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arXiv:2609.07744

Where Is the \(p\)-Wave Superfluid? Correlated Phase Diagram of Microwave-Shielded Polar Molecules

Tao Shi

Published Sep 7, 2026• 0 citations
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Abstract

Chiral $p_x\!\pm\! i p_y$ superfluidity in fermionic polar molecules offers a direct route to topological quantum matter with non-Abelian excitations, yet the parameter regime in which pairing survives strong correlations and competing instabilities has remained unresolved. Here we determine this regime for microwave-shielded polar molecules. Under tight confinement along the \(z\) direction, the microscopic molecular interaction collapses onto a universal quasi-two-dimensional form specified by an interaction length $σ$, defined as the position of its attractive minimum, and a single dimensionless coupling. We combine Fermi-hypernetted-chain Euler--Lagrange theory with correlated-basis pairing theory, thereby treating the correlation hole, density response, stability of the homogeneous fluid, and $p$-wave pairing within one framework. The largest pairing gap occurs immediately on the stable side of a long-wavelength spinodal instability at a two-dimensional density $4\times10^{-2}/σ^2$. Mapping this universal regime onto microscopic shielding schemes exposes an intrinsic limitation of single-microwave dressing: weakening the attraction to the optimal pairing range simultaneously weakens collisional shielding. Dual-microwave dressing removes this constraint by compensating the long-range attraction while retaining a large repulsive core. Imposing explicit requirements on collisional loss, confinement, and microwave-amplitude stability, we identify the regime of molecular mass and dipole moment favorable for \(p\)-wave superfluidity and determine experimentally realistic microwave and confinement conditions for its realization. These results turn the search for molecular $p$-wave superfluidity into a quantitative optimization problem and define a route toward the topological weak-pairing phase.

DOI
10.48550/arxiv.2609.07744

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Preprint arXiv:2602.22447 Submitted on 25 Feb 2026

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Where Is the ppp-Wave Superfluid? Correlated Phase Diagram of Microwave-Shielded Polar Molecules
Chiral px ⁣± ⁣ipyp_x\!\pm\! i p_ypx​±ipy​ superfluidity in fermionic polar molecules offers a direct route to topological quantum matter with non-Abelian excitations, yet the parameter regime in which pairing survives strong correlations and competing instabilities has remained unresolved. Here we determine this regime for microwave-shielded polar molecules. Under tight confinement along the (z) direction, the microscopic molecular interaction collapses onto a universal quasi-two-dimensional form specified by an interaction length σσσ, defined as the position of its attractive minimum, and a single dimensionless coupling. We combine Fermi-hypernetted-chain Euler--Lagrange theory with correlated-basis pairing theory, thereby treating the correlation hole, density response, stability of the homogeneous fluid, and ppp-wave pairing within one framework. The largest pairing gap occurs immediately on the stable side of a long-wavelength spinodal instability at a two-dimensional density 4×10−2/σ24\times10^{-2}/σ^24×10−2/σ2. Mapping this universal regime onto microscopic shielding schemes exposes an intrinsic limitation of single-microwave dressing: weakening the attraction to the optimal pairing range simultaneously weakens collisional shielding. Dual-microwave dressing removes this constraint by compensating the long-range attraction while retaining a large repulsive core. Imposing explicit requirements on collisional loss, confinement, and microwave-amplitude stability, we identify the regime of molecular mass and dipole moment favorable for (p)-wave superfluidity and determine experimentally realistic microwave and confinement conditions for its realization. These results turn the search for molecular ppp-wave superfluidity into a quantitative optimization problem and define a route toward the topological weak-pairing phase.
We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field may acquire an attractive 1/r(3) dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological p(x) + ip(y) phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities approximately 10(8) cm(-2).
We discuss the topological px+ipy{p}_{x}+{\mathit{ip}}_{y}px​+ipy​ superfluid phase in a two-dimensional (2D) gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential V0(r){V}_{0}(r)V0​(r) that has an attractive dipole-dipole 1/r31/{r}^{3}1/r3 tail, which provides ppp-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic ppp-wave scattering in the potential V0(r){V}_{0}(r)V0​(r) taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second-order Gor'kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature Tc{T}_{c}Tc​ can be varied within a few orders of magnitude by modifying the short-range part of the potential V0(r){V}_{0}(r)V0​(r). The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities  109~{10}^{9} 109 cm${}^{\ensuremath{-}2}$. This leads to Tc{T}_{c}Tc​ of up to a few tens of nanokelvins and makes it realistic to obtain the topological px+ipy{p}_{x}+{\mathit{ip}}_{y}px​+ipy​ phase in experiments with ultracold polar molecules.
Double microwave shielding employs σ+σ^{+}σ+- and πππ-polarized microwave fields, tuned close to the lowest rotational transition, to engineer a long-range repulsive barrier between polar molecules. By preventing molecules from reaching the short range, this technique suppresses detrimental two-body losses and recently enabled the realization of molecular Bose-Einstein condensates and self-bound droplets. Yet, the optimal operating regimes of the shielding mechanism remain largely unexplored. Here, by leveraging the underlying universality of the scattering problem, we systematically map the four-dimensional microwave parameter space-spanned by the detunings and intensities of the two fields-to identify configurations that maximize both shielding efficiency and interaction tunability. We define optimal operating regimes as configurations that are strictly free of field-linked bound states while sufficiently suppressing two-body losses to exceed typical lifetimes of ultracold samples. In these regimes, we evaluate the elastic-to-inelastic collision ratios required for efficient evaporative cooling and explore the accessible tuning range of the effective dipolar interactions. Finally, to identify the best platforms for future quantum simulation experiments, we conduct a global survey of candidate molecular species under realistic field constraints. We identify heavy, strongly dipolar molecules as the most promising candidates, demonstrating that they can achieve extreme loss suppression-reaching two-body loss rates as low as 10−1810^{-18}10−18 cm3^{3}3/s-alongside robust interaction tunability using only moderate field strengths.
Long-range anisotropic dipole-dipole interactions between ultracold polar molecules are predicted to drive exotic quantum phases, yet direct many-body signatures of these interactions in degenerate Fermi gases have remained elusive. Here, we report the observation of an interaction-induced controlled deformation of the Fermi surface, providing a clear many-body signature in a deeply degenerate Fermi gas of 23Na40K^{23}\text{Na}^{40}\text{K}23Na40K molecules. Using double microwave (MW) shielding, we prepare 8×1038 \times 10^38×103 molecules at 0.23(1)0.23(1)0.23(1) times the Fermi temperature, achieving a three-fold suppression of inelastic losses compared to single MW shielding while preserving strong elastic dipolar scattering. We observe Fermi surface deformations of up to 7 %7\,\%7%, more than two times larger than those observed in magnetic atoms, despite operating at two orders of magnitude lower densities. Crucially, we demonstrate continuous tuning of the interaction potential from axial U(1) to biaxial C2_{2}2​ symmetry, directly imprinting this geometry onto the Fermi surface. We find excellent agreement between our experimental results and parameter-free Hartree-Fock theory. These results establish MW-shielded polar molecules as a highly tunable platform for exploring strongly correlated dipolar Fermi matter and offer a promising path towards topological superfluidity.
Ultracold polar molecules with microwave shielding provide a powerful platform for exploring quantum many-body physics with strong, anisotropic interactions. We develop an extended Gross-Pitaevskii framework for bosonic molecules under single microwave shielding, incorporating effective interactions and quantum fluctuations, and benchmark it against exact Quantum Monte Carlo simulations. In the regime of positive scattering lengths, our approach captures superfluid, supersolid, and droplet phases with excellent accuracy. We show that elliptic microwave polarization induces direction-dependent superfluidity--absent in cylindrically symmetric systems. A quasi-1D theory reveals that roton softening and instabilities can be controlled via ellipticity, consistent with recent experiments. Furthermore, we find that the nature of the superfluid-to-supersolid transition is strongly influenced by the ellipticity: the transition is sharp at low ellipticity and continuous at higher values. This tunability offers a potential route for low entropy preparation of molecular supersolids via adiabatic ramps. While double shielding is often used experimentally, our results demonstrate that single-shielded molecules already offer rich, controllable behavior, laying the groundwork for future studies with more complex shielding schemes.
Long-range anisotropic dipole-dipole interactions between ultracold polar molecules are predicted to drive exotic quantum phases, yet direct many-body signatures of these interactions in degenerate Fermi gases have remained elusive. Here, we report the observation of an interaction-induced controlled deformation of the Fermi surface, providing a clear many-body signature in a deeply degenerate Fermi gas of 23Na40K^{23}\text{Na}^{40}\text{K}23Na40K molecules. Using double microwave (MW) shielding, we prepare 8×1038 \times 10^38×103 molecules at 0.23(1)0.23(1)0.23(1) times the Fermi temperature, achieving a three-fold suppression of inelastic losses compared to single MW shielding while preserving strong elastic dipolar scattering. We observe Fermi surface deformations of up to 7 %7\,\%7%, more than two times larger than those observed in magnetic atoms, despite operating at two orders of magnitude lower densities. Crucially, we demonstrate continuous tuning of the interaction potential from axial U(1) to biaxial C2_{2}2​ symmetry, directly imprinting this geometry onto the Fermi surface. We find excellent agreement between our experimental results and parameter-free Hartree-Fock theory. These results establish MW-shielded polar molecules as a highly tunable platform for exploring strongly correlated dipolar Fermi matter and offer a promising path towards topological superfluidity.