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Out-of-equilibrium fluids of pairs of fermions

(Theoretical PhD on Quantum gases and Condensed Matter, in collaboration with the experimental team``Ultracold Quantum Matter’’ from Yale)

by Hadrien Kurkjian - 12 March 2021

All the versions of this article: English , français

PhD supervisors: Hadrien Kurkjian, Nir Navon

Understanding and predicting the behavior of a fluid of quantum particles from its microscopic details (the nature of particles and interactions) is one of the most difficult problems in theoretical physics. This is due to the difficulty of computing the spectrum of a Hamiltonian describing N strongly correlated and strongly entangled particles. Yet, to follow the rapid development of experimental techniques, in quantum gases or in condensed matter, it is now necessary to go beyond the weakly-interacting or weakly-excited regime, and describe the strongly-excited dynamics of a strongly-interacting fluid.

This is the objective of this PhD, which deals more specifically with the superfluids formed of Cooper pairs of fermions, systems which we can now prepare using laser-cooled atoms. To benefit from the strong dynamism of experimental research on those systems, and to better compare her or his research with the experimental results, the doctoral student will be hosted both in the Laboratoire de Physique Théorique of the Université Paul Sabatier and in the experimental ``Ultracold Quantum Matter’’ group from Yale University.

We will mainly be interested in the dynamic phenomena affecting Fermi superfluids: in a first stage, the eigenmodes resulting from weak excitations of the system around its equilibrium state (sound waves, pairing ``Higgs’’ modes, fermionic pair-breaking excitations). In a second stage, we will study the far-out-of-equilibrium evolution, as observed in the Yale experiment following a quench of the system.

We will answer several questions that are both of fundamental interest, and confrontable with experimental measurements: How much is the gap of a condensate of Cooper pairs, quantitatively? Is it really equal to the order-parameter as claimed by BCS mean field theory? What is the value, in a well-isolated system (such as experimentally prepared atomic gases), of the quasiparticle collision rate (a fundamental quantity which determines how the system relaxes towards equilibrium)? How do the eigenmodes (especially the pairing modes) evolve in the vicinity of the transition temperature to the normal phase?

Based on these intermediate results, the final objective of the PhD will be to develop a theory (both ergodic and non-perturbative) able to describe the evolution (including the dissipative evolution) pair condensate after a quench. To go beyond integrable approaches incapable of describing relaxation [5], we can draw inspiration from cumulant-expansion methods recently developed to describe quenches in Bose gases [6,7]. Once the theoretical framework has been established, numerical simulations will be carried out predicting the evolution of the main observable. Once the theoretical framework has been established, we will carry out numerical simulations predicting the evolution of the main observables. The PhD student will compare her or his results to measurements from the Yale experiment, but will also discuss possible applications to other systems, such as superconductors (taking into account, if necessary, effects specific to solid-state physics, such as Coulomb interaction).

This PhD requires a good knowledge of standard theoretical tools for many-body quantum physics, and a taste for analytical calculations. The doctoral student can be funded by a pre-allocated grant of the French government.

Candidates should send their application to Hadrien Kurkjian with a CV including Master’s results and a brief cover letter One or two recommendation letters would be a plus.


[1] Wilhelm Zwerger, editor. The BCS-BEC Crossover and the Unitary Fermi Gas. Springer Verlag, 2012.

[2] Sascha Hoinka, Paul Dyke, Marcus G. Lingham, Jami J. Kinnunen, Georg M. Bruun, and Chris J. Vale. Goldstone mode and pair-breaking excitations in atomic Fermi superfluids. Nature Physics, 13:943–946, 2017.

[3] H. Kurkjian, S. N. Klimin, J. Tempere, and Y. Castin. Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases. Phys. Rev. Lett., 122 :093403, 2019.

[4] Senne Van Loon, Jacques Tempere, and Hadrien Kurkjian. Beyond Mean-Field Corrections to the Quasiparticle Spectrum of Superfluid Fermi Gases. Phys. Rev. Lett., 124:073404, 2020.

[5] E. A. Yuzbashyan, M. Dzero, V. Gurarie, and M. S. Foster. Quantum quench phase diagrams of an s-wave BCS-BEC condensate. Phys. Rev. A, 91 :033628, 2015.

[6] Christoph Eigen, Jake A. P. Glidden, Raphael Lopes, Nir Navon, Zoran Hadzibabic, and Robert P. Smith. Universal scaling laws in the dynamics of a homogeneous unitary bose gas. Phys. Rev. Lett., 119:250404, 2017.

[7] V. E. Colussi, H. Kurkjian, M. Van Regemortel, S. Musolino, J. van de Kraats, M. Wouters, and S. J. J. M. F. Kokkelmans. Cumulant theory of the unitary Bose gas : Prethermal and Efimovian dynamics. Phys. Rev. A, 102:063314, 2020.