Figure 2
Spin-dependent trajectories of a single atom (a),(b) and spin-dependent evolution of the density profiles of an ensemble of atomic gas (c),(d) under gravity (which provides an effective electric filed) and a light-induced gauge potential. The spin current along the
direction is a manifestation of the spin Hall effect. The gauge potentials in (a),(c) and (b),(d) are generated by the laser configurations I and II, respectively. The sinusoids in (b) denote the effective gauge fields
. The directions of the Lorentz forces
change periodically in this case and are shown by the arrows there. The dotted (solid) vertical lines in (b) and (d) denote the stable equilibrium positions for spin-up (spin-down) atoms. In (c) and (d), the density profiles of the atomic gas are shown at time
, 4, 6 ms. For calculations in (a)–(d), we take the following typical experimental parameters with
,
,
for the laser configuration I, and
for the laser configuration II. In both configurations,
. In (a),(b), the initial atomic velocity is assumed to be zero, and the initial positions
,
for (a) and (
,
,
) for (b). The parameters for the atomic ensemble in (c),(d) are given by
and
. The atomic mass is taken to be the one for
. With the above parameters, we have checked the adiabatic condition is well satisfied during the evolution.
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