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arXiv:2503.15027 · Physical Review Letters

Tunable Anomalous Diffusion in Subrecoil-Laser-Cooled Atoms

Soma Shiraki, Eli Barkai, Takuma Akimoto

Published Mar 12, 2026• 0 citations
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Abstract

Laser cooling of atomic motion enables advances in quantum information and precision metrology. However, the spatial spreading of subrecoil-laser-cooled atoms-crucial for understanding cooling mechanisms and atomic confinement-remains largely unexplored. Here, we analyze anomalous diffusion in subrecoil-laser-cooled atoms, where a velocity-dependent fluorescence rate R(v)∝|v|^{α} governs transport properties. By tuning α, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at α=3/2, diffusion is minimized, leading to optimal atomic confinement. We further identify a conceptual link between subrecoil laser cooling and the Pomeau-Manneville map from nonlinear dynamics, revealing that anomalous diffusion can generically exhibit a nontrivial minimum in spatial spreading-even across seemingly unrelated physical systems.

DOI
10.1103/9pb2-v6zs

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Laser cooling of atomic motion enables advances in quantum information and precision metrology. However, the spatial spreading of subrecoil-laser-cooled atoms-crucial for understanding cooling mechanisms and atomic confinement-remains largely unexplored. Here, we analyze anomalous diffusion in subrecoil-laser-cooled atoms, where a velocity-dependent fluorescence rate R(v)∝|v|^{α} governs transport properties. By tuning α, we uncover transitions between normal, subdiffusive, and superdiffusive regimes. Notably, at α=3/2, diffusion is minimized, leading to optimal atomic confinement. We further identify a conceptual link between subrecoil laser cooling and the Pomeau-Manneville map from nonlinear dynamics, revealing that anomalous diffusion can generically exhibit a nontrivial minimum in spatial spreading-even across seemingly unrelated physical systems.
Anomalous diffusion processes, dominated by rare events, are shown to exist and to play a central role in certain subrecoil laser cooling schemes. We present a new statistical analysis of these processes, in terms of L\'evy flights, which provides a precise analytical description of the cooled atoms in the long time limit, where the standard methods of quantum optics are inappropriate. These analytical predictions are quantitatively checked by comparison with the results of quantum Monte Carlo simulations of the cooling process at intermediate times.
Laser cooling allows now the velocity spread of an ensemble of atoms to be reduced below the value corresponding to the recoi l \nvelocity of an atom emitting or absorbing a single photon (subrecoil cooling) . This is achieved by using a random walk in velocit y \nspace with a jump rate which vanisches at zero velocity . We will review a few possible theoretical descriptions of such a coolin g \nmechanism . The anomalous character of the corresponding random walk will be analysed using Lvy statistical distributions an d \ncertain nonergodic features of the atomic evolution will be emphasized . Recent experimental developments will be also described . \nThey have allowed temperatures of a few nanokelvins to be reached and measured .
Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-Andr\'e model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.
In this chapter, we first recall (in Section 2.1) a few properties of the most usual laser cooling schemes, which involve a friction force. In such standard situations, the motion of the atom in momentum space is a Brownian motion which reaches a steady-state, and the recoil momentum of an atom absorbing or emitting a single photon appears as a natural limit for laser cooling. We then describe in Section 2.2 some completely different laser cooling schemes, based on inhomogeneous random walks in momentum space. These schemes, which are investigated in the present study, allow the ‘recoil limit’ to be overcome. They are associated with non-ergodic statistical processes which never reach a steady-state. Section 2.3 is devoted to a brief survey of various quantum descriptions of subrecoil laser cooling, which become necessary when the ‘recoil limit’ is reached or overcome. The most fruitful one, in the context of this work, is the ‘quantum jump description’ which will allow us in Section 2.4 to replace the microscopic quantum description of subrecoil cooling by a statistical study of a related classical random walk in momentum space. It is this simpler approach that will be used in the subsequent chapters to derive some quantitative analytical predictions, in cases where the quantum microscopic approach is unable to yield precise results, in particular in the limit of very long interaction times, and/or for a momentum space of dimension D higher than 1.
We demonstrate subrecoil cooling of rubidium atoms by velocity-selective coherent population trapping. By adiabatic transfer of the cooled atoms into a spin polarized single momentum state we show the coherence of the trapped state. Our cooling scheme takes advantage of the rubidium hyperfine structure to integrate subrecoil and sub-Doppler cooling. Starting from an initial velocity distribution of twice the recoil temperature $[{T}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{\Elzxh}k{)}^{2}{/k}_{B}M]$, we cool down to 100 nK $(\ensuremath{\approx}\frac{1}{3}{T}_{\mathrm{rec}})$ within 1 ms, while almost completely suppressing the diffusive heating of velocity-selective coherent population trapping.