Controlled symmetry breaking of the Fermi surface in ultracold polar molecules

This paper reports the first observation of interaction-induced, continuously tunable Fermi surface deformations in a deeply degenerate gas of microwave-shielded $^{23}\text{Na}^{40}\text{K}$ polar molecules, demonstrating a highly controllable platform for exploring strongly correlated dipolar quantum matter.

The Gist

Imagine a crowded dance floor where everyone is trying to move in perfect, chaotic harmony. In the world of physics, this dance floor is a gas of particles called Fermions (specifically, ultracold molecules of Sodium and Potassium). Normally, these particles are shy; they refuse to occupy the same space or move in the same direction due to a rule called the "Pauli Exclusion Principle." Because of this, they arrange themselves in a perfect, invisible sphere of movement, known as the Fermi Surface. Think of it like a perfectly round, inflated balloon representing all the possible ways the dancers can move.

For years, physicists have wanted to see what happens if you introduce a strong, long-range "magnetism" between these dancers. Would the perfect sphere stay round, or would it get squished and stretched?

This paper reports a major breakthrough: They successfully squished the balloon.

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

1. The Problem: The "Shy" Dancers

In previous experiments with magnetic atoms (like tiny magnets), scientists tried to make these particles interact strongly. But it was like trying to get shy dancers to hold hands while they were also trying to avoid tripping over each other. The interactions were too weak, or the dancers would crash and disappear (a process called "inelastic loss") before they could form a new pattern.

2. The Solution: The "Microwave Force Field"

The researchers used a special trick called Microwave Shielding. Imagine putting a force field around each dancer.

• The Shield: They blasted the molecules with microwaves. This created a repulsive barrier that stopped the molecules from crashing into each other and dying (losing energy).
• The Magic: But here's the clever part. While the shield kept them safe from crashing, it also allowed them to feel a long-range "attraction" to each other, like invisible rubber bands connecting them.

3. The Innovation: The "Double Shield"

Usually, one microwave field is enough to stop the crashes. But these molecules are tricky. The team added a second microwave field, almost perpendicular to the first one.

• Think of it like using two different types of noise-canceling headphones at once.
• This "Double Shield" reduced the number of crashes by three times compared to using just one.
• This allowed them to cool the gas down to a temperature so low that it became "degenerate"—meaning the quantum dance floor was packed so tight that the particles had to move in unison. They reached a state where the gas was only 23% as hot as the "Fermi temperature" (a very, very cold state).

4. The Result: Squishing the Balloon

Once the gas was this cold and the "rubber bands" (dipolar interactions) were active, something amazing happened.

• The Shape Shift: The perfect spherical "balloon" of movement didn't stay round. It got stretched and squished into an egg shape (an ellipsoid).
• The Control: The team could twist the knobs on their microwave fields to change the shape of the "rubber bands."
  • If they made the attraction symmetrical (like a cylinder), the balloon stretched in one direction.
  • If they made the attraction asymmetrical (like a cross), the balloon got squished in two different directions.
• The Scale: They managed to stretch this shape by 7%. To put that in perspective, previous experiments with magnetic atoms only saw a 3% stretch, but those experiments had to use 100 times more particles to do it. These molecules achieved a bigger effect with far fewer particles because their "rubber bands" are so much stronger.

5. Why Does This Matter?

This isn't just about making shapes; it's about discovering new states of matter.

• The "Topological" Superfluid: The paper suggests that by controlling these shapes, we might be able to create a superfluid (a liquid that flows with zero friction) that has a "twist" in its structure. This is called a topological superfluid.
• The Future: These twisted superfluids are the holy grail for building quantum computers that are immune to errors. If you can control the shape of the Fermi surface, you can potentially control how information is stored and processed in the future.

The Big Picture Analogy

Imagine a crowd of people in a room.

• Normal Gas: Everyone is walking randomly in a circle.
• This Experiment: The researchers put up invisible walls and magnetic ropes. Suddenly, the crowd stops walking in a circle and starts flowing in a specific, stretched-out oval pattern because they are all pulling on each other in a coordinated way.
• The Breakthrough: They didn't just see the crowd move; they proved they could design the shape of that movement by changing the angle of the ropes.

In short: The team used advanced microwave tricks to cool a gas of molecules so much that they could see the invisible "shape" of their quantum movement change from a sphere to an egg. This proves we can now engineer exotic new states of matter, paving the way for future quantum technologies.

Technical Summary

1. Problem Statement

Ultracold polar molecules possess long-range, anisotropic dipole-dipole interactions (DDI) predicted to drive exotic quantum phases, such as chiral $p_x + ip_y$ superfluidity and topological phase transitions. However, experimental observation of the many-body signatures of these interactions in degenerate Fermi gases has been elusive.

• The Challenge: Achieving the necessary conditions requires simultaneously reaching deep quantum degeneracy (low $T/T_F$) and maintaining strong anisotropic interactions without inelastic collisional losses.
• The Gap: While Fermi surface deformation (FSD) has been observed in magnetic atoms, it has not been demonstrated in polar molecules due to the difficulty of suppressing inelastic losses while preserving strong dipolar scattering. Furthermore, previous methods lacked the ability to continuously tune the interaction symmetry from axial ($U(1)$) to biaxial ($C_2$).

2. Methodology

The authors utilized a deeply degenerate Fermi gas of $^{23}\text{Na}^{40}\text{K}$ molecules, employing a novel double microwave (MW) shielding technique to overcome loss barriers.

• System Preparation:

  • Molecules: $8 \times 10^3$ $^{23}\text{Na}^{40}\text{K}$ molecules prepared in their ro-vibrational ground state.
  • Cooling: Evaporative cooling in an optical dipole trap to reach $T = 0.23(1) T_F$ (deeply degenerate regime).
  • Double MW Shielding: Instead of a single circularly polarized MW field, the team applied two fields:
    1. A circularly polarized field ($\sigma$).
    2. A nearly orthogonally linearly polarized field ($\pi$).
  • Loss Suppression: This dual-field configuration suppresses inelastic two-body losses by a factor of three compared to single-field shielding, reducing the loss coefficient to $2.3(1) \times 10^{-13} \text{ cm}^3\text{s}^{-1}$. This allowed for higher densities ($2.4 \times 10^{12} \text{ cm}^{-3}$) essential for observing FSD.

• Interaction Engineering:

  • The effective interaction potential $V_{dd}(r)$ is tunable via the polarization ellipticity ($\xi$) and Rabi frequencies ($\Omega$) of the MW fields.
  • Symmetry Control: By adjusting $\xi$, the interaction symmetry is tuned from axial $U(1)$ (cylindrical symmetry) to biaxial $C_2$ (two-fold symmetry), allowing control over the anisotropy of the attractive interaction.

• Detection:

  • Time-of-Flight (TOF): MW fields were switched off, followed by reverse-STIRAP to dissociate molecules into free Na and K atoms.
  • Imaging: Absorption imaging of the K atoms after 14–16 ms of ballistic expansion.
  • Analysis: The momentum distribution was analyzed by fitting 2D Fermi-Dirac profiles and calculating the dimensionless deformation parameter $\Delta_{xy} = \sigma_x/\sigma_y - 1$. Residual analysis (subtracting circular fits from elliptical fits) revealed the characteristic four-lobe quadrupolar pattern.

3. Key Contributions

• First Observation of FSD in Polar Molecules: This work provides the first direct experimental evidence of interaction-driven reshaping of the Fermi surface in a degenerate Fermi gas of polar molecules.
• Double MW Shielding: Demonstrated a robust method to suppress inelastic losses in fermionic polar molecules, enabling the preparation of a deeply degenerate gas at densities previously unattainable for this species.
• Continuous Symmetry Tuning: Successfully demonstrated the continuous tuning of interaction potential from $U(1)$ to $C_2$ symmetry and the direct imprinting of this geometric change onto the Fermi surface.
• Parameter-Free Theory Agreement: The experimental results showed excellent agreement with finite-temperature Hartree-Fock theory without any adjustable parameters, confirming the many-body nature of the effect.

4. Key Results

• Magnitude of Deformation: The team observed Fermi surface deformations of up to 7%.
  • This is more than two times larger than deformations observed in magnetic atoms (e.g., Erbium), despite operating at densities two orders of magnitude lower.
  • This highlights the significantly stronger electric dipolar interactions in molecules (dipolar length $\sim 3000 a_0$) compared to magnetic dipoles ($\sim 100 a_0$).
• Symmetry Breaking:
  • $U(1)$ Limit: At $\xi \approx 0^\circ$, the interaction is cylindrically symmetric, resulting in an axially symmetric ellipsoidal Fermi surface.
  • $C_2$ Limit: At $\xi = \pm 10^\circ$, the interaction exhibits biaxial symmetry. The Fermi surface deforms accordingly, elongating along the direction of strongest attraction and rotating its principal axes by $\sim 90^\circ$ as $\xi$ changes sign.
• Temperature Dependence: The deformation increases monotonically as the reduced temperature $T/T_F$ decreases, consistent with the dominance of anisotropic Fock exchange energy over isotropic kinetic pressure.
• Theoretical Validation: The experimental data matched parameter-free Hartree-Fock calculations, confirming that the deformation arises from the mean-field correction in the $l=2$ angular momentum channel.
• Dipolar-to-Fermi Energy Ratio: The system achieved a ratio $E_{dd}/E_F \approx 0.046$, which is approximately five times larger than in magnetic atom experiments, bringing the system closer to the strongly correlated regime where density-wave instabilities and topological phases are predicted.

5. Significance and Outlook

• Platform for Strongly Correlated Matter: MW-shielded polar molecules are established as a highly tunable platform for exploring strongly correlated dipolar Fermi matter, offering superior control over interaction strength and symmetry compared to magnetic atoms.
• Pathway to Topological Superfluidity: The ability to tune symmetry from $U(1)$ to $C_2$ provides a direct route to drive Lifshitz topological transitions between chiral ($p_x + ip_y$) and nematic ($p_x$ or $p_y$) superfluid phases.
• Future Directions: The work paves the way for:
  • Realizing $p$-wave superfluidity in polar molecules (predicted below $0.14 T_F$).
  • Investigating collective excitation modes (e.g., Scissor mode, quadrupolar motion) to probe anisotropic hydrodynamics.
  • Exploring non-equilibrium dynamics and multi-particle excitations in dipolar systems.

In conclusion, this paper represents a major breakthrough in ultracold molecular physics, overcoming the loss barrier to access the deeply degenerate regime and demonstrating precise control over the quantum geometry of the Fermi surface, a prerequisite for realizing novel topological quantum states.