We explore the dynamics of a tuneable box-trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power-law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.We explore the dynamics of a tuneable box-trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power-law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.

Physical Review LettersMar 11, 202415 citations

Energy-space random walk in a driven disordered Bose gas

Yansheng Zhang, Gevorg Martirosyan, C. J. Ho +3 more

Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, E ∝ t η with η = 0 . 46 ( 2 ) , and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from η ≈ 0 . 5 to η ≈ 0 . 4 with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from E ∝ t 1 / 2 to E ∝ t 2 / 5 scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system’s energy. Our results provide the theoretical foundation for further experiments.Motivated by the experimental observation [1] that driving a non-interacting Bose gas in a 3D box with weak disorder leads to power-law energy growth, E ∝ t η with η = 0 . 46 ( 2 ) , and compressed-exponential momentum distributions that show dynamic scaling, we perform systematic numerical and analytical studies of this system. Schrödinger-equation simulations reveal a crossover from η ≈ 0 . 5 to η ≈ 0 . 4 with increasing disorder strength, hinting at the existence of two different dynamical regimes. We present a semi-classical model that captures the simulation results and allows an understanding of the dynamics in terms of an energy-space random walk, from which a crossover from E ∝ t 1 / 2 to E ∝ t 2 / 5 scaling is analytically obtained. The two limits correspond to the random walk being limited by the rate of the elastic disorder-induced scattering or the rate at which the drive can change the system’s energy. Our results provide the theoretical foundation for further experiments.

arXiv:2309.12308Comptes Rendus PhysiqueFeb 2, 20244 citations

From Inverse-Cascade to Subdiffusive Dynamic Scaling in Driven Disordered Bose Fluids

Elisabeth Gliott, Adam Rançon, Nicolas Cherroret

We explore 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 find 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. We show that all three dynamical regimes can be described by self-similar scaling laws.We explore 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 find 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. We show that all three dynamical regimes can be described by self-similar scaling laws.

arXiv:2405.15915Physical Review LettersDec 3, 20243 citations

Soliton turbulence of a strongly driven one-dimensional Bose gas

Manon Ballu, Romain Dubessy, A. Perrin +2 more

We study the out-of-equilibrium dynamics of a weakly interacting one-dimensional Bose gas in a box trap, subjected to a drive realized by a periodically oscillating linear potential. After a transient regime, the gas reaches a quasi-steady state, characterized by the presence of several solitons. At weak driving amplitude, the solitons are only weakly perturbed by one another, while at strong driving amplitude a regime analogous to turbulence is reached, where the solitons are strongly intertwined with each other. We show that a hallmark of both regimes can be found in the momentum distribution, which displays a power-law decay $n(k) \sim k^{-2}$ at weak driving amplitude and $n(k) \sim k^{-α}$ with a power-law exponent $α\in [7,9]$ at large amplitude. We further characterize each of the two regimes by following the space-time maps and characterizing the solitons using the inverse scattering transform. The protocol analyzed in this study is amenable to experimental realization in current experimental setups.We study the out-of-equilibrium dynamics of a weakly interacting one-dimensional Bose gas in a box trap, subjected to a drive realized by a periodically oscillating linear potential. After a transient regime, the gas reaches a quasi-steady state, characterized by the presence of several solitons. At weak driving amplitude, the solitons are only weakly perturbed by one another, while at strong driving amplitude a regime analogous to turbulence is reached, where the solitons are strongly intertwined with each other. We show that a hallmark of both regimes can be found in the momentum distribution, which displays a power-law decay $n(k) \sim k^{-2}$ at weak driving amplitude and $n(k) \sim k^{-α}$ with a power-law exponent $α\in [7,9]$ at large amplitude. We further characterize each of the two regimes by following the space-time maps and characterizing the solitons using the inverse scattering transform. The protocol analyzed in this study is amenable to experimental realization in current experimental setups.

arXiv:2603.24832Physical Review AJul 13, 20260 citations

Observation of an Inverse Turbulent-Wave Cascade in a Driven Quantum Gas

Andrey Karailiev, Martin Gazo, Maciej Gałka +3 more

We observe an inverse turbulent-wave cascade, from small to large length scales, in a driven homogeneous 2D Bose gas. Starting with an equilibrium condensate, we drive the gas isotropically on a length scale much smaller than its size, and observe a nonthermal population of modes with wavelengths larger than the drive one. At long drive times, the gas exhibits a steady nonthermal momentum distribution. At length scales increasing from the drive one to the system size, this distribution features in turn: (i) a power-law spectrum with an exponent close to the analytical result for a particle cascade in weak-wave turbulence, and (ii) a spectrum reminiscent of a nonthermal fixed point associated with universal coarsening in an isolated 2D gas. In further experiments, based on anisotropic driving, we reveal the complete qualitative picture of how the steady-state cascade forms.We observe an inverse turbulent-wave cascade, from small to large length scales, in a driven homogeneous 2D Bose gas. Starting with an equilibrium condensate, we drive the gas isotropically on a length scale much smaller than its size, and observe a nonthermal population of modes with wavelengths larger than the drive one. At long drive times, the gas exhibits a steady nonthermal momentum distribution. At length scales increasing from the drive one to the system size, this distribution features in turn: (i) a power-law spectrum with an exponent close to the analytical result for a particle cascade in weak-wave turbulence, and (ii) a spectrum reminiscent of a nonthermal fixed point associated with universal coarsening in an isolated 2D gas. In further experiments, based on anisotropic driving, we reveal the complete qualitative picture of how the steady-state cascade forms.

arXiv:2405.01537Physical Review LettersDec 9, 202412 citations

Universal dynamics of a turbulent superfluid Bose gas

Arnol Daniel Garcia Orozco, Lucas Madeira, Michelle A. Moreno-Armijos +6 more

We study the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, parametrically driven to a turbulent state. We demonstrate that the out-of-equilibrium dynamics post excitation is described by a single function due to nearby nonthermal fixed points. The observed behavior connects the dynamics of a quantum turbulent state to several far-from-equilibrium phenomena. We present a controllable protocol to explore universality in such systems, obtaining the associated scaling exponents. Our experimental results thus offer a promising route to investigate the complex dynamics of the quantum turbulent regime.We study the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, parametrically driven to a turbulent state. We demonstrate that the out-of-equilibrium dynamics post excitation is described by a single function due to nearby nonthermal fixed points. The observed behavior connects the dynamics of a quantum turbulent state to several far-from-equilibrium phenomena. We present a controllable protocol to explore universality in such systems, obtaining the associated scaling exponents. Our experimental results thus offer a promising route to investigate the complex dynamics of the quantum turbulent regime.

arXiv:2107.07421Physical Review AAug 22, 202242 citations

n(k) \sim k^{-2}

at weak driving amplitude and

n(k) \sim k^{-α}

with a power-law exponent

α\in [7,9]

at large amplitude. We further characterize each of the two regimes by following the space-time maps and characterizing the solitons using the inverse scattering transform. The protocol analyzed in this study is amenable to experimental realization in current experimental setups.