Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules

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 $\sim 10^8$ cm$^{-2}$.

💡 Research Summary

In this paper Cooper and Shlyapnikov propose a realistic route to a topological p‑wave superfluid of single‑component fermionic polar molecules confined to a two‑dimensional geometry. By applying a circularly polarized microwave (MW) field whose frequency is tuned close to the rotational transition |J = 0, M = 0⟩ → |J = 1, M = 1⟩, the molecules are dressed into a superposition state |+⟩ that carries an effective electric dipole moment d_eff rotating in the plane at the microwave frequency. Time‑averaging the dipole‑dipole interaction yields an attractive 1/r³ potential V₀(r)=−d_eff²/(2r³) for inter‑molecular separations larger than a characteristic length r_δ set by the detuning δ. At short distances the detuning creates a repulsive core of radius r_δ, preventing molecules from approaching each other too closely and strongly suppressing inelastic “ultracold chemistry’’ processes.

The authors analyze the many‑body problem in the weak‑coupling BCS regime (k_F r* ≪ 1, where r* = M d_eff²/(2ħ²) is the analogue of the van‑der‑Waals length). Solving the regularized gap equation shows that the dominant pairing channel carries orbital angular momentum l = 1, and the energetically favored order parameter has pₓ ± i p_y symmetry. The gap magnitude grows linearly with momentum for k ≲ k_F and saturates at Δ ≈ E_F exp(−3π/4 k_F r*) for k ≫ k_F. Consequently the critical temperature is

 T_c ≈ E_F exp(−3π/4 k_F r*),

which can reach the order of 10 nK for realistic parameters (k_F r* ≈ 1). Because the system is two‑dimensional, the transition is of the Kosterlitz‑Thouless type, but in the weak‑coupling limit the KT temperature essentially coincides with the BCS estimate.

A crucial part of the work is the quantitative assessment of loss mechanisms. The main decay channel is binary inelastic collisions in which one or both |+⟩ molecules are transferred to lower‑energy dressed states |−⟩ or |1, −1⟩, releasing kinetic energy ≈ħδ. The authors compute the non‑adiabatic transition probability P_l by solving the full two‑body scattering problem including all even‑parity channels. They find that the inelastic rate constant α scales as (k_F r*)² and exhibits a pronounced minimum when the ratio r_δ/λ_δ (with λ_δ = ħ/√(Mδ) the characteristic momentum transfer length) is about 10.5. For typical experimental densities n ≈ 10⁸–10⁹ cm⁻² this yields a lifetime τ ≈ (α n)⁻¹ of order one second, which is ample for observing superfluidity and probing topological properties.

Importantly, the chosen parameters (δ > 0, Ω_R ≲ δ) ensure that the effective potential V₀(r) does not support bound two‑molecule states, eliminating three‑body recombination as a fast loss channel. The resulting superfluid, with chemical potential μ > 0, belongs to the non‑trivial topological class: vortices host zero‑energy Majorana modes, leading to non‑Abelian exchange statistics. The authors discuss experimental signatures, including density profiles, collective mode frequencies, and radio‑frequency (RF) spectroscopy. In particular, RF absorption on a vortex core should reveal a distinct peak associated with the Majorana mode, providing a direct probe of the topological nature of the phase.

In summary, the paper demonstrates that microwave‑dressed polar molecules provide a controllable, long‑lived platform for realizing a pₓ + i p_y topological superfluid in two dimensions. The scheme circumvents the severe losses associated with p‑wave Feshbach resonances, offers a transition temperature in the experimentally accessible nanokelvin range, and yields lifetimes of seconds at realistic densities. This opens a concrete pathway toward experimental studies of Majorana fermions, non‑Abelian statistics, and topologically protected quantum information processing with ultracold molecular gases.