Super-resolution optical trapping of multiple cold atoms

Abstract

Arrays of optical tweezers form the backbone of neutral atoms analog and digital quantum processors. However, the inter-trap distance remains generally much larger than the size of the tweezers to avoid interference-induced trap distortions, limiting the trap density. Here, we report single-atom trapping in four super-resolved tweezers, meaning with a separation below the Sparrow diffraction limit. The optical pattern is generated using superoscillatory phenomenon leading to subwavelength traps with full control of the trap relative phases. We investigate two sets of relative phases that impede or allow the hopping and the reshuffling of atoms. We envision that superoscillatory light structuring will bridge the gap between large-distance traps generated by tweezer arrays and short-distance traps formed with optical lattices.

Figures (4)

• Figure 1: (a) Sketch of the experiment that shows the 3D MOT beams, the fluorescence path, and the ODT beam path at $1064\,$nm. The imaging system is diffraction-limited at $1064\,$nm, with NA = 0.39. The insets illustrate image samples obtained on CCD cameras and a phase pattern loaded into the SLM. They are presented in (b)-(d) with greater resolutions. (b) Fluorescence image of four atoms in the Airy tweezers with $3.5\lambda$ separation. (c) The Airy hologram loaded into the SLM. For clarity purposes, the period of the blazed grating is represented with a multiplication factor of 10. (d) Airy pattern corresponding to the hologram depicted in (c). (e) and (f) [(g) and (h)] Measured and simulated SO light pattern for $2\pi$ ($4\pi$) winding of the trap relative phase. The scale in (d)-(h) corresponds to the object plane located in the science chamber.
• Figure 2: (a) Neighboring trap separation, and (b) tweezer radial FWHM size. The $2\pi$- ($4\pi$-) winding cases are in blue (red), whereas the diamond and square (triangle and circle) symbols represent measurements of the Airy (SO) tweezers. The colored solid and dotted curves are simulations using Collins integrals without free parameters. The black dashed line in (a) corresponds to ideal point-like tweezers where the imposed separation is equal to the measured separation. The simulated Sparrow limits for two tweezers (dotted line) and four tweezers (dash-dotted line) are shown in (a). The measured (black dot) and expected (black lines) FWHM sizes of a single Airy and SO tweezers are shown in (b).
• Figure 3: (a) Schematic of the time sequences, comprising four phases: a loading and initial imaging, a polarization gradient cooling (PGC), an Airy-SO-Airy transfer, and a final imaging (see Supplemental Material SM for more details). A four-atom probability matrix after an Airy-SO-Airy round trip for the case of (b) $4\pi$-winding and (c) the $2\pi$-winding. The theory predictions are shown in (d) and (e). The matrix elements $M_{i,j}$ give the probability to measure $i$ ($j$) atoms in the initial (final) image. The index $i$ ($j$) corresponds to the row (column). The $M_{i,j}$ values are given in percentage normalized for each initial atom number, regardless of the arrangement of the atoms in the traps. The image panels illustrate a case where three atoms are loaded (left image). After transfer, this case might contribute to $M_{3,1}$ (right image highlighted in fuchsia) due for example to a two-body loss. A contribution to the diagonal term $M_{3,3}$ is shown in the right image highlighted in red. Each experimental matrix is computed using $10^4$ runs. The standard deviations above 1$\%$ are indicated and large values mainly reflect the low occurrence of a realization. The uncertainty for the theory in (d) and (e) comes from the statistical incertitude on the temperature and atom lifetime.
• Figure 4: (a) Conditional probability for an atom to remain in the same trap after an Airy-SO-Airy round trip as a function of an adiabatic reduction in tweezer power during $60\,$ms in the SO tweezer phase. $P_{0}$ (respectively $P$) is the SO tweezer power before (after) reduction. An example of a positive count is illustrated on the image panels above. The dashed black line indicates the conditional probability of a complete reshuffling. The conditional probability is derived from simulations and shown as shaded areas for a 1.4$\lambda$ (red) and a 1.7$\lambda$ (blue) trap separation. The solid area width represents a standard deviation error that comes from the initial temperature uncertainty. (b) one-body survival probability as a function of the reduction in tweezer power. An atom loss is illustrated in the image panels above. In (a) and (b) the red circles (blue squares) correspond to a trap separation of 1.4$\lambda$ (1.7$\lambda$). Each data point corresponds to an average over $\sim180$ occurrences, and the error bars correspond to the standard deviations.