Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array

We describe a blue-detuned optical lattice for atom trapping which is intrinsically two-dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using an arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection of single Cs atoms in 6- and 49-site two-dimensional arrays.

Figure 1

Intensity distribution of Gaussian beam array in the $x$-$y$ (a) and $x$-$z$ (b) planes. Beams propagate along the $z$ axis, giving an array of traps lying in the $x$-$y$ plane. The trap array has periodicity $d$ and forms atom traps at the center of each four-beam plaquette where the intensity is $I_c$. Lateral confinement in the $x$-$y$ plane is provided by the saddles with intensity $I_s$. Localization normal to the $x$-$y$ plane along $z$ is provided by diffractive spreading of the beams.

Figure 2

Normalized trapping depth [solid (red) curve] and intensity at trap center [dashed (blue) curve] versus normalized array period for half-incoherent array. Variation at constant peak intensity $I_0$ (a) and at constant average intensity $I_d$ (b).

Figure 3

Standard deviation of $x$ position (a) and $z$ position (b) for a half-incoherent array (dashed curves) and full-incoherent array (solid curves). Vertical lines are at the $s$ values for which the trap depths are maximized. Parameters are $\lambda =0.78\mu$m, $d=3.6\mu$m, $T=10\mu$K, and $U_t=k_B\times 300\mu$K.

Figure 4

Normalized trapping depth (solid curve) and intensity at trap center (dashed curve) versus normalized array period for full-incoherent array. The plot assumes constant average intensity $I_d$.

Figure 5

Making a half-incoherent array with a Dammann grating and calcite displacers. The illustration shows creation of a 16-beam array with six trapping sites. Arrows indicate the direction of linear polarization of each beam.

Figure 6

Optical system for creating a half-incoherent GBA with six trapping sites. The intensity image shows the array before focusing onto the atoms with parameters $\lambda =0.78\mu \mathrm{m}$, $d=250\mu \mathrm{m}$, $w_0=120\mu \mathrm{m}$, and $s=2.1$. The 780-nm source is based on a frequency-doubled, single-frequency, 1560-nm laser.

Figure 7

Experimental setup for creating a full-incoherent GBA with 49 trapping sites. Two $4\times 4$ arrays created by diffractive elements (DBS) are combined by a polarizing beam-splitter (PBS). Lenses L${}_1$ and L${}_2$ create a 1:1 telescope to image the arrays onto the calcite that combined them into a 64-beam array. Pin-hole arrays are placed in the foci of lenses (L) to block unwanted zeroth and higher orders of diffraction from the DBS. The spatial parameters of the resulting array are the same as in Fig. 6.

Figure 8

Fluorescence image (a) and atom number histogram (b) in the six-site half-incoherent array. The image is an average of 105 of 5000 events where all six sites loaded a single atom. Each pixel is $0.63\times 0.63\mu {\mathrm{m}}^2$. The atom number histogram has 5000 events taken from one of the six sites showing clear separation of the zero-atom background from the one-atom peak. The solid line is a Poissonian model fitted to the one-atom peak.

Figure 9

Parametric heating measurement of trap frequencies.

Figure 10

Atom trapping in a 49-site full-incoherent array. (a) Distribution of number of occupied sites with fluorescence image. The fluorescence image is an average over 100 atom loading shots, with noise filtered by performing a principal-component analysis on the data set and combining the 49 components with the highest eigenvalues to form the image. (b) Histogram from one of the sites, showing a 59.7$\%$ single-atom loading rate. The solid line is a Poissonian model fitted to the one-atom peak.

Figure 11

Stark shift of the $6s_{1/2},f=4\leftrightarrow 6p_{3/2},f=5$ transition in the 49-site array. Inset: Atom blow-away curve as the laser frequency is scanned.