Figure 1

Schematic representation of the light-atom interaction for generation of effective spin-dependent gauge fields. (a) Three-level $\Lambda$-type atoms interacting with laser beams characterized by the Rabi frequencies ${\Omega }_1$, ${\Omega }_2$ through the Raman-type coupling with a large single-photon detuning $\Delta$. (b) The configurations of the Raman laser beams. Configuration I: two counterpropagating and overlapping laser beams with shifted spatial profiles (see also Ref. 18). (c) Configuration II: A periodic gauge field can be created by four overlapping laser beams propagating along the shown directions. The upper two form the Raman beam ${\Omega }_1$ while the lower two form ${\Omega }_2$. (d) A Raman configuration to transfer the bright state to a different hyperfine level $|F^{\prime }⟩$ for detection. The $|1⟩$ and $|2⟩$ are assumed to be different Zeeman states on the same hyperfine level $|F⟩$.Reuse & Permissions

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 $x$ 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 $B_{\sigma }$. The directions of the Lorentz forces $F_{\sigma }$ 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 $t=0$, 4, 6 ms. For calculations in (a)–(d), we take the following typical experimental parameters with ${\sigma }_0=10\mu \mathrm{m}$, $\Delta x=2.5\mu \mathrm{m}$, $k={10}^7{\mathrm{m}}^{-1}$ for the laser configuration I, and $k\sin \alpha =5\times {10}^5{\mathrm{m}}^{-1}$ for the laser configuration II. In both configurations, ${\Omega }_0^2/\Delta ={10}^6\mathrm{Hz}$. In (a),(b), the initial atomic velocity is assumed to be zero, and the initial positions $x=0$, $y=0$ for (a) and ($x=2.5$, $5\mu \mathrm{m}$, $y=0$) for (b). The parameters for the atomic ensemble in (c),(d) are given by ${\sigma }_r=2.0\mu \mathrm{m}$ and ${\sigma }_v=0.5\mathrm{cm}/\mathrm{s}$. The atomic mass is taken to be the one for ${}^{87}\mathrm{Rb}$. With the above parameters, we have checked the adiabatic condition is well satisfied during the evolution.Reuse & Permissions