Synchronization phenomena have been recently reported in the quantum realm at atomic level due to collective dissipation. In this work we propose a dimer lattice of trapped atoms realizing a dissipative spin model where quantum synchronization occurs instead in presence of local dissipation. Atoms synchronization is enabled by the inhomogeneity of staggered local losses in the lattice and is favored by an increase of spins detuning. A comprehensive approach to quantum synchronization based on different measures considered in the literature allows to identify the main features of different synchronization regimes. PACS numbers:Spontaneous synchronization (SS) among different interacting units is a paradigmatic collective phenomenon arising in a broad range of contexts [1]. In the last decade it has been explored into the quantum regime, which triggered novel questions related to the essence of this phenomenon and to its non-classical signatures. The very same definition of quantum synchronization has led to a variety of approaches and measures [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], that can be broadly categorized as (i) time correlation of the dynamics of local quantum observables, whose occurrence can be compared with quantum correlations [3][4][5][6][7][8][9][10][11]; or as (ii) reduction of noise in some collective variables, being then itself a form of global quantum correlations [12][13][14][15][16][17][18][19][20][21].The study of quantum SS has enriched the perspective on this phenomenon in different dynamical regimes. Classical SS has been broadly studied in self-sustained oscillators, encompassing regular periodic, but also chaotic and stochastic evolutions [1,22,23]. Quantum selfsustained oscillators can also display quantum SS, as reported in , optomechanical systems [2,12,24], micromasers [18], spin-1 systems [25], and ions [11]. Apart from this, different dynamical scenarios have been explored in the quantum regime, leading either to SS in the steady state or in transient dynamics, as in steady superradiant emission [16,17,20,21,26] and in presence of decoherence free subspaces [7,9], relaxing networks of harmonic oscillators [4,7] or spins [3,5,6,8,10,19]. In atomic systems genuine quantum features of synchronization come into play, as in superradiant lasers [26], in supercooling [20], between two atomic clouds [16,21], in two spins subradiance [3,5,6,10], among optically pumped interacting dipoles [17] and in trapped ions [13,14,27]. A common key feature enabling quantum synchronization in these atomic systems is the presence of a collective dissipative coupling among atoms either because this leads to a subradiant mode in relaxing systems or because superradiance allows overcoming other incoherent effects.In this Letter, building on the proposed experimental scheme of Ref.[28], we design a different setup, consisting of an atomic lattice in a dimer configuration, where quantum simulation of SS can be realized. Atomic lat-tices represent a rich platform for many-bo...

The transport and storage of quantum information, excitations, and entanglement, within and across complex quantum networks is crucially affected by the presence of noise induced by their surroundings. Generally, the interaction with the environment deteriorates quantum properties initially present, thus limiting the efficiency of any quantum-enhanced protocol or phenomenon. This is of key relevance, for example, in the design of quantum communication networks and for understanding and controlling quantum harvesting on complex systems. Here, we show that complex quantum networks, such as random and small-world ones, can admit noiseless clusters for collective dissipation. We characterize these noiseless structures in connection to their topology addressing their abundance, extension, and configuration, as well as their robustness to noise and experimental imperfections. We show that the network degree variance controls the probability to find noiseless modes and that these are mostly spanning an even number of nodes, like breathers. For imperfections across the network, a family of quasi-noiseless modes is also identified shielded by noise up to times decreasing linearly with frequency inhomogeneities. Large noiseless components are shown to be more resilient to the presence of detuning than to differences in their coupling strengths. Finally, we investigate the emergence of both stationary and transient quantum synchronization showing that this is a rather resilient phenomenon in these networks.

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