Properties of the Bose-Einstein Condensate

When the temperature T decreases below the critical temperature Tc BEC starts at first only for a small fraction of all atoms in the magnetic trap, i.e. not all atoms are immediately transferred into the coherent state of BEC. With decreasing temperature the fraction of the condensed atoms increases (Fig. 9.35). The BEC-state is separated from the normal state with T Tc by an energy gap similar to the energy gap between the Cooper pair state in supra-conductivity and the normal state. One therefore has to pump energy into the condensate in order to convert the assemble into the normal state. Also the energy distribution changes from a Maxwell-Boltzmann distribution above to a distribution 

Since the atomic density in a BEC is very high, collisions between atoms take place. Because of the low temperature (a few nano-Kelvin) the relative velocity is extremely small. Since the angular momentum L = ( = 1 2 3...) is quan- 

The question is, which role collision play in a BEC. The atoms are exposed to a laser field which excites them into higher electronic states. In collisions between excited atoms and ground state atoms the excitation energy can be transferred either into excitation energy of the other atom or into translational energy. The latter case will increase the velocity of atoms which then cannot be kept by the trapping potential and leave the trap. Another possibility is the associative recombination of a collision pair (see Fig. 9.17 and Sect. 9.1.6), where a stable dimer molecule is formed which, however, cannot be kept in the magnetic trap because its spin is different from that of the atoms. 

All atoms for which BEC has achieved, have a magnetic moment which is due to the vector sum of electron spin and nuclear spin. Collisions between such atoms can flip the spin and therefore the direction of the magnetic moment. This will lead to an escape of the atoms from the trap and will decrease the density of the trapped atoms. Spin flips during a collision are due either to the direct dipole-dipole interaction between the collision partners or to an indirect interaction between the nuclear spins which is mediated by the electron spins, since they are coupled through the hyperfine-interaction with the nuclear spins. 

The potential energy of these interactions can be positive of negative which is determined by the sign of the scattering length a [1180]. For a 0 the interaction potential is attractive, for a 0 repulsive. Any BEC can only be stable for a 0 because for an attractive potential the atoms would condense into a solid [1181, 1182]. However, it could be shown that for a Li BEC the condensate was stable below a critical density even for a 0 [1185]. 

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