Superresolution Microscopy of Cold Atoms in an Optical Lattice

Superresolution microscopy has revolutionized the fields of chemistry and biology by resolving features at the molecular level. In atomic physics, such a scheme can be applied to resolve the atomic density distribution beyond the diffraction limit and to perform quantum control. Here we demonstrate superresolution imaging based on the nonlinear response of atoms to an optical pumping pulse. With this technique, the atomic density distribution can be imaged with a full-width-at-half-maximum resolution of 32(4) nm and a localization precision below 500 pm. The short optical pumping pulse of $1.4\mu \mathrm{s}$ enables us to resolve fast atomic dynamics within a single lattice site. A by-product of our scheme is the emergence of moiré patterns on the atomic cloud, which we show to be immensely magnified images of the atomic density in the lattice.

Popular Summary

In recent years, cold atoms have emerged as a versatile platform for studying many interesting quantum phenomena. Their low entropy and ease of manipulation make cold atoms an ideal system to explore new quantum phases and dynamics and to realize quantum information processing. Diffraction-limited microscopy of cold atoms has revealed features at the $1\text{−}\mu \mathrm{m}$ length scale of optical wavelengths. Surpassing the diffraction limit would enable physicists to reveal features of the microscopic atomic density distribution that have been inaccessible with traditional methods. Drawing inspiration from the counterpart in chemistry and biology, we demonstrate a superresolution imaging technique for cold atoms with resolution far below the diffraction limit.

We apply a standing light wave to atoms confined in an optical lattice, which optically pumps some atoms to a different spin state; atoms near the nodes of the light wave remain unexcited. We count the number of excited atoms, then shift the phase of the standing light wave to line up the nodes elsewhere along the chain and count again. By repeating this procedure many times, we build up a plot that maps out the shape of the atomic density distribution with a resolution reaching 32 nm. A byproduct of our scheme is the emergence of moiré patterns on the atomic cloud, which we show to be immensely magnified images of the microscopic atomic density distribution.

Our study is a proof of concept—the quantum states are relatively simple, with little mystery to their dynamics. But with this technique in hand, we can now image subwavelength details of atomic density distributions in scenarios that are more interesting and complex.

Figure 1

Superresolution imaging of ultracold atoms based on optical pumping. (a) Given an intense standing wave of OP light, the excitation probability (red solid line) is nearly unity unless the atoms (blue shaded area) are within a narrow window at the nodes of the OP lattice (red dashed line) where the intensity vanishes. Red shaded area approximates the fraction of the atoms that are not excited. (b) The trapping lattice (cyan) and OP lattice (red) overlap on the atoms. The relative displacement between the two lattices is controlled by a piezoelectric transducer behind one of the retroreflection mirrors. The atomic distribution is measured by scanning the piezoelectric displacement $\mathrm{\Delta }x$. A CCD camera from the side images atoms in situ on the strong $|F=4⟩\to |F^{\prime }=5⟩$ cycling transition. (c) Relevant atomic levels. Atoms initially in the $|F=3⟩$ ground state are optically pumped to $|F=4⟩$ and imaged with the imaging beam. Primed and unprimed letters refer to levels within the excited-state $6^2{P}_{3/2}$ and ground-state $6^2{S}_{1/2}$ manifolds, respectively.

Figure 2

Performance of superresolution imaging. (a) Images of excitation fraction $\mathcal{F}$ taken at different piezoelectric displacements $\mathrm{\Delta }x$. For these images, the OP intensity is $I/I_{\mathrm{sat}}=1.3$, and atoms are prepared in a trapping lattice with detuning $\delta =10\mathrm{GHz}$ and lattice depth $U=200\mu \mathrm{K}$. The region outlined in green indicates the area from which the data in panels (b)–(d) are collected. (b) As the optical pumping intensity increases, the atom response becomes more nonlinear, and the dips in the excitation fraction narrow. These dips reflect the atomic density distribution in each lattice site. From low to high, the traces show measurements at increasing intensity with $I/I_{\mathrm{sat}}=0.017$ (light blue), 0.041 (green), 0.22 (orange), 1.3 (blue), 2.1 (purple), and 2.7 (gray). Solid curves show fits based on a sum of Gaussians separated by ${\lambda }_{\mathrm{OP}}/2$. Piezoelectric displacement is interferometrically measured with nanometer accuracy [31]. (c) FWHMs of the fitted Gaussians at different OP intensities (orange circles) are compared with those of the ground state (40 nm, green), a thermal state with 90% ground-state occupation (45 nm, purple), theoretical resolution (blue), and the expected width (orange) of the convolution of the thermal state and the point-spread function $g(x)$ [31]. Error bars show 1 standard error. (d) Derived single-site atomic density distribution. The measurement reflects the density distribution averaged over sites contained within the green-outlined region in panel (a). From Gaussian fits, we determine $\mathrm{FWHM}=55(2)$ and 62(1) nm, and uncertainty in the peak positions of 0.8 and 0.4 nm, for $I/I_{\mathrm{sat}}=2.1$ (purple) and 1.3 (blue), respectively. (e) A typical optical density (OD) image of all atoms. (f) Distribution of the FWHM across the cloud at $I/I_{\mathrm{sat}}=2.1$. Only the area containing signal sufficient for fitting is shown.

Figure 3

Microscopic dynamics revealed by superresolution microscopy. (a) An illustration of the experimental procedure. After preparing atoms in the ground state, the trapping lattice is displaced by an amplitude $A=79\mathrm{nm}$, causing the atoms to oscillate. (b) Atomic density evolution within a single lattice site. After a hold time $\tau$, we record the atomic density using the same procedure as Fig. 2. Here, the trapping lattice detuning is $\delta =20\mathrm{GHz}$, lattice depth $U=10\mu \mathrm{K}$, and OP intensity $I/I_{\mathrm{sat}}=1.3$. Jagged motion of the atoms results from anharmonicity of the lattice potential and can be described by the quantum motion in the lattice [31]. Data are extracted from the location shown in the red box in panel (d). The data presented in (b) are smoothed using a window of ${\lambda }_{\text{trap}}/20$ [31]. (c) Evolution of the atomic position determined from Gaussian fits. Blue and red circles are based on measured data from bins of the same color in panel (d). Solid curves show exponentially decaying cosine fits $x_c=-A{e}^{-\gamma \tau }\cos 2\pi f_{\mathrm{osc}}\tau$, where $\gamma$ is the decay constant and $f_{\mathrm{osc}}$ is the oscillation frequency. Error bars show 1 standard error. (d) Typical absorption image of the atomic cloud. (e) Map of fitted oscillation frequency $f_{\mathrm{osc}}$ across the cloud. (f) Map of fitted decay constant $\gamma$ across the cloud.

Figure 4

Moiré magnification of the atomic density distribution. (a) When two periodic structures of slightly different pitch are overlapped, a large-scale moiré pattern emerges. (b) Magnification of the atomic density distribution based on moiré interference. The OP lattice (red) interrogates the atomic density distribution (blue shaded) at different positions (red dots) within each confining lattice site. If the atomic density distribution in every site is identical, then the resulting excitation fraction across the cloud traces out the density distribution with large magnification. (c) In situ images of excitation fraction taken at different lattice detunings $\delta$ with a field of view of $(2.44\mathrm{mm}{)}^2$ with $I/I_{\mathrm{sat}}=0.89$. In each image, the moiré pattern reflects the microscopic atomic density distribution. Spacing between stripes is ${\lambda }_{\text{trap}}/2$. White bars show the microscopic length scale. (d) Comparison of the moiré pattern within the orange rectangle in panel (c) (orange circles) to the microscopic atomic density distribution measured in the cyan box in panel (c) by piezoelectric scan (cyan circles). The horizontal axis of each dataset is scaled to match spatial periodicity and translated to overlap the peaks. (e) Dependence of moiré magnification $M$ on detuning $\delta$ [31]. The solid line is based on Eq. (4). The statistical errors are smaller than the marker size. (f) Evolution of the moiré pattern after a 79-nm lattice phase jump with detuning $\delta =200\mathrm{GHz}$. After hold time $\tau$, the moiré pattern oscillates and becomes distorted, indicating that the dynamics of the atoms in the lattice are not uniform across the sample. The dashed green line serves as a reference indicating the initial position of the center stripe.