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Out-of-equilibrium quantum gases

Quantum thermalization of Bose superfluids

During Clément Duval’s thesis from 2020 to 2023, we developed a comprehensive microscopic theoretical approach to the thermalization dynamics of 2D Bose superfluids following a quench [Duval, Cherroret, Phys. Rev. A 107, 043305 (2023)]. This approach was based on the quantum hydrodynamic theory of cold atom superfluids, combined with a Keldysh field theory to describe out-of-equilibrium dynamics. It allowed to put on a full microscopic basis the prethermalization-to-thermalization dynamical scenario expected for near-integrable systems out of equilibrium (see right picture). Our approach also provided a complete description of the dynamics of several measurable observables, such as the coherence function or the structure factor, from the quench to the final thermalization of the superfluid. In parallel to this work, we also theoretically and numerically explored the long-time relaxation of Bose superfluids within the same framework [Duval, Cherroret, arXiv:2405.08606 (2024)]. In this system, we have identified a regime of very slow relaxation where the thermalization dynamics becomes purely algebraic, a phenomenon which we believe is connected with the diffusive transport of local energy expected in generic non-integrable systems.

Typical behavior of the dynamics of the correlation function C(r,τ) of an isolated quantum system close to integrability after a sudden perturbation. The dynamics first exhibit a quasi-stationary metastable phase called ‘pre-thermalization,’ followed by a late relaxation towards a final thermal state.

Universal dynamic scaling in quenches across phase transitions

In non-equilibrium quantum physics, a particularly interesting phenomenon occurs when one ‘quenches’ a quantum many-body system across a phase transition: its correlations exhibit universal spatio-temporal scaling laws, which are thought to extend the concept of critical scaling to non-equilibrium physics. Such dynamic scaling laws have been observed in many systems like the O(N) or Ising models, as well as in more complex many-body Hamiltonians describing Bose gases. ln our recent work [Gliott et al., Phys Rev. Lett. 133, 233403 (2024)], for instance, we have explored the emergence of universal dynamic scaling in an interacting Bose gas around the condensation transition, under the combined influence of an external driving force and spatial disorder. As time progresses, we have found that the Bose gas crosses over three distinct dynamical regimes: (i) an inverse turbulent cascade where interactions dominate the drive, (ii) a stationary regime where the inverse cascade and the drive counterbalance one other, and (iii) a sub-diffusive cascade in energy space governed by the drive and disorder, a phenomenon recently observed experimentally in Cambridge. We have explored the phase diagram of these dynamical phases (see figure on the right) and have shown that all three dynamical regimes can be described by self-similar scaling laws.

Dynamical phase diagram of a 3D non-equilibrium interacting Bose gas quenched across the BEC transition while subjected to a periodic drive and disorder, parametrized by the parameter D. For small drive the energy distribution of the gas exhibits an inverse cascade , while for strong drive it spreads sub-diffusively. At intermediate drive, sub-diffusion and inverse cascade compensate each other and a stationary regime emerges.

Out-of-equilibrium physics with quantum fluids of light

In the recent years, our team has developed a collaboration with the Quantum Fluids of Light group (QFL) at LKB, to explore theoretically and experimentally non-equilibrium many-body physics in optical systems of effectively interacting photons, achieved by propagating paraxial laser light through atomic vapor cells. In this system, the possibility to tailor optical wavefronts and perform precise measurements via a rich optical toolbox provide a new testbed for quantum simulation. In this system, we have for instance theoretically characterized a phenomenon of pre-thermalization for non-equilibrium photons experiencing an effective interaction quench [Bardon-Brun et al., Phys. Rev. Research 2, 013297 (2020)], which has been observed experimentally in 2022 in the QFL Lab [Abuzarli et al., Phys. Rev. Lett. 129, 100602]. More recently, we have also investigated both theoretically and experimentally the non-equilibrium dynamics of the so-called spin and density modes in a binary mixture of optical superfluids [Piekarski et al., arXiv:2412.08718 (2024)]. At a theoretical level, we have also proposed strategies to explore novel types of dynamical phases transitions using time-dependent fluids of light in nonlinear dispersive vapors [Cherroret, Phys. Rev. A 109, 013519 (2024)].

Hot rubidium vapor cell used to create a non-equilibrium ‘quantum fluid of light’. Picture taken from the Quantum Fluids of Light group website.

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