Imaging and addressing of individual fermionic atoms in an optical lattice

We demonstrate fluorescence microscopy of individual fermionic potassium atoms in a 527-nm-period optical lattice. Using electromagnetically induced transparency cooling on the 770.1-nm $D_1$ transition of ${}^{40}\mathrm{K}$, we find that atoms remain at individual sites of a 0.2-mK-deep lattice, with a $1/e$ pinning lifetime of $67\left(9\right)\mathrm{s}$, while scattering $\sim {10}^3$ photons per second. The plane to be imaged is isolated using microwave spectroscopy in a magnetic-field gradient, and can be chosen at any depth within the three-dimensional lattice. With a similar protocol, we also demonstrate patterned selection within a single lattice plane. High-resolution images are acquired using a microscope objective with 0.8 numerical aperture, from which we determine the occupation of lattice sites in the imaging plane with 94(2)% fidelity per atom. Imaging with single-atom sensitivity and addressing with single-site accuracy are key steps towards the search for unconventional superfluidity of fermions in optical lattices, the initialization and characterization of transport and nonequilibrium dynamics, and the observation of magnetic domains.

Figure 1

High-resolution fluorescence image of fermionic potassium atoms in a single sparsely filled plane of a 527-nm-period cubic optical lattice. The false-color scale indicates the number of counts recorded by an electron-multiplying CCD camera, where one photoelectron corresponds to 16 counts. Atoms outside of a $40\times 40$ site box have been removed using the addressing protocol described in the main text. In the inset, one can clearly discern individual atoms. In this 2.6-s-long exposure, an average of $\sim 160$ photons are detected per atom.

Figure 2

Microscopy. (a) A sapphire window (SW) with a thickness of $\mu 200\mathrm{m}$ and a clear aperture of 5 mm separates UHV from air. This allows for the placement of a microscope objective (MO) with NA $=0.8$ and 3 mm working distance outside the vacuum with its focal plane on the inside. (b) Single-shot image of a single atom. With image magnification of $78\times$, each camera pixel has a virtual size of $192\mathrm{nm}$. (c) Averaging the signal from 200 isolated atoms in the imaging plane yields the effective PSF of the imaging system. The coordinates $X$ and $Y$ are aligned with the principal axes of the images. (d) The radial average of the PSF has a FWHM of $\mu 0.60\left(1\right)\mathrm{m}$. Note that this effective PSF includes not only optical effects but also the finite size of lattice orbitals and drifts of the lattice during exposure. The color scale in (b) and (c) is the same as in Fig. 1.

Figure 3

Selection of lattice sites. (a) Plane selection occurs in three steps. Atoms to be preserved are first transferred from $|F,m_F\rangle =|9/2,-9/2\rangle \equiv |g1\rangle$ to $|7/2,-7/2\rangle \equiv |g2\rangle$ using microwaves at frequency $2\pi \nu$, in the presence of a magnetic field $B\left(z\right)$ that has a linear gradient. Here $F$ is the total angular momentum and $m_F$ is the magnetic quantum number. At $105\mathrm{G}/\mathrm{cm}$, the 5.5-mG field difference across $\mathrm{\Delta }z={\lambda }_L/2$ translates to $\mathrm{\Delta }\nu =14\mathrm{kHz}$ between adjacent planes. Atoms remaining in $|g1\rangle$ are removed from the lattice with a resonant laser beam operating on the $D_2$ transition, before the atoms shelved in $|g2\rangle$ are brought back to $|g1\rangle$. This selects a single $xy$ plane of the lattice, as shown in (b). Patterning in the $x$ or $y$ plane (see Fig. 1) follows a similar procedure. (c) Varying the microwave frequency range chosen to isolate a plane allows for selection of any plane within the bulk 3D lattice.

Figure 4

Cooling and background reduction. (a) Coupling (C) and probe (P) beams are blue-detuned ($\mathrm{\Delta }>0$) from the $D_1$ transition. (b) Laser cooling in the $xy$ plane involves a retroreflected probe beam (${\mathrm{P}}_{xy}$) and a coupling beam (${\mathrm{C}}_{xy}$), both with an angle of ${30}^{\circ }$ relative to the nearest lattice beam. ${\mathrm{P}}_{xy}$ and ${\mathrm{C}}_{xy}$ enter the chamber linearly polarized along the $z$ axis, and the retroreflection of ${\mathrm{P}}_{xy}$ is linearly polarized in the $xy$ plane. (c) An additional coupling beam ${\mathrm{C}}_z$, linearly polarized along the direction of propagation of ${\mathrm{C}}_{xy}$, passes downward through the sapphire window and extends the cooling to the $z$ direction. Background light from backscattering of the ${\mathrm{C}}_z$ beam is minimized by pulsing it synchronously with a chopper wheel blocking all light falling on the EMCCD camera.

Figure 5

Reconstruction of the lattice occupation. (a) Magnified subimage of Fig. 1. (b) Deconvolution of the image with the PSF [see Fig. 2] gives a sharpened image which we use to pin the lattice grid. (c) A lattice-site binned image is then used to select potentially occupied sites via a threshold. (d) The final best-fit digitization is determined by comparing all possible occupation patterns for the selected sites and their immediate neighbors with the sharpened image. In this step we allow for discrete variation of brightness of $\pm 20\%$, and we assume a Gaussian spatial distribution for each atom with a width determined by the typical feature size in the sharpened image. (e) Histogram of signal per lattice site obtained from 12 sharpened and binned images similar to (c). Gray bars correspond to the signal from all lattice sites, while the red and blue bars, respectively, display the signal from sites determined to be occupied or unoccupied. (f) Histogram of signal obtained from fits of Gaussian functions to the same images used for (e). Here, the signal for each site is obtained from a simultaneous fit to the sharpened subimage of the target site and its immediate neighbors. The width of the Gaussian functions is the same as for the digitization step.

Figure 6

Fidelity. Plots show the fraction of atoms in the first digitized image that are pinned (filled circles), hop to a different site (open circles), or are lost completely (crosses) in the successive image. Unless otherwise indicated, $\delta =0$, the ${\mathrm{C}}_z$ chopping rate is 100 Hz, the ${\mathrm{C}}_z$ duty cycle is 35%, and the exposure time is 2.6 s with 0.4 s between exposures. Maximal pinning occurs for (a) Raman detuning $\delta \approx 0$, (b) exposure time between 2 and 5 s, (c) a chopping frequency that is $>100\mathrm{Hz}$, and (d) a duty cycle of ${\mathrm{C}}_z$ that is at least 30%. Lines shown in (b) are $0.002\left(28\right)+0.004\left(3\right)t$ for the loss fraction and $0.07\left(2\right)+0.011\left(2\right)t$ for the hopping fraction and fit only to points at $t>4\mathrm{s}$.