Spin waves in ultracold gases with exchange and spin-orbit interactions
- PDF / 136,252 Bytes
- 3 Pages / 612 x 792 pts (letter) Page_size
- 49 Downloads / 182 Views
AND LIQUIDS
Spin Waves in Ultracold Gases with Exchange and Spin–Orbit Interactions T. L. Andreeva and P. L. Rubin Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia email: [email protected] Received January 31, 2012
Abstract—The dynamics of spin waves in ultracold gases is investigated with allowance for exchange and spin–orbit interaction. The exact basis of atomic states is used taking into account all rotational quantum numbers of the atom. The dispersion relation for spin waves is obtained for fermions and bosons in the hydro dynamic approximation. DOI: 10.1134/S1063776112070011
Cold and ultracold gases continue to be important objects of theoretical and experimental investigations (see, e.g., [1] and literature therein). In some publica tions, atoms are investigated not only in the S state, but also in the P state (with a nonzero orbital angular momentum). The atoms of indium, gallium, iodine (In(2P1/2), Ga(2P1/2), I(2P1/2)) and other elements were studied in [2]. It was found that collisional Zeeman relaxation of Ga(2P1/2) and In(2P1/2) atoms in cold 4He gas differs very strongly (by many orders of magnitude) from the corresponding quantities in the 2P3/2 state [2]. An interesting result was obtained in [3]; it was shown that an ultracold neutral gas may behave as a “nonneutral plasma” due to the presence of an effec tive electric charge associated with neutral atoms. As a result, neutral atoms repel one another as if they were charged. Natu and Mueller [4] analyzed specific fea tures of spin waves in Bose gases with unit spin. It should be noted that the microscopic structure of the quantum Boltzmann collision integral, taking into account all internal degrees of freedom of the atom (spin, orbital angular momentum, etc.; see, e.g., [5, 7]), is still being disregarded. Consistent computation of the quantum collision integral based on the chain of the Bogoliubov equations (using the quantum scatter ing amplitude or the T matrix) makes it possible to construct a theory of spin waves in cold gases without introducing phenomenological corrections into the kinetic equation. We used precisely this method in our studies, devoted to analysis of spin waves in cold para magnetic gases with atoms in the S states [8]. In our previous publication, we analyzed the effect of spin–orbit interaction in the P state on the propa gation of spin waves in magnetic traps. We used the simplified scheme of the LS interaction, which can be employed only for light atoms. Here, this simplifica tion is removed and the exact basis of atomic states is used, taking into account the total angular momentum
J = L + S. We will employ the Wigner J symbols [9]. In addition, the exchange interaction will be taken into account, which we disregarded in our previous publication devoted to atoms with a nonzero orbital angular momentum [10]. The scattering matrix of colliding atoms (1 and 2) with allowance for the spin–orbit interaction can be written in operator form as ˆ = ˆt + θSˆ Sˆ + K
Data Loading...
