abstract

We investigate the spin tunnelling of spin-1 Bose-Einstein condensates in a linearly sweeping magnetic field with a mean-field treatment. We focus on the two typical alkali Bose atoms $^{87}Rb$ and $^{23}Na$ condensates and study their tunnelling dynamics according to different sweeping rates of external magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunnelling is observed. For the case of moderate sweeping rates, the tunnelling dynamics is found to be very sensitive on the sweeping rates with showing a chaotic-like tunnelling regime. With magnifying the regime, however, we find interestedly that the plottings become resolvable under a resolution of $10^{-4}$ G/s where the tunnelling probability with respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found can dramatically affect the above picture of the spin tunnelling. Theoretically we have given a reasonable interpretation to the above findings and hope our studies would bring more attention to spin tunnelling experimentally.

DOI
10.48550/arxiv.cond-mat/0611734

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We investigate the spin tunnelling of spin-1 Bose-Einstein condensates in a linearly sweeping magnetic field with a mean-field treatment. We focus on the two typical alkali Bose atoms 87Rb^{87}Rb87Rb and 23Na^{23}Na23Na condensates and study their tunnelling dynamics according to different sweeping rates of external magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunnelling is observed. For the case of moderate sweeping rates, the tunnelling dynamics is found to be very sensitive on the sweeping rates with showing a chaotic-like tunnelling regime. With magnifying the regime, however, we find interestedly that the plottings become resolvable under a resolution of 10−410^{-4}10−4 G/s where the tunnelling probability with respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found can dramatically affect the above picture of the spin tunnelling. Theoretically we have given a reasonable interpretation to the above findings and hope our studies would bring more attention to spin tunnelling experimentally.
With a mean-field treatment, the spin tunneling of spin-1 Bose-Einstein condensates in a linearly sweeping magnetic field is investigated. We focus on a typical alkali Bose atoms 87Rb condensate and study its tunneling dynamics under different sweeping rates of external magnetic field. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunneling is observed. In the case of moderate sweeping rates, the tunneling dynamics is found to be very sensitive to the sweeping rate, showing a chaotic-like tunneling regime. By magnifying the apparently chaotic regime, however, we find interestingly that the plot becomes resolvable at a resolution of 10-8T/s where the tunneling probability with respect to the sweeping rate shows a regular pseudo-periodic pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found which can dramatically affect the above picture of the spin tunneling. Theoretically, we give a reasonable interpretation to the above findings.
We investigate the spin tunnelling of spin-1 Bose–Einstein condensates in a linearly swept magnetic field with a mean-field treatment. We focus on the two typical alkali Bose atoms 87Rb and 23Na condensates and study their tunnelling dynamics according to the sweep rates of the external magnetic fields. In the adiabatic (i.e. slowly sweeping) and sudden (i.e. fast sweeping) limits, no tunnelling is observed. For the case of moderate sweep rates, the tunnelling dynamics is found to be very sensitive to the sweep rates, so the plots of tunnelling probability versus sweep rate only become resolvable at a resolution of 10−4 G s−1. Moreover, a conserved quantity standing for the magnetization in experiments is found to affect dramatically the dynamics of the spin tunnelling. Theoretically we have given a complete interpretation of the above findings, and our studies could stimulate the experimental study of spinor Bose–Einstein condensates.
We present a comprehensive analysis of the Landau-Zener tunneling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunneling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of the linear case. In particular, the tunneling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunneling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunneling probability when the nonlinear ``internal field'' resonate with the external field. We also discuss the asymmetry of the tunneling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.
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.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
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 $\ensuremath{-}1$-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.