A Strontium Quantum-Gas Microscope

The development of quantum-gas microscopes has brought novel ways of probing quantum degenerate many-body systems at the single-atom level. Until now, most of these setups have focused on alkali atoms. Expanding quantum-gas microscopy to alkaline-earth elements will provide new tools, such as SU($N$)-symmetric fermionic isotopes or ultranarrow optical transitions, to the field of quantum simulation. Here we demonstrate the site-resolved imaging of a ${}^{84}\mathrm{Sr}$ bosonic quantum gas in a Hubbard-regime optical lattice. The quantum gas is confined by a two-dimensional in-plane lattice and a light-sheet potential, which operate at the strontium clock-magic wavelength of 813.4 nm. We realize fluorescence imaging using the broad 461-nm transition, which provides high spatial resolution. Simultaneously, we perform attractive Sisyphus cooling with the narrow 689-nm intercombination line. We reconstruct the atomic occupation from the fluorescence images, obtaining imaging fidelities above $94\mathrm{\%}$. Finally, we realize a ${}^{84}\mathrm{Sr}$ superfluid in the Bose-Hubbard regime. We observe its interference pattern upon expansion, a probe of phase coherence, with single-atom resolution. Our strontium quantum-gas microscope provides a new platform to study dissipative Hubbard models, quantum optics in atomic arrays, and SU($N$) fermions at the microscopic level.

Popular Summary

Quantum-gas microscopes are instruments that can detect individual atoms in an optical lattice in the quantum regime. These are powerful tools to simulate quantum systems made of many particles, such as electrons in real materials. Most of these microscopes have been realized with alkali atoms, which have one valence electron. However, unlocking quantum-gas microscopy for atomic species with more complex electronic structures will offer new opportunities. A popular atom is strontium, used for quantum computing and atomic clocks. In this article, we demonstrate a quantum-gas microscope with atomic strontium.

For our experiment, we chose the bosonic isotope strontium-84, which has excellent interaction properties. We prepare an ultracold gas of atoms in a flat trap with a lattice potential, generated by interfering four laser beams. We then shine blue light on the atoms, making them fluoresce hundreds of photons that we detect with a very sensitive camera. This short-wavelength light provides very high spatial resolution but also increases the atoms’ kinetic energy such that they could escape the trap. We counteract this undesirable heating by simultaneously laser cooling the atoms in the lattice. Finally, we let the atoms expand after switching off the lattice and detect a beautiful interference pattern. This confirms the quantum nature of our gas, which is in a superfluid state in the lattice.

In future works, our microscope can be extended to study quantum gases of fermionic strontium. While electrons have only two spin states, fermionic strontium-87 can be used to realize systems with up to ten different spin states, allowing us to investigate exotic magnetism. Additionally, we will be able to perform high-resolution spectroscopy via the strontium optical clock transition, the same one used by the best clocks in the world.

Figure 1

Strontium quantum-gas microscope. (a) Top view of the experimental setup, showing the lattice beam passing four times through the quartz glass cell. The light-sheet beam is tightly focused (waist in the $z$ direction approximately $3.5$ µm) and provides the vertical confinement into the plane. The lattice and light-sheet beams are vertically polarized (${\overrightarrow{ϵ}}_{813}$) and operate at a wavelength of 813.4 nm. The objective, placed below the glass cell, captures the fluorescence signal of the atoms generated by a blue imaging beam at 461 nm that is horizontally polarized. (b) Two-dimensional potential created by the fourfold interference of the lattice beams (bottom). The tighter confinement in the ${}^3{P}_1$ excited state compared with the ${}^1{S}_0$ ground state (top) allows attractive Sisyphus cooling on the red intercombination transition at 689 nm. (c) Side view of the experimental setup, depicting the six red cooling beams and the objective placed below the glass cell. (d) Energy-level diagram of strontium, with the broad-linewidth imaging transition and the narrow-linewidth cooling transition. Shown are also the repumping transitions (481 nm [45] and 679 nm [46]) used to recover atoms that leaked into the long-lived states ${}^3{P}_0$ and ${}^3{P}_2$. (e) Azimuthal average of the PSF (blue circles), with a Gaussian fit (solid line) and the ideal Airy disk (dashed line). The inset shows the PSF obtained by averaging the signal of 1187 isolated atoms. (f) Raw fluorescence image of a dilute thermal cloud showing around $500$ individual ${}^{84}\mathrm{Sr}$ atoms. NA, numerical aperture.

Figure 2

Reconstruction of the atomic occupation from a fluorescence image. (a) Raw experimental image of a thermal cloud loaded in the lattice. (b) Deconvolution of the image in (a) with the PSF to obtain a cleaner signal. The black circles mark the positions of the reconstructed lattice grid, while the green circles indicate the lattice sites detected as occupied. (c) Histogram of the counts at each lattice site for the deconvolved picture in (b). The plot indicates the distinguishability between the zero-atom case (left peak) and the one-atom case (right peak). To choose the threshold value in counts, we fit a double Gaussian function to the histogram. From the fit we estimate that more than $99.9\mathrm{\%}$ of the one-atom distribution lies above the threshold in this image. (d) Binary occupation obtained from the reconstruction of the picture.

Figure 3

Fidelity of the site-resolved single-atom detection. (a) Two consecutive images ($15.5\times 15.5$ µm² region) of the same cloud after being deconvolved. In the first picture, the one on the left, we mark sites where an atom has been detected with green circles. In the second picture, the one on the right, lost atoms are indicated with red circles, atoms that hopped are indicated in orange, and those that remained in the same position are indicated in green. The single-shot pinning fidelity $F$ is $96.5\mathrm{\%}$. (b) Pinning fidelity $F$ as a function of imaging time. We take ten images of the same cloud within 35 s and compare the reconstructed occupation with either the occupation corresponding to the initial shot (blue circles) or the occupation corresponding to the previous shot (green squares). The solid green line marks the average of all green-square fidelity data, which is around $95\mathrm{\%}$. The inset shows the accumulated losses for each consecutive measurement (red diamonds) compared with those caused by background-gas losses (dashed gray line). Error bars indicate one standard error of the mean.

Figure 4

Spatial inhomogeneity of Sisyphus cooling. Top: Four individual fluorescence images of atomic clouds at different red-cooling detunings. Frequencies closer to the free-space resonance lead to larger cloud sizes. Bottom: Red-cooling frequency corresponding to the position of the cloud edge. The edge positions of the cloud along the $x$ and $y$ axes are extracted by fitting an error function to the fluorescence signal within a sliced region (see the rectangular boxes in the second fluorescence image) integrated along the perpendicular direction. The shape allows us to extract the trapping frequency directly from the spectral dependence of the cloud size. The right axis indicates the potential $V$ experienced by the ground state ${}^1{S}_0$, computed from the differential polarizability. The inset in the lower plot illustrates the overall differential trapping, and how it shifts the red transition out of resonance. Horizontal dashed lines indicate the frequencies corresponding to the pictures at the top. The error bars are smaller than the marker size.

Figure 5

Detection of a Bose-Hubbard superfluid. (a) In situ image of a quantum gas loaded into the optical lattice at a depth of $V_0=2.3(1)E_r$. (b) Image taken after an in-trap 2D expansion, during which the lattice is abruptly switched off for $t_{\exp }=2\mathrm{ms}$ while the atoms are held in plane by means of the harmonic trap produced by the light-sheet beam. An average over ten such pictures is displayed in (c), where higher-order interference peaks are visible at the corners of the image. The color scale in (c) has been adjusted to better discern the pattern.

Figure 6

Fluorescence spectrum of Sisyphus cooling. We detect the fluorescence of the atoms in the optical lattice (blue circles) for differing cooling frequencies detuned by $\delta$ from the free-space resonance of the $m_J=0$ transition (vertical dotted line). The three peaks are fitted with three independent Gaussian functions, and correspond to the light-shifted $m_J$ transitions of the ${}^3{P}_1$ excited state. The free-space resonance for the $|m_J|=1$ transitions (vertical dashed and dot-dashed lines) are centered at around zero and are Zeeman-split by $\pm 0.8\mathrm{MHz}$. Typically we detune the cooling light $\delta /2\pi \approx -0.4\mathrm{MHz}$ from the free-space resonance in order to cool a large region; see the inset.