Spin-resolved microscopy of $^{87}$Sr SU($N$) Fermi-Hubbard systems

This paper reports the first realization of a spin-resolved quantum-gas microscope for fermionic $^{87}$Sr, enabling site-resolved detection of all 10 spin states in SU(N) Fermi-Hubbard systems to probe exotic magnetism and magnetic correlations.

The Gist

Imagine you are trying to understand a massive, chaotic dance party happening inside a tiny box. The dancers are atoms, and the way they move and interact with each other determines the rules of the universe's most complex materials. For decades, scientists have been able to watch these parties, but they've only been able to see the dancers' locations, not their personalities or moods.

This paper is about a team of scientists who finally built a camera powerful enough to not only see where every dancer is standing but also to identify exactly who they are, what "mood" (spin state) they are in, and how they are interacting with their neighbors.

Here is the story of how they did it, explained simply.

The Problem: The "Spin" Mystery

In the quantum world, atoms have a property called spin. Think of spin like a tiny internal compass needle.

• In most experiments, scientists only looked at atoms with two possible compass directions (Up or Down). It's like a dance with only two types of moves.
• But nature is more complex. Some atoms, like Strontium-87 ($^{87}\text{Sr}$), have 10 different compass directions (from -9/2 to +9/2). This creates a much richer, more complex dance called an SU(N) system.

The problem? Previous microscopes were like black-and-white cameras. They could tell you "There is a dancer here," but they couldn't tell you which of the 10 types of dancers it was. To figure it out, they had to take 10 separate photos of the same party, hoping the dancers didn't move or change their minds between shots. This was messy and inaccurate.

The Solution: A Super-Camera with a "Magic Filter"

The team at ICFO (in Barcelona) built a new kind of microscope specifically for these 10-state Strontium atoms. Here is how their trick works:

1. The "Narrow-Line" Flashlight
Imagine trying to take a photo of a specific person in a crowd wearing 10 different colored hats. If you use a regular white flash, everyone looks the same.
The scientists used a very specific, "narrow" laser light (689 nm). It's like a flashlight that only illuminates the person wearing the Red Hat (the -9/2 state).

• When they shine this light, only the "Red Hat" atoms glow and can be photographed.
• The other 9 types of atoms stay dark and invisible.

2. The "Magic Hat Switch" (Optical Pumping)
Now, how do they see the Blue Hats, Green Hats, and so on?
They use a second laser trick called optical pumping. Think of this as a magical conveyor belt.

• They shine a specific light that gently nudges the "Blue Hat" dancers and forces them to change their hat to a "Red Hat."
• Now, the Blue Hats are invisible, but the Red Hats (which were originally Blue) glow!
• They take a photo.
• Then, they nudge the "Green Hat" dancers to become "Red Hats," take another photo, and repeat this for all 10 types.

3. The "One-Shot" Miracle
The genius of this paper is that they did this sequentially in a single run. They didn't have to restart the experiment 10 times. They took one photo of the Red Hats, switched the hats, took a photo of the new Red Hats (who were originally Blue), and so on.
By the end, they had 10 images that, when stacked together, showed the complete map of every single atom and its specific "spin" state in the entire grid.

Why Does This Matter?

This is a huge leap forward for three reasons:

• Solving the "Magnetism" Puzzle: Scientists believe that if you can see how these 10 different spins interact, you might discover new states of matter, like "chiral spin liquids" (think of a liquid that flows like water but has the magnetic order of a solid). This is the "Holy Grail" for understanding high-temperature superconductors (materials that conduct electricity with zero resistance).
• The "Quantum Computer" Upgrade: These 10 spin states are like having a dial with 10 numbers instead of a switch with just 0 and 1. This allows for much more powerful quantum computing (using "qudits" instead of "qubits"). This microscope proves we can read and write these 10 states reliably.
• Precision Metrology: Because they can control these atoms so precisely, they can build better atomic clocks, which are the most accurate timekeepers in the universe.

The "Larmor Precession" Test

To prove their camera worked, they did a cool test. They made the atoms' compass needles spin in a circle (like a spinning top wobbling).

• They watched the atoms rotate from "Red Hat" to "Blue Hat" to "Green Hat" and back again.
• Their microscope captured this rotation perfectly, frame by frame.
• The fact that the data matched their math perfectly proved that their camera wasn't just seeing the atoms; it was seeing their quantum souls without messing them up.

The Bottom Line

Before this, studying these complex 10-state atoms was like trying to understand a symphony by listening to a muffled recording where you couldn't tell which instrument was playing.
This paper gives us high-definition, 3D surround sound. We can now see every instrument, every note, and how they harmonize. This opens the door to discovering entirely new laws of physics and building the next generation of quantum technology.

Technical Summary

Here is a detailed technical summary of the paper "Spin-resolved microscopy of 87Sr SU(N) Fermi-Hubbard systems".

1. Problem Statement

Quantum-gas microscopes have revolutionized the study of the Fermi-Hubbard model by enabling site-resolved detection of atoms, crucial for understanding quantum magnetism and interactions. However, existing microscopic studies have largely been limited to spin-1/2 systems (SU(2)).

• The Challenge: Extending this to SU(N) systems (where $N > 2$) is difficult because:
  1. Detection Complexity: Standard methods (like Stern-Gerlach separation or spin-to-position mapping) do not scale well to atoms with large nuclear spins (e.g., $N=10$ for $^{87}\text{Sr}$).
  2. Spin Stability: Multi-component mixtures often suffer from spin-exchange collisions, leading to population leakage.
  3. Imaging Limitations: Alkaline-earth(-like) atoms (like Strontium) possess unique internal structures (narrow transitions, decoupled nuclear spin) ideal for SU(N) physics, but previous quantum-gas microscopes for these species were limited to bosonic isotopes or lacked spin resolution.
• The Goal: To realize a quantum-gas microscope for fermionic $^{87}\text{Sr}$ capable of spin-resolved, single-atom detection of all 10 nuclear spin states ($I=9/2$) in a single experimental run, enabling the study of exotic SU(N) magnetic phases.

2. Methodology

The authors developed a novel imaging and manipulation protocol based on the narrow intercombination line of Strontium at 689 nm.

• Experimental Setup:

  • Atoms: Fermionic $^{87}\text{Sr}$ loaded into a 2D square optical lattice (magic wavelength 813.4 nm).
  • Cooling & Imaging: Utilizes the narrow linewidth ($\Gamma/2\pi = 7.4$ kHz) of the $^1S_0 \to {}^3P_1$ transition. This allows for Sisyphus cooling during imaging, preventing atom loss due to heating.
  • Spin Resolution: A bias magnetic field ($B \approx 20$ G) creates a Zeeman splitting ($\sim 8$ MHz) between the $m_F$ sublevels. This is orders of magnitude larger than the transition linewidth, allowing the imaging laser to resonantly address only the stretched state $|F=9/2, m_F=-9/2\rangle$ while remaining off-resonant for all other 9 states.

• Spin-Selective Optical Pumping Protocol:
  To detect all 10 states sequentially in one experimental cycle, the authors implemented a 10-step detection block:

  1. Target Selection: Use optical pumping pulses to transfer atoms from a specific target spin state ($m_F$) into the "stretched" imaging state ($m_F = -9/2$).
  2. Imaging: Perform fluorescence imaging on the $m_F = -9/2$ state.
  3. Spin Removal: Use a blue-detuned pulse on the imaging transition to heat and eject the detected atoms from the lattice (spin-removal), ensuring they are not counted in subsequent steps.
  4. Repetition: Repeat this process for all 10 spin states ($m_F = -9/2$ to $+9/2$).

• Benchmarking: The system's fidelity was tested by observing Larmor precession of the nuclear spin in a magnetic field, tracking the coherent evolution of the spin distribution across all 10 states.

3. Key Contributions

• First SU(N) Quantum-Gas Microscope: This is the first demonstration of a quantum-gas microscope for a fermionic alkaline-earth species ($^{87}\text{Sr}$) with full spin resolution.
• Sequential Spin-Resolved Detection: The protocol successfully reconstructs the occupation matrix of all 10 spin states in a single experimental realization, a capability previously unattainable for $N=10$.
• High-Fidelity Spin Manipulation: The authors quantified the fidelity of the optical pumping and imaging processes, demonstrating that spin-selective manipulation can be performed without significant atom loss or hopping.
• Diagnostic Capability: The system acts as a sensitive diagnostic tool, identifying spurious processes like trap-induced spin depolarization (off-resonant Raman scattering) that were previously difficult to detect.

4. Key Results

• Imaging Performance:
  • Pinning Fidelity ($F_{pin}$): $92.5(7)%$. This is the probability that an atom detected in one frame is still present in the next.
  • Optical Pumping Fidelity:
    • For the stretched state ($m_F = -9/2$): $F_{OP,1} = 95.6(8)\%$.
    • For central states: $F_{OP,2} = 99.8(1)\%$.
  • Spin Depolarization: The primary source of error is off-resonant Raman scattering from the lattice light, causing $\sim 4.2\%$ of atoms to change spin states during the imaging cycle. This leads to "multi-detection events" (an atom appearing in multiple spin images), which were quantified and found to be primarily nearest-neighbor in spin space.
• Larmor Precession Benchmark:
  • The team observed coherent precession of the $F=9/2$ nuclear spin over hundreds of milliseconds.
  • The experimental data matched theoretical predictions (including all identified infidelities) with no free fitting parameters other than the oscillation period, confirming the robustness of the detection protocol.
• Spin Population Reconstruction: In a thermal cloud with 253 atoms evenly distributed across 10 spin states, the system successfully reconstructed the spin-resolved occupation matrix, distinguishing between different spin populations site-by-site.

5. Significance and Future Outlook

• Unlocking Exotic Magnetism: This technique opens the door to studying SU(N) quantum magnetism, a regime where theoretical predictions include spontaneous dimerization, plaquette order, and chiral spin liquids (for large $N$).
• Beyond SU(2): It moves beyond the standard spin-1/2 paradigm, allowing direct measurement of higher-order spin correlators and the competition between itinerancy and magnetism in multi-component systems.
• Applications:
  • Quantum Simulation: Direct observation of magnetic phases in the SU(N) Fermi-Hubbard model (e.g., zig-zag antiferromagnetism in SU(3)).
  • Quantum Computing: The ability to resolve and manipulate nuclear spin states ($N=10$) provides a scalable platform for qudit-based quantum computing.
  • Metrology: The state-resolved detection could improve coherence times in optical lattice clocks via erasure-conversion strategies.

In summary, this work establishes a powerful new tool for quantum simulation, enabling the microscopic exploration of complex, high-symmetry quantum many-body systems that were previously inaccessible to direct observation.