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arXiv:0901.1763 · Physical Review A

Spinor condensate of Rb87 as a dipolar gas

Tomasz Świsłocki, Mirosław Brewczyk, Mariusz Gajda, Kazimierz Rza̧żewski

Published Mar 10, 2010• 22 citations
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Abstract

We consider a spinor condensate of $^{87}\mathrm{Rb}$ atoms in the $F=1$ hyperfine state confined in an optical dipole trap. Putting initially all atoms in the ${m}_{F}=0$ component, we find that the system evolves toward a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin-mixing contact potential. Our results show that because of a dynamical separation of magnetic components, the spin-mixing dynamics in the $^{87}\mathrm{Rb}$ condensate is governed by the dipolar interaction which plays no role in a single-component rubidium system in a magnetic trap.

DOI
10.1103/physreva.81.033604

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We consider a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in the F=1F=1F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in the mF=0{m}_{F}=0mF​=0 component, we find that the system evolves toward a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin-mixing contact potential. Our results show that because of a dynamical separation of magnetic components, the spin-mixing dynamics in the 87Rb^{87}\mathrm{Rb}87Rb condensate is governed by the dipolar interaction which plays no role in a single-component rubidium system in a magnetic trap.
We theoretically study a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in a F=1F=1F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in an mF=1{m}_{F}=1mF​=1, component we observe a significant transfer of atoms to other, initially empty Zeeman states exclusively due to dipolar forces. Because of conservation of a total angular momentum the atoms going to other Zeeman components acquire an orbital angular momentum and circulate around the center of the trap. This is a realization of the Einstein-de Haas effect in a system of cold gases. We show that the transfer of atoms via dipolar interactions is possible only when the energies of the initial and the final sates are equal. This condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. We found that there are many final states of different spatial density, which can be tuned selectively to the initial state. We show a simple model explaining high selectivity and controllability of weak dipolar interactions in the condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms.
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We consider a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in its F=1F=1F=1 hyperfine state at finite temperatures. Putting initially all atoms in mF=0{m}_{F}=0mF​=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a steplike process and when established it manifests itself in distinguishable ways. The atoms in states mF=+1{m}_{F}=+1mF​=+1 and ${m}_{F}=\ensuremath{-}1$ start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the mF=+1{m}_{F}=+1mF​=+1 and ${m}_{F}=\ensuremath{-}1$ spinor condensate components periodically lose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.
Einstein-de Haas effect for a 87^{87}87Rb atoms condensate
We consider a condensate of 87^{87}87Rb atoms in an F=1 hyperfine state confined in an optical dipole trap. Assuming the magnetic moments of all atoms are initially aligned along the magnetic field we observe, after the field's direction is reversed, a transfer of atoms to other Zeeman states due to the dipolar interaction. We find that there exist resonances which amplify the effect of dipolar interaction. When the resonance condition is satisfied the transfer of atoms to mF=0,−1m_F=0,-1mF​=0,−1 states might be of the order of the initial population of mF=1m_F=1mF​=1 component. While changing the magnetic moments during the transfer, the atomsacquire an orbital angular momentum and start to circulate around the center of the trap. This is a realization of the famous Einstein-de Haas effect in systems of cold gases. Due to the dipolar resonances, it becomes possible to observe this phenomenon even in a condensate of 87^{87}87Rb (F=1) atoms that have very small magnetic moment.
We study spin mixing dynamics in a chromium dipolar Bose-Einstein condensate, after tilting the atomic spins by an angle $\ensuremath{\theta}$ with respect to the magnetic field. Spin mixing is triggered by dipolar coupling, but, once dynamics has started, it is mostly driven by contact interactions. For the particular case $\ensuremath{\theta}=\ensuremath{\pi}/2$, an external spin-orbit coupling term induced by a magnetic gradient is required to enable the dynamics. Then the initial ferromagnetic character of the gas is locally preserved, an unexpected feature that we attribute to large spin-dependent contact interactions.
We numerically investigate a condensate of 87Rb atoms in an F=1 hyperfine state confined in an optical dipole trap. Assuming the magnetic moments of all atoms are initially aligned along the magnetic field we observe, after the field's direction is reversed, a transfer of atoms to other Zeeman states. Such transfer is allowed by the dipolar interaction. The atoms in m_F=0, −1 start to circulate around the center of the trap. We find resonances which amplify this phenomenon making it observable even in rubidium condensates.