Preparation of quasi-two-dimensional Bose mixture of ultracold $^{23}$Na and $^{87}$Rb atoms

This paper reports the successful preparation of a quasi-two-dimensional heteronuclear quantum degenerate mixture of ultracold $^{23}$Na and $^{87}$Rb atoms using a versatile experimental apparatus, demonstrating quantum immiscibility that aligns with mean-field theories and establishing a platform for future low-dimensional quantum studies.

The Gist

Imagine you are trying to build a tiny, perfect city made of atoms, but instead of letting them spread out in a big 3D room, you want to squeeze them all down onto a single, flat sheet of paper. This is exactly what the scientists in this paper did. They created a special laboratory machine to turn two different types of atoms—Sodium (Na) and Rubidium (Rb)—into a super-cold, flat "pancake" of quantum matter.

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

1. The Setup: A High-Tech "Atom Factory"

Think of the experiment as a multi-stage factory assembly line.

• The Source: At the beginning, they have two ovens. One spits out Sodium atoms, and the other spits out Rubidium atoms. These atoms are hot and moving fast, like a chaotic crowd of people running in a stadium.
• The Cooling Zone (The 2D-MOTs): To slow them down, the atoms enter a "cooling tunnel." Here, they are hit by lasers from all sides. Imagine these lasers as a gentle but firm wind that pushes the running atoms until they are almost standing still. The scientists built special, compact tunnels for each type of atom to catch as many as possible.
• The Trap (The 3D-MOT): Once slowed, the atoms are caught in a magnetic and laser "net" in the middle of the machine. This is like a holding pen where they are cooled even further, until they are so cold they start acting like a single, giant wave rather than individual particles. This state is called a Bose-Einstein Condensate (BEC).

2. The Journey: Moving the Atoms Without Spilling

Once the atoms are super-cold and ready, they need to move from the "cooling room" to the "science room" where the real experiments happen.

• The Air-Bearing Train: The scientists use a beam of light (an optical trap) to pick up the atoms. Imagine this light beam as a invisible, magnetic train track. They slide the atoms along this track using a precision stage that floats on air (like a hovercraft) to avoid any vibrations.
• The Handoff: They gently transfer the atoms from the first room to the second room. The transfer is so smooth that almost none of the atoms are lost, and they don't get "shaken up" or heated during the trip.

3. The Squeeze: Making the "Pancake"

Now the atoms are in the science chamber. The goal is to make them flat (2D).

• The Pancake Trap: The scientists use lasers to create a trap that is very wide but very thin. Imagine a giant, invisible sandwich press. They squeeze the cloud of atoms from the top and bottom.
• The Result: The atoms are forced to spread out sideways but can't move up or down. They are now living in a quasi-two-dimensional world. It's like taking a fluffy cloud and pressing it down until it's a flat sheet of fog.

4. The Big Discovery: The "Oil and Water" Effect

Here is the most exciting part. The scientists mixed Sodium and Rubidium atoms together in this flat sheet.

• The Expectation: Usually, when you mix two things, they blend together like milk and coffee.
• The Reality: Because of the way these atoms interact in this flat, 2D world, they refused to mix. The Rubidium atoms huddled together in the center, while the Sodium atoms were pushed out to the edges, forming a ring.
• The Analogy: It's like putting oil and water in a bowl. They separate because they don't like each other. In this experiment, the "oil" (Rubidium) sank to the middle, and the "water" (Sodium) floated around it. This is called quantum immiscibility.

5. Why Does This Matter?

This machine is like a new kind of microscope for the quantum world.

• Testing Physics: By squeezing atoms into 2D, scientists can see weird quantum behaviors that are hidden in 3D, like the BKT transition (a special phase change that only happens in flat worlds).
• Future Tech: This setup could help us build better quantum computers or create new types of materials. It also allows scientists to study "impurities" (one atom acting like a guest in a crowd of others) or even turn these atoms into tiny, polar molecules to study how they stick together.

Summary

In short, these scientists built a sophisticated, ultra-cold machine that catches two types of atoms, slows them down to a near-stop, moves them to a new room, squashes them flat, and watches them separate like oil and water. This gives us a powerful new way to study the strange, magical rules that govern the universe at its smallest scale.

Technical Summary

1. Problem Statement

While ultracold atomic mixtures have been extensively studied in three dimensions (3D) to explore tunable interactions and quantum few-body physics, there is a significant gap in the experimental realization of heteronuclear mixtures confined to reduced dimensions (specifically quasi-2D).

• Limitations of Current Systems: Existing experiments primarily focus on homonuclear systems or 3D heteronuclear mixtures.
• Scientific Need: Confining quantum gases to 2D introduces unique critical behaviors (e.g., Berezinskii-Kosterlitz–Thouless phase transitions) and novel quantum phases (e.g., quantum droplets, immiscible phases, and polar molecules).
• Technical Challenge: Creating a versatile apparatus capable of simultaneously cooling, trapping, and imaging two distinct atomic species (Sodium-23 and Rubidium-87) with high flux, while providing precise control over optical lattices and electric fields for future polar molecule studies, is a complex engineering task.

2. Methodology

The authors developed a custom experimental apparatus designed specifically for the efficient preparation of a dual-species $^{23}$Na–$^{87}$Rb mixture in a quasi-2D regime. The methodology is divided into four main stages:

A. Vacuum and Laser Cooling System Design

• Modular 2D-MOT Sources:
  • $^{87}$Rb: Utilizes a compact, modular 2D$^+$-MOT with permanent magnets (NdFeB) and a 45° inclined aluminum mirror to reflect axial cooling light, enhancing atomic flux. It achieves a loading rate of $2 \times 10^9$ atoms/s.
  • $^{23}$Na: Uses a compact Zeeman slower combined with a 2D-MOT. The Zeeman slower employs a specific magnet configuration to decelerate atoms from an oven, followed by transverse 2D-MOT cooling. It achieves a loading rate of $\sim 2.2 \times 10^8$ atoms/s.
• 3D-MOT and Hybrid Trapping:
  • Atoms are captured in a Dark-SPOT configuration to increase density.
  • Sub-Doppler Cooling: Standard molasses cooling is used for Rb, while a "gray molasses" scheme (using a $\Lambda$-type system) is employed for Na to reach temperatures of $\sim 36$ $\mu$K.
  • Hybrid Evaporation: Atoms are transferred to a hybrid magnetic-optical trap. A unique feature is the use of a single RF frequency to simultaneously evaporate both species due to their nearly identical Zeeman splittings in the low-field regime. This is followed by evaporation in a crossed optical dipole trap (ODT).

B. Optical Transport and Science Chamber

• Transport: An air-bearing translation stage moves the optical trap focus from the 3D-MOT chamber to the science chamber over 375 mm. The motion follows an S-curve profile to minimize heating, achieving >85% transport efficiency.
• Science Chamber Capabilities:
  • Features extensive optical access (CF25 and CF16 windows) for various lattice geometries.
  • Houses a precision in-vacuum electrode assembly (ITO-coated plates and tungsten rods) for future control of dipolar interactions in polar molecules.
  • Equipped with a high-resolution imaging system (NA = 0.75) capable of sub-micron resolution.

C. Quasi-2D Preparation

• Lattice Loading: The mixture is loaded into a vertical long optical lattice (VLL) formed by two 1064 nm beams intersecting at 20°.
• Single-Layer Selection: By adjusting the phase of the lattice via galvanometer mirrors, the atoms are adiabatically loaded into a single layer of the lattice, effectively creating a 2D gas.
• Imaging: In-situ absorption imaging is performed using high-intensity, short pulses to resolve the density profiles of both species simultaneously.

3. Key Contributions

1. First Efficient Quasi-2D Heteronuclear Mixture: The successful preparation of a dual-species $^{23}$Na–$^{87}$Rb mixture in a quasi-2D geometry, a regime previously unexplored for this specific pair.
2. Novel Apparatus Design:
   • Development of a compact, modular 2D$^+$-MOT for Rb and a Zeeman slower for Na.
   • Implementation of a single-frequency RF evaporation scheme for simultaneous cooling of two different species.
   • Integration of a precision in-vacuum electrode assembly within a high-resolution imaging path, enabling future studies of polar molecules.
3. High-Resolution Imaging: Demonstration of sub-micron resolution imaging for both species in a 2D trap, allowing for the direct observation of density distributions and phase separation.

4. Results

• Quantum Degeneracy: The team successfully produced a balanced dual-species Bose-Einstein Condensate (BEC) with $\sim 2.8 \times 10^5$ Na atoms and $\sim 6.6 \times 10^5$ Rb atoms in the hybrid trap.
• 2D Confinement Verification: Matter-wave interference experiments confirmed that atoms were loaded into a single lattice layer (lattice spacing $\approx 3.0$ $\mu$m), with no interference fringes indicating multi-layer occupation.
• Observation of Quantum Immiscibility:
  • The in-situ density profiles of the 2D mixture revealed spatial separation: Rb atoms formed a dense central core, while Na atoms were partially expelled, forming a ring-like structure.
  • This immiscibility arises because the inter-species scattering length ($a_{12} = 76.3 a_0$) exceeds the critical value ($a_c \approx 66 a_0$) defined by the geometric mean of the intra-species interactions.
• Theoretical Agreement:
  • The experimental density profiles matched well with Hartree-Fock mean-field (HFMF) theory for the thermal wings.
  • In the high-density superfluid core ($\tilde{\mu} > 0.3$), the data agreed with superfluid mean-field theory, confirming the presence of a robust BKT superfluid core.
  • The measured phase-space density (PSD) for Na reached 83, far exceeding the critical value for the BKT transition ($\approx 9$).

5. Significance

This work establishes a versatile and advanced platform for investigating low-dimensional quantum many-body physics. The apparatus enables:

• Exploration of Novel Phases: Studying the miscible-immiscible phase boundary, quantum droplets, and Andreev-Bashkin effects in 2D.
• Quantum Impurities: Investigating Bose polarons and mediated interactions between impurities in a 2D fluid.
• Polar Molecules: The integrated electrode system allows for the creation and control of $^{23}$Na$^{87}$Rb polar molecules in 2D, enabling the study of collisional shielding and long-range dipolar interactions (e.g., quantum crystals or supersolids) in a regime previously accessible only to fermionic systems.

In summary, the paper provides a comprehensive blueprint for constructing and operating a state-of-the-art ultracold atom experiment, successfully demonstrating the preparation and characterization of a 2D heteronuclear quantum mixture with implications for future quantum simulation and molecular physics.