Topological Quantum Synchronization of Fractionalized Spins.

The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.

Autonomous Implementation of Thermodynamic Cycles at the Nanoscale.

There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics. Autonomous models, which do not rely on any external time dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations. Here, we bridge the two paradigms by constructing an autonomous model, which implements a thermodynamic cycle in a certain parameter regime. This effect is made possible by self-oscillations, realized in our model by the well-studied electron shuttling mechanism. Based on experimentally realistic values, we find that a thermodynamic cycle analysis for a single-electron working fluid is not justified, but a few-electron working fluid could suffice to justify it. Furthermore, additional open challenges remain to autonomously implement the more studied Carnot and Otto cycles.

Synchronized states in a ring of dissipatively coupled harmonic oscillators.

The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We consider the case of a finite number of harmonic oscillators arranged on a ring, with bilinear, dissipative nearest-neighbor coupling. We show that by tuning the gain and loss appropriately, stable synchronized dynamics may be achieved. These findings are interpreted using the complex eigenvalues and eigenvectors of the non-Hermitian matrix describing the dynamics of the system. We provide a complete discussion for the case of two oscillators. Ring sizes with a small number of oscillators are discussed taking the case of N=5 oscillators as an example. For N≳10 we focus on the case where the frequency fluctuations of each oscillator are chosen from a Gaussian distribution with zero mean and standard deviation σ. We derive a scaling law for the largest standard deviation σ_{full} that still permits all oscillators to be fully synchronized: σ_{full}∼N^{-3/2}. Finally, we discuss how such random fluctuations influence the timescale on which the synchronized state is reached and on which timescale the synchronized state then decays.