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arXiv:2604.02879 · Physical review. B./Physical review. B

Mesoscopic scattering dynamics under generic uniform SU(2) gauge fields: Spin-momentum relaxation and coherent backscattering

Anonymous, Christian Miniatura, Keith Slevin

Published Jul 7, 2026• 0 citations
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Abstract

We investigate the time- and momentum-resolved dynamics of matter waves undergoing elastic scattering from a disordered potential in the presence of spatially uniform SU(2) gauge fields. We derive the disorder-averaged density matrix as a function of time and momentum within the weak-localization regime. By accurately approximating the frequency dependence of the ladder and maximally crossed diagram series beyond the diffusion approximation, we describe short-time spin-momentum dynamics on timescales comparable to the scattering mean free time, for arbitrary strengths of the SU(2) gauge fields and disorder. We also present a cubic equation that determines the spin isotropization time, which gives accurate asymptotic forms in the limits where the spin-orbit length is much longer (Dyakonov-Perel spin relaxation regime) or much shorter than the scattering mean free path, as well as in the SU(2)-symmetric (persistent spin helix) limit. Comparison with numerical simulations over a broad range of spin-orbit coupling strengths shows quantitative agreement for the predicted spin isotropization time. The same framework also reproduces both the relaxation of the momentum distribution and the transient backscattering peak with a momentum offset coexisting with the robust coherent backscattering dip.

DOI
10.1103/kyk8-71l4

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We investigate the time- and momentum-resolved dynamics of matter waves undergoing elastic scattering from a disordered potential in the presence of spatially uniform SU(2) gauge fields. We derive the disorder-averaged density matrix as a function of time and momentum within the weak-localization regime. By accurately approximating the frequency dependence of the ladder and maximally crossed diagram series beyond the diffusion approximation, we describe short-time spin-momentum dynamics on timescales comparable to the scattering mean free time, for arbitrary strengths of the SU(2) gauge fields and disorder. We also present a cubic equation that determines the spin isotropization time, which gives accurate asymptotic forms in the limits where the spin-orbit length is much longer (Dyakonov-Perel spin relaxation regime) or much shorter than the scattering mean free path, as well as in the SU(2)-symmetric (persistent spin helix) limit. Comparison with numerical simulations over a broad range of spin-orbit coupling strengths shows quantitative agreement for the predicted spin isotropization time. The same framework also reproduces both the relaxation of the momentum distribution and the transient backscattering peak with a momentum offset coexisting with the robust coherent backscattering dip.
We study interference effects in the dynamics of a spin-1/21/21/2 particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.
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We investigate the dynamics of a coherent matter wave packet launched in a random potential. As predicted by Cherroret et al. [Phys. Rev. A 85 011604(R) (2012)], the coherent backscattering signal in the momentum distribution freezes at the onset of Anderson localization. At the same time, a novel interference peak rises in the forward direction. An explanation in terms of chained maximally crossed diagrams predicts that the forward scattering peak emerges on a time scale τloc∗=2mξ2/ℏ\tau_\text{loc}^* = 2m\xi^2/\hbarτloc∗​=2mξ2/ℏ set by the localization length ξ\xiξ.
Abstract We study the elastic scattering time τ s of ultracold atoms propagating in optical disordered potentials in the strong scattering regime, going beyond the recent work of Richard et al (2019 Phys. Rev. Lett. 122 100403). There, we identified the crossover between the weak and the strong scattering regimes by comparing direct measurements and numerical simulations to the first order Born approximation. Here we focus specifically on the strong scattering regime, where the first order Born approximation is not valid anymore and the scattering time is strongly influenced by the nature of the disorder. To interpret our observations, we connect the scattering time τ s to the profiles of the spectral functions that we estimate using higher order Born perturbation theory or self-consistent Born approximation. The comparison reveals that self-consistent methods are well suited to describe τ s for Gaussian-distributed disorder, but fails for laser speckle disorder. For the latter, we show that the peculiar profiles of the spectral functions, as measured independently in Volchkov et al (2018 Phys. Rev. Lett. 120 060404), must be taken into account. Altogether our study characterizes the validity range of usual theoretical methods to predict the elastic scattering time of matter waves, which is essential for future close comparison between theory and experiments, for instance regarding the ongoing studies on Anderson localization.
We report on an extensive study of the elastic scattering time τ_{s} of matter waves in optical disordered potentials. Using direct experimental measurements, numerical simulations, and comparison with the first-order Born approximation based on the knowledge of the disorder properties, we explore the behavior of τ_{s} over more than 3 orders of magnitude, ranging from the weak to the strong scattering regime. We study in detail the location of the crossover and, as a main result, we reveal the strong influence of the disorder statistics, especially on the relevance of the widely used Ioffe-Regel-like criterion kl_{s}∼1. While it is found to be relevant for Gaussian-distributed disordered potentials, we observe significant deviations for laser speckle disorders that are commonly used with ultracold atoms. Our results are crucial for connecting experimental investigation of complex transport phenomena, such as Anderson localization, to microscopic theories.