Continuous generation of an ultracold atomic beam using crossed moving optical lattices

Using orthogonally crossed moving lattices, we demonstrate the continuous transport of ${}^{88}\mathrm{Sr}$ atoms in the long-lived metastable ${}^3{P}_0$ and ${}^3{P}_2$ states to a region free from scattered laser-cooling light, while two-stage cooling on the ${}^1{S}_0–{}^1{P}_1$ and ${}^3{P}_2–{}^3{D}_3$ transitions is being conducted. The transfer efficiency between the crossed lattices was close to unity when laser cooling was applied in the crossed region. For a clock laser propagating along the lattice axis, such a lattice-trapped atomic beam enables continuous interrogation of the clock transition free from the Doppler effect arising from the thermal motion of atoms.

Figure 1

Experimental platform. (a) Magneto-optical trapping (MOT) of ${}^{88}\mathrm{Sr}$ on the ${}^1{S}_0–{}^1{P}_1$ transition continuously populates the ${}^3{P}_2$ metastable state. Atoms in the ${}^3{P}_2$ metastable state are trapped by a quadrupole magnetic field created by a 50-mm-long permanent magnet (light-green line) and a coil (not shown). A cooling laser at $461\mathrm{nm}$ (light blue) is used for the MOT. An IR cooling laser at $2.92\text{μ}\mathrm{m}$ (orange) cools the magnetically trapped atoms on the ${}^3{P}_2–{}^3{D}_3$ transition. Ultracold atoms cooled by the IR cooling transition are loaded into a moving optical lattice (brown lines) formed inside a bowtie cavity. After traveling 21 mm in the $+x$ direction, the atoms are redirected to the $+y$ direction by the crossed moving lattice. A probe laser at 461 nm and a cooling laser at 689 nm illuminate the intersection of the moving lattices (thick lines in purple and red). (b) An image of atoms covers the area of $3.5\times 3.5{\mathrm{mm}}^2$ at the intersection. (c) Relevant energy levels for Sr. Pumping lasers at $679$, $688$, and $707\mathrm{nm}$ are superimposed on the $x$ lattice as shown by the pink dashed line in (a). (d) Gravito-optical potential along the $y$ direction at the atom loading position $x_0=-21$ mm. Effective trap depths are dependent on the electronic states and the lattice polarization $\theta$ (see main text).

Figure 2

(a) Lattice intensity distribution for the lattice laser polarization ${\mathbf{E}}_L^{(\perp )}$ perpendicular to the cavity plane. The lattice periods are exaggerated for visibility. Interference of two orthogonal moving lattices guides the atoms with the velocity $\mathbf{v}=(v_L,v_L)$. (b) For the lattice laser polarization ${\mathbf{E}}_L^{(\parallel )}$ parallel to the cavity plane, the lattice depth is given by the sum of the orthogonal lattices.

Figure 3

Number of atoms in the ${}^3{P}_0$ (red circles), ${}^3{P}_2$ (green squares), and ${}^1{S}_0$ (blue triangles) states outcoupled by the moving lattice with velocities $v_L$. The upper axis corresponds to the traveling time $t$ of atoms over 20 mm, where the dashed line shows the fraction of remaining atoms, assuming the collision-limited lifetime of $\tau =2\mathrm{s}$.

Figure 4

Fluorescence images of atoms in the ${}^3{P}_0$, ${}^3{P}_2$, and ${}^1{S}_0$ states for lattice velocities of $v_L=16\mathrm{mm}/\mathrm{s}$ (upper row) and $v_L=57\mathrm{mm}/\mathrm{s}$ (lower row).

Figure 5

(a) Atom flux as a function of the traveling time from the loading position $x_0$ with $v_L=16\mathrm{mm}/$s. Atoms pass through the intersection at $t=1.268–1.291$ s shown by the grey region. Different colors correspond to the atomic states, i.e., ${}^3{P}_0$ (red), ${}^3{P}_2$ (green), ${}^1{S}_0$ (blue), and ${}^1{S}_0$ with the additional cooling (purple). The colors also apply to the following panels. Atom flux $\varphi =6\times {10}^4/\mathrm{s}$ is observed for atoms in the ground state when applying laser cooling. (b) Lattice velocity-dependent transfer efficiencies. Application of laser cooling (purple stars) improves the transfer efficiencies to unity for $v_L<10\mathrm{mm}/\mathrm{s}$. (c) Temperatures of atoms before (filled symbols) and after (empty symbols) the intersection as a function of the lattice velocity.

Figure 6

Trajectory of atoms for the moving lattice with polarization ${\mathbf{E}}_L^{(\parallel )}$ parallel to the cavity plane. (a) Atoms partially change their direction for $v_L=16\mathrm{mm}/\mathrm{s}$. (b) Atoms move along the $x$ lattice for $v_L=97\mathrm{mm}/\mathrm{s}$. (c) Fraction of atoms transitioning to the right-angle trajectory (filled circles) versus maintaining a straight path (empty circles).

Figure 7

(a),(c) Simulated atom trajectories for the two lattice polarizations: (a) ${\mathbf{E}}_L^{(\perp )}$ and (c) ${\mathbf{E}}_L^{(\parallel )}$. Red, blue, and grey trajectories show the atoms changing direction, going straight, and being lost from the lattice, respectively. (b),(d) Fraction of atoms transitioning from the $x$-moving lattice to the $y$-moving lattice (filled circles) and remaining in the $x$-moving lattice (empty circles) for the two lattice polarizations: (b) ${\mathbf{E}}_L^{(\perp )}$ and (d) ${\mathbf{E}}_L^{(\parallel )}$. Results of simulations are indicated by black symbols. The interference term $|{\mathbf{e}}_x\cdot {\mathbf{e}}_y|\ne 0$ facilitates transferring atoms from the $x$ lattice to the $y$ lattice for higher moving lattice velocity $v_L>60\mathrm{mm}/\mathrm{s}$. Experimental results for atoms in the ${}^3{P}_0$ state are indicated by red symbols.