Evaporation of microwave-shielded polar molecules to quantum degeneracy

The study targets the long-standing challenge of achieving deeply quantum-degenerate gases of interacting polar molecules in three dimensions. Although polar molecules possess strong electric dipole moments suitable for quantum simulation, information processing, and precision tests, efficient evaporative cooling in 3D has been hampered by rapid inelastic loss during short-range collisions, including collapse into attractive head-to-tail configurations when polarized. Even non-reactive molecules display inelastic losses at short range, with mechanisms still under investigation. Previous successes involved stabilizing molecules via confinement to two dimensions with strong dc electric fields or tuning resonances between rotational states in 3D, but reaching degeneracy through collisional cooling in 3D remained out of reach due to low elastic-to-inelastic collision ratios and low initial phase-space densities. The authors hypothesize that microwave shielding with blue-detuned circularly polarized fields can suppress short-range losses while enhancing elastic dipolar collisions, enabling efficient 3D evaporative cooling to quantum degeneracy.

Prior work established degenerate gases of polar molecules by assembling from degenerate atomic mixtures without active cooling. Evaporative cooling has been limited by inelastic loss; stabilization strategies include dc electric fields with 2D confinement leading to sub-TF temperatures, and in 3D, resonant tuning of rotational states via dc fields reduced loss but still did not achieve degeneracy due to insufficient elastic-to-inelastic ratios. Theoretical proposals have suggested microwave or optical shielding to engineer repulsive barriers, and recent tweezer experiments observed reduced losses between CaF molecules using blue-detuned circularly polarized microwaves. The present work builds on theoretical proposals of microwave shielding and dipolar interaction control, aiming to realize efficient evaporative cooling in 3D bulk gases.

• Microwave shielding: Implement a blue-detuned circularly polarized microwave field generated by a helical antenna to couple the rotational ground state |J=0, mJ=0> to |J=1, mJ=-1>. The microwave frequency is near 2B_rot/ħ with B_rot ≈ 2.822 GHz; on-resonance Rabi frequency Ω/(2π)=11 MHz, and detuning Δ chosen typically comparable to Ω and blue of resonance. The dressing forms upper and lower dressed states |+> and |-> with mixing angle set by Δ and Ω. Molecules are prepared in the upper dressed state |+>.
• Effective interactions: The dressing induces a rotating dipole moment that yields a long-range dipolar interaction with effective dipole moment d_eff tunable via Δ/Ω. At intermediate range, dipole-dipole coupling dominates and, assisted by spectator states, couples colliding molecules in |++> to a repulsive branch that creates a barrier preventing approach to short range, suppressing inelastic processes. Residual two-body loss primarily arises from non-adiabatic transitions to lower-lying dressed channels (such as |+0>) releasing energy ~ħΩ and ejecting molecules from the trap.
• Molecular sample preparation: Fermionic 23Na40K molecules are created from ultracold atoms via a magnetic Feshbach resonance followed by STIRAP to the absolute ground state. For rate measurements, typical initial temperature T≈800 nK and average density n0≈3.0×10^11 cm^-3; for elastic-rate measurements in the strong-collision regime, density may be reduced to n0≈0.7×10^10 cm^-3 to avoid deep hydrodynamics.
• Trap configuration: Up to three optical dipole traps (two horizontal beams support against gravity; an additional vertical beam can be ramped to maintain confinement during evaporation). A dc magnetic offset field defines quantization for microwave coupling.
• Collision-rate measurements: Inelastic two-body loss coefficient β_in is extracted from number decay in thermal samples, distinguishing from one-body loss (dominated by microwave phase-noise–induced coupling to other dressed states; typical one-body lifetime ~600 ms when two-body loss is small). Elastic collision rate coefficient β_el is determined via cross-dimensional thermalization: apply parametric heating along z to create T_perp and T_parallel anisotropy; monitor re-equilibration and fit the coupled time evolution of molecule number N and temperatures (T_perp, T_parallel) using differential equations modeling loss and rethermalization. Coupled-channel calculations include residual microwave polarization ellipticity for comparison.
• Evaporative cooling protocol: Begin with a low-entropy, initially non-thermalized sample of ~2.5×10^4 ground-state molecules from a density-matched degenerate atomic mixture. With optimal detuning (Δ≈2π×8 MHz) providing high γ, lower the power of horizontal trap beams exponentially over 150 ms to set the effective trap depth U_trap and enable hot molecules to escape. Strong elastic dipolar collisions rethermalize the sample; due to very high collision rates, rethermalization saturates at the hydrodynamic limit set by trap frequencies (ω/(2π) ≈ 60–120 Hz depending on stage). To maintain rethermalization while reducing trap depth, ramp up an additional vertical beam to reinforce horizontal confinement. Characterize evaporation by varying final trap depth and performing time-of-flight imaging after 10 ms; extract temperature and T/TF from polylogarithmic fits to momentum distributions and check consistency with Gaussian fits to thermal wings.

• Microwave shielding in 3D strongly suppresses inelastic two-body loss while enhancing elastic dipolar scattering:
  • Without microwave: measured two-body loss coefficient β ≈ 7.7(5)×10^-11 cm^3 s^-1 at T=800 nK (theory: 4.9×10^-11 cm^3 s^-1).
  • With blue detuning near optimal shielding (e.g., Δ/(2π)≈8 MHz), two-body losses are suppressed by about an order of magnitude; measurements and coupled-channel theory show strong agreement away from the hydrodynamic limit.
  • Elastic scattering dominated by dipolar interactions; cross sections scale approximately as d_eff^4, tunable via Δ. For small Δ (strong coupling), elastic collision rates become so large that the mean free path is smaller than the cloud size, entering the hydrodynamic regime and saturating observed rethermalization rates at ~ω/(2π)≈120 Hz for rate measurements.
  • Measured maximum elastic-to-inelastic ratio γ ≈ 460(110), limited by hydrodynamic saturation. Theory indicates γ can exceed 1,000 for ideal detunings and reach ~5,000 with improved microwave polarization purity.
• Evaporative cooling results:
  • Starting from ~2.5×10^4 molecules, forced evaporation over 150 ms reduces trap depth and cools the gas efficiently.
  • Without reducing trap depth (no forced evaporation), after 150 ms: N ≈ 1.43(5)×10^4, T ≈ 176(5) nK, T/TF ≈ 1.00(3).
  • With optimized forced evaporation to N ≈ 3.6(3)×10^3 (final U_trap ≈ kB TF ≈ 250 nK): T ≈ 38(2) nK, T/TF ≈ 0.47(2).
  • Additional plain evaporation during a hold time t_h after the forced stage further cools the gas; at t_f=150 ms total, achieve T ≈ 21(5) nK and T/TF ≈ 0.36(9), well below TF.
  • Lifetime of the degenerate sample up to ~0.6 s at the lowest temperatures, with inelastic collisions becoming negligible.
• Interaction strength: For the coldest samples, dipolar interaction energy corresponds to about 5% of the Fermi energy, about three times larger than reached in degenerate Fermi gases of magnetic atoms.
• Hydrodynamics: During strong shielding (e.g., Δ≲2π×10 MHz), elastic rates exceed trap frequencies and the gas enters the hydrodynamic regime; measured β_el values saturate at the hydrodynamic limit N_coll ω/(2π η) with N_coll≈2 for rethermalization in this system.

The results demonstrate that blue-detuned circularly polarized microwave dressing creates a robust repulsive barrier that suppresses short-range inelastic processes while inducing strong, tunable elastic dipolar interactions in a 3D bulk molecular gas. This directly addresses the key obstacle to evaporative cooling of polar molecules in 3D—large inelastic loss—and enables efficient rethermalization and cooling to deep quantum degeneracy (T/TF≈0.36). The observed high γ (∼500 measured; >1,000 predicted) far surpasses prior 3D efforts and rivals or exceeds 2D stabilized systems, validating microwave shielding as a general strategy for collisional cooling of polar molecules. The degenerate, strongly dipolar Fermi gas created here paves the way for studies of many-body dipolar physics in 3D, including modifications of collective modes, Fermi surface distortions or collapse, and prospects for anisotropic superfluid pairing. The methodology’s technical simplicity (single microwave source, standard optical trapping) suggests broad applicability across molecule species. Further performance gains are anticipated by increasing initial phase-space density, reducing microwave phase noise, improving polarization purity, and optimizing evaporation strategies in the hydrodynamic regime, potentially reaching T<0.1 TF where rich quantum phases are expected.

The study establishes a general and efficient approach to evaporatively cool ultracold polar molecules to deep quantum degeneracy in three dimensions by microwave shielding with a blue-detuned circularly polarized field. The technique achieves very low temperatures (down to 21 nK, T/TF≈0.36) with strong, tunable dipolar interactions and high elastic-to-inelastic collision ratios, overcoming the traditional barrier of short-range inelastic loss. Owing to its simplicity and effectiveness, the method is readily transferable to other ultracold-molecule platforms and opens avenues to explore long-lived, strongly interacting dipolar many-body phases and to pursue applications in quantum simulation and information. Future work should enhance initial phase-space density, suppress microwave-induced one-body loss via lower phase noise and improved polarization, and develop evaporation protocols tailored to hydrodynamic conditions to push into regimes T<0.1 TF and investigate emergent dipolar phenomena such as anisotropic superfluidity.

• Measurement of β_el and γ is limited by entry into the hydrodynamic regime at strong shielding, saturating rethermalization rates at ≈ω/(2π) and capping the observable γ (~460(110)).
• One-body loss due to microwave phase noise induces coupling to other dressed states, yielding an exponential decay with ~600 ms lifetime when two-body loss is small, reducing overall sample lifetime during evaporation and hold.
• Imperfect microwave polarization (residual ellipticity) reduces shielding performance; theory indicates substantially higher γ with improved polarization purity.
• Initial samples are non-thermalized and exhibit sloshing; damping and associated particle loss degrade phase-space density without forced evaporation, reducing overall efficiency.
• Imaging signal-to-noise at the coldest conditions limits conclusive interpretation of a central optical density excess relative to Fermi-Dirac fits; potential interaction effects remain unresolved.
• Achieved T/TF≈0.36, not yet below 0.1 TF; further technical improvements are required to access lower temperatures and longer lifetimes.