We derive an analytic solution for the ensemble-averaged collective dephasing dynamics of N noninteracting atoms in a fluctuating homogeneous external field. The obtained Kraus map is used to specify families of states whose entanglement properties are preserved at all times under arbitrary field orientations, even for states undergoing incoherent evolution. Our results apply to arbitrary spectral distributions of the field fluctuations.PACS numbers: 03.65. Yz, 03.65.Ud, 03.67.Mn Control of the coherent evolution of quantum systems in noisy environments [1] is one of the crucial prerequisites for exploiting nontrivial quantum effects in composite systems of increasing complexity. Whether in the context of controlled molecular reactions [2], of many-particle quantum dynamics [3], or of quantum computers and simulators [4], uncontrolled fluctuations and noise are detrimental to most purposes of optimal control. Various strategies may be followed to counteract the harmful influence of the environment: shielding the system degrees of freedom [5], correcting environmentinduced errors [6], exploiting basins of attraction in dissipative systems [8], or compensating dissipation-e.g., by coherent dynamics [7], dynamical decoupling [9], or periodic measurements [10]. Such approaches can effectively reduce the environmental effects and can enhance coherence times, but a perfect protection of the quantities of interest is generally not possible.By restricting to superposition states within a decoherencefree subspace, initially entangled states can be shielded completely from collective noise sources, hence protecting their entanglement at all times [11,12]. However, such subspaces are rather fragile to small perturbations, which limit their applicability in the context of dynamical processes [13]. Here, we identify conditions that ensure complete preservation of arbitrary degrees of entanglement, even for states that are not invariant under an incoherent time evolution. Specifically, we consider an important class of environment-induced fluctuations, which are frequently encountered in state-of-the-art experiments [14][15][16]: they manifest in intensity fluctuations of spatially homogeneous experimental control fields, giving rise to an effective dephasing process. We show how control of the external field's orientation can lead to the complete preservation of entanglement in bipartite-as well as multipartitesettings, for arbitrary spectral characteristics of the control field fluctuations. We further identify families of states exhibiting time-invariant entanglement for arbitrary orientations of the external field.To set the stage, let us consider a collection of N noninteracting atomic two-level systems with identical energy splitting ω controlled, e.g., by a homogeneous magnetic field. Integration over the unavoidable fluctuations of the latter's strength will induce a probability distribution p(ω) of the characteristic energy splitting, and the N-atom quantum state at time t therefore needs to be described by the st...

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We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.