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arXiv:2309.12308 · Comptes Rendus Physique

Energy-space random walk in a driven disordered Bose gas

Yansheng Zhang, Gevorg Martirosyan, C. J. Ho, Jiří Etrych, Christoph Eigen, Zoran Hadzibabic

Published Feb 2, 2024• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.5802/crphys.168

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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.
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.
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)∼k−2n(k) \sim k^{-2}n(k)∼k−2 at weak driving amplitude and n(k)∼k−αn(k) \sim k^{-α}n(k)∼k−α with a power-law exponent α∈[7,9]α\in [7,9]α∈[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 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 consider an impurity in a one-dimensional weakly interacting Bose gas and analytically calculate the density profile of the Bose gas. Within the mean-field approximation, by increasing the distance from the impurity, the Bose gas density saturates exponentially fast to its mean thermodynamic-limit value at distances beyond the healing length. The effect of quantum fluctuations drastically changes this behavior, leading to a power-law decay of the density deviation from the mean density. At distances longer than the healing length and shorter than a new length scale proportional to the impurity coupling strength, the power-law exponent is 2, while at the longest distances the corresponding exponent becomes 3. The latter crossover does not exist in two special cases. The first one is realized for infinitely strongly coupled impurity; then the density deviation always decays with the exponent 2. The second special case occurs when the new length scale is smaller than the healing length, i.e., at weak impurity coupling; then the density deviation always decays with the exponent 3. The obtained results are exact in the impurity coupling strength and account for the leading order in the interaction between the particles of the Bose gas.
We use ultracold atoms in a quasiperiodic lattice to study two outstanding problems in the physics of disordered systems: a) the anomalous diffusion of a wavepacket in the presence of disorder, interactions and noise; b) the transport of a disordered superfluid.a) Our results show that the subdiffusion, observed when interaction alone is present, can be modelled with a nonlinear diffusion equation and the peculiar shape of the expanding density profiles can be connected to the microscopic nonlinear diffusion coefficients.Also when noise alone is present we can describe the observed normal diffusion dynamics by existing microscopic models.In the unexplored regime in which noise and interaction are combined, instead, we observe an anomalous diffusion, that we model with a generalized diffusion equation, where noise-and interaction-induced contributions add each other.b) We find that an instability appearing at relatively large momenta can be employed to locate the fluid-insulator crossover driven by disorder.By investigating the momentum-dependent transport, we observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum.The set of critical disorder and interaction strengths for which such critical momentum vanishes, can be identified with the separation between a fluid regime and an insulating one and can be related to the predicted zero-temperature superfluid-Bose glass transition.