Excitation Spectrum of a Fermionic Condensate

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Excitation spectrum of a fermionic condensate Hadrien Kurkjian, Serghei Klimin, Senne Van Loon, Jacques Tempere, Alice Sinatra & Yvan Castin UAntwerpen - LKB - ENS - Université Paul Sabatier (Toulouse) 16 novembre 2020 Excitation spectrum of a fermionic condensate Pair-condensed Fermi gases Condensate of pairs of fermionic atoms, BCS-BEC crossover Experiments in Yale (N. Navon), MIT (M.Zwierlein), Lens (G. Roati), Swinburne (Vale)... Single-particle excitations Collective modes Phonons • • Higgs modes = • • Excitation) • Pairing mode BCS (T Tc) • • ≈ Excitation spectrum of a fermionic condensate Method: Linear Response (in RPA) 2 2 Z X ~ k y 3 y y H^ = µ a^ a^k + g d r ^ (r) ^ (r) ^#(r) ^"(r); 0 2m − k 0 " # k response to drive forces: Z " # ^ 3 ^y ^y X ^y ^ Hdrive = d r φ(r; t) " # + h.c + u(r; t) σ σ σ Density and pair-ﬁeld response to the drive 0 1 0 1 i∆δθ 2Re(φ) −1 @δ ∆ A = χ(!; q) @2iIm(φ)A ; det χ (zq; q) = 0 δρj j u z Im 2∆ ~ω2(q) q q 2 + k 0 ~ω×B,q × × Rez q k + q • • z q k k ×q 2 − Excitation spectrum of a fermionic condensate Higgs modes 2.4 2 2 2.3 µ ~ q 3 zq = 2∆ + ζ + O(q ) 2.2 ∆ 2.1 ∆ 2m / q 2 ω ~ 1.9 1.8 1.7 3.5 3 2.5 ∆ / q 2 Γ ~ 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 qξ So far measurements only in q = 0 (quench of interactions). Analogy with superconductors. Also visible in the density response Excitation spectrum of a fermionic condensate Phonons The sign of the dispersion can 3 change ~!q = ~cq + γq 0, 3 2,5 0, 25 2 0, 2 ∆ / 1,5 q 0, 15 ω ~ 1 0, 1 0,5 0, 05 0 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 ~q/(2m∆)1/2 1.15 γ = 0.084 γ = 0.044 − 1.1 1.05 2 ) ψ 1 (1 + 0.95 4 2 0 2 4 6 8 10 − − (x ct)/σ − Excitation spectrum of a fermionic condensate Phonons: damping mechanisms For dissipative properties (viscosity, thermal conductivity...) you need phonon-phonon interactions. ~!q ~!q i~Γq=2 ! − ^ X ^y ^ ^ ^ Hhydro = E0 + ~!qbqbq + H3 + H4 + ::: q Convex branch Concave branch 3-phonons processes 4-phonons processes q1 q q q3 q q2 • • • q2 q4 q2 q1 Beliaev Landau Landau-Khalatnikov y y H^3 ^b ^b ^bq + h.c. y y q1 q2 3 H^ ^b ^b ^bq ^bq ! 4 ! q3 q4 1 2 BL 5 Γq q at T = 0 LK / Γq = 0 at T = 0 BL 5 Γq T ΓLK T 7 ~!q ≈/kBT q ~!q ≈/kBT Excitation spectrum of a fermionic condensate Pairing mode at and above Tc At Tc, the window of visibility of phonons/Higgs modes shrinks to ! . 2∆ and q . 1/ξpair. Else- where: quadratic pairing mode 2 2 (Tc) ~ q 3 3 zq = + O(q =k ) 4m∗ F Exists above Tc as a precursor of the phase transition. 2 2 (Tc) ~ q zq = α(T T ) 4m∗ − − c Excitation spectrum of a fermionic condensate Pairing mode at and above Tc At Tc, the window of visibility of phonons/Higgs modes shrinks to ! . 2∆ and q . 1/ξpair. Else- where: quadratic pairing mode 2 2 (Tc) ~ q 3 3 zq = + O(q =k ) 4m∗ F Exists above Tc as a precursor of the phase transition. 2 2 (Tc) ~ q zq = α(T T ) 4m∗ − − c Excitation spectrum of a fermionic condensate Fermionic quasiparticles beyond mean-ﬁeld The fermionic quasiparticles are perturbed by the presence of collective modes At T = 0 At T = 0 6 q q k0 k 2$1 2$2 0 • Ak;q Ak;k ;q • k q k q0 − T 7 Γ k0 / c6ρ2 Nice analogy with rotons in He- lium or dipolar Bose gases. Excitation spectrum of a fermionic condensate.

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