Multi-state detection and spatial addressing in a microscope for ultracold molecules

This paper demonstrates a high-resolution, multi-state detection and spatial addressing technique for ultracold 87Rb133Cs molecules in a bulk sample, achieved by pinning them in a 2D optical lattice, dissociating them into constituent atoms for fluorescence imaging, and mapping internal molecular states to distinct atomic species to enable precise measurements of density distributions, collisional losses, and rotational state-dependent addressing.

The Gist

Imagine you have a jar filled with thousands of tiny, invisible marbles floating in a gas. These aren't ordinary marbles; they are ultracold molecules made of two different atoms stuck together (Rubidium and Cesium). Scientists want to study how these molecules bump into each other, but there's a problem: they are too small to see, and if you try to look at them too closely, they might move or break apart before you can count them.

This paper describes a clever "magic trick" the researchers at Durham University used to freeze these molecules in place, take a high-definition photo of every single one, and even tell them apart based on their internal "mood" (their quantum state).

Here is how they did it, broken down into simple steps:

1. The "Flypaper" Trap (Pinning the Molecules)

Normally, these molecules are floating around like dust motes in a sunbeam. To take a picture, the researchers first had to stop them. They used a 2D optical lattice, which is like a grid of invisible laser light.

• The Analogy: Imagine spreading a sheet of sticky flypaper over the floating dust. The molecules get stuck in the tiny squares of the grid.
• The Result: The molecules are now frozen in their exact positions, preserving a "snapshot" of where they were floating before the trap was turned on.

2. The "Break-Apart" Photo (Dissociation and Imaging)

Once the molecules are stuck, the researchers need to see them. But molecules don't glow brightly enough to be photographed easily. So, they break the molecules apart.

• The Analogy: Think of the molecule as a sandwich made of two different ingredients: a slice of Rubidium bread and a slice of Cesium bread. The researchers use a laser to gently pull the sandwich apart. Now, instead of one invisible sandwich, you have two glowing atoms.
• The Trick: They use a special cooling technique (like a gentle breeze) to keep these atoms from running away while they glow. They then take a picture using a super-powerful camera lens.
• The Outcome: By looking at the glowing atoms, they can reconstruct exactly where the original "sandwiches" (molecules) were sitting. They can count them one by one, even if there are only a few dozen in the whole sample.

3. The "Color-Coded" ID (Multi-State Detection)

The researchers didn't just want to know where the molecules were; they wanted to know what state they were in. Molecules can exist in different "rotational states" (think of them as spinning at different speeds).

• The Analogy: Imagine you have a crowd of people wearing either Red Hats or Blue Hats. You want to know who is wearing which hat without asking them.
• The Method: The researchers set up a rule: If a molecule is spinning slowly (State A), when they break it apart, the Rubidium atom stays behind. If it's spinning fast (State B), the Cesium atom stays behind.
• The Result: By taking pictures of the Rubidium atoms and the Cesium atoms separately, they can create a map showing exactly which molecules were spinning slowly and which were spinning fast. It's like seeing a crowd where the Red Hats glow red and the Blue Hats glow blue.

4. The "Spotlight" Surgery (Spatial Addressing)

Finally, they wanted to be able to change the state of just a specific group of molecules, leaving the rest alone.

• The Analogy: Imagine shining a bright spotlight on a specific group of people in a dark room. The light makes them feel "hot" and changes their behavior, while everyone else in the dark stays the same.
• The Method: They used a focused beam of light to hit only a small circle of the trapped molecules. This light shifted the energy levels of the molecules in that circle, making them "immune" to a microwave signal that would normally change their spin.
• The Result: They could selectively change the state of the molecules in the spotlight while leaving the others untouched. They even used this to "cut out" a small, perfect circle of molecules from the larger cloud to study them in isolation.

Why Does This Matter?

The paper claims this technique allows scientists to:

1. Count exactly how many molecules are in a sample, even if the number is very small (down to about 50).
2. Measure density precisely to see how fast molecules crash into each other and disappear (collisions).
3. Map internal states to see how the "spins" of the molecules are distributed in space.

The authors suggest this is a major step forward for studying ultracold molecular collisions and quantum magnetism (how these tiny particles interact like magnets). They note that while their current molecules are a bit "hot" (energetic) for some advanced experiments, this method provides all the necessary tools to eventually build complex quantum systems where every single molecule is known and controlled.

In short: They built a high-tech camera that can freeze, break apart, and photograph individual molecular sandwiches, telling them exactly where they were and how they were spinning, all with incredible precision.

Technical Summary

Technical Summary: Multi-state detection and spatial addressing in a microscope for ultracold molecules

Problem Statement
Precise measurement of particle number, spatial distribution, and internal state is fundamental to experiments with ultracold molecules in both bulk gases and optical lattices. Existing detection methods face significant limitations: absorption imaging of associated molecules suffers from poor signal-to-noise ratios due to a lack of closed cycling transitions, while dissociation-based imaging of atoms can alter spatial distributions and typically has a noise floor of $\sim 100$ molecules. Furthermore, standard techniques struggle to simultaneously resolve density and spin (internal rotational state) distributions in disordered samples, which is crucial for comparing experimental results with theoretical models of quantum magnetism and dipolar interactions. While quantum gas microscopy has enabled single-atom resolution in atomic gases, extending these capabilities to bulk molecular gases to resolve individual molecules and their internal states remains a challenge.

Methodology
The authors demonstrate an in-situ detection scheme for individual $^{87}\text{Rb}^{133}\text{Cs}$ (RbCs) molecules in a thermal bulk gas, adapting techniques from atomic quantum gas microscopy. The experimental protocol involves the following steps:

1. Pinning: A sample of $\sim 1500$ Rb molecules in an optical dipole trap is pinned in place using a deep, two-dimensional optical lattice (1064 nm, square lattice with 752 nm spacing). This preserves the spatial information of the gas.
2. Dissociation and State Mapping: The pinned molecules are dissociated into constituent Rb and Cs atoms via reverse Stimulated Raman Adiabatic Passage (STIRAP).
   • For single-state detection, the process converts molecules into specific hyperfine states of Rb ($5S_{1/2}, F=1, m_F=1$) and Cs ($6S_{1/2}, F=3, m_F=3$). One species is selectively removed using resonant light to prevent light-assisted collisions during imaging.
   • For multi-state detection, the internal rotational state of the molecule is mapped onto the atomic species. Molecules in state $|\downarrow\rangle$ ($N=0, M_F=5$) are dissociated first, while $|\uparrow\rangle$ ($N=1, M_F=6$) molecules are preserved. Through a sequence of microwave pulses and Adiabatic Rapid Passage (ARP) on the atomic hyperfine states, $|\downarrow\rangle$ sites are mapped to Rb atoms and $|\uparrow\rangle$ sites to Cs atoms.
3. Imaging: The remaining atoms are cooled via Polarization Gradient Cooling (PGC) while fluorescing. Fluorescence is collected using a high-numerical-aperture objective (NA 0.7) and imaged onto a CMOS camera.
4. Reconstruction: A single-layer neural network deconvolution algorithm is used to reconstruct lattice occupancy from the fluorescence images, resolving single atoms despite the lattice spacing being below the Sparrow limit of the imaging system.

Key Contributions and Results

• Single-Molecule Detection in Bulk Gases: The authors successfully image individual molecules in a bulk sample, achieving resolution down to the sub-micron lattice spacing. They observe a binary fluorescence histogram for lattice sites, where sites with even initial occupancy appear empty due to pair losses, while odd sites show a single molecule.
• Density Reconstruction: By correcting for pair losses (assuming a Poissonian distribution of molecules per site) and STIRAP inefficiencies, the team reconstructs the true molecular density distribution. This allows for precise measurement of thermodynamic properties, yielding a sample temperature of 2.3(4) $\mu$K.
• Collisional Loss Measurements: Using the direct density measurement, the authors quantify one- and two-body loss rates in the dipole trap. They determine a one-body loss coefficient $k_1 = 0.49(2) \text{ s}^{-1}$ and a two-body coefficient $k_2 = 5.1(4) \times 10^{-11} \text{ cm}^3 \text{ s}^{-1}$. They also measure atom-molecule collisions, finding a decay rate of $13(1) \text{ s}^{-1}$ for RbCs immersed in a Rb gas, corresponding to a collision rate of $1.5(5) \times 10^{-11} \text{ cm}^3 \text{ s}^{-1}$.
• Simultaneous Multi-State Detection: The technique enables the simultaneous readout of two rotational states ($N=0$ and $N=1$) in a single experimental cycle by mapping them to different atomic species (Rb and Cs). This allows for the complete characterization of a disordered spin system. Rabi oscillations between these states were measured with a frequency of 20.0(1) kHz.
• Spatial Addressing: A focused 817 nm beam is used to induce a local light shift on the rotational transition, allowing for the addressing of a specific circular region (radius 12.5 $\mu$m) within the gas. This enables the selective preparation of spin regions or the removal of specific subsets of molecules.
• Thermometry via Expansion: The authors demonstrate a novel thermometry method by measuring the time-of-flight expansion of a locally addressed subset of pinned molecules, determining a temperature of 5.0(1) $\mu$K.

Significance and Claims
The paper claims to provide a direct method for accessing the density distribution of small molecular samples, enabling precise measurements of density-dependent collisional losses that were previously difficult to obtain with high precision. The ability to simultaneously detect position and rotational state offers a pathway to study microscopic correlations of spin and charge in disordered molecular gases.

The authors position this work as a foundational step toward studying many-body physics with dipole-dipole interactions in optical lattices. They note that while the current high temperature of the molecules (after pinning) precludes immediate many-body studies due to dephasing and differential light shifts, the demonstrated components—multi-state microscopic detection and spatial addressing—are the necessary prerequisites for such experiments. The authors suggest that with the implementation of magic-wavelength lattices and ground-band preparation, these techniques could be applied to study spin-squeezing and quantum magnetism. They also highlight the immediate applicability of their methods to studying ultracold molecular collisions, including the search for collision resonances and the investigation of state-dependent loss rates.