Noise-Induced Quantum Synchronization

Energetic Cost for Speedy Synchronization in Non-Hermitian Quantum Dynamics

Quantum synchronization is crucial for understanding complex dynamics and holds potential applications in quantum computing and communication. Therefore, assessing the thermodynamic resources required for finite-time synchronization in continuous-variable systems is a critical challenge. In the present work, we find these resources to be extensive for large systems. We also bound the speed of quantum and classical synchronization in coupled damped oscillators with non-Hermitian anti-PT-symmetric interactions, and show that the speed of synchronization is limited by the interaction strength relative to the damping. Compared to the classical limit, we find that quantum synchronization is slowed by the noncommutativity of the Hermitian and anti-Hermitian terms. Our general results could be tested experimentally, and we suggest an implementation in photonic systems.

Anomalous thermodynamic cost of clock synchronization

Clock synchronization is critically important in positioning, navigation and timing systems. While its performance has been intensively studied in a wide range of disciplines, much less is known for the fundamental thermodynamics of clock synchronization‒what limits the precision and how to optimize the energy cost for clock synchronization. Here, we report the first experimental investigation of two stochastic autonomous clocks synchronization, unveiling the thermodynamic relation between the entropy cost and clock synchronization in an open cavity optomechanical system. Two interacting clocks are synchronized spontaneously owing to the disparate decay rates of hybrid modes by engineering the controllable cavity-mediated dissipative coupling. The measured dependence of the degree of synchronization on the overall entropy cost exhibits an unexpected non-monotonic characteristic, while the relation between the degree of synchronization and the entropy cost for the synchronization is monotonically decreasing. The investigation of transient dynamics of clock synchronization exposes a trade-off between energy and time consumption. Our results demonstrate the possibility of clock synchronization in an effective linear system, reveal the fundamental relation between clock synchronization and thermodynamics, and have a great potential for precision measurements, distributed quantum networks, and biological science.

Reliability for music-induced heart rate synchronization

Common inputs synchronize various biological systems, including human physical and cognitive processes. This mechanism potentially explains collective human emotions in theater as unintentional behavioral synchronization. However, the inter-subject correlation of physiological signals among individuals is small. Based on findings on the common-input synchronization of nonlinear systems, we hypothesized that individual differences in perceptual and cognitive systems reduce the reliability of physiological responses to aesthetic stimuli and, thus, disturb synchronization. We tested this by comparing the inter- and intra-subject Pearson's correlation coefficients and nonlinear phase synchronization, calculated using instantaneous heart rate data measured while appreciating music. The results demonstrated that inter-subject correlations were consistently lower than intra-subject correlations, regardless of participants' music preferences and daily moods. Further, music-induced heart rate synchronization depends on the reliability of physiological responses to musical pieces rather than mood or motivation. This study lays the foundation for future empirical research on collective emotions in theater.

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.

Measurement-Induced Quantum Synchronization and Multiplexing

Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.

Macroscopic Quantum Synchronization Effects

We theoretically describe macroscopic quantum synchronization effects occurring in a network of all-to-all coupled quantum limit-cycle oscillators. The coupling causes a transition to synchronization as indicated by the presence of global phase coherence. We demonstrate that the microscopic quantum properties of the oscillators qualitatively shape the synchronization behavior in a macroscopically large network. Specifically, they result in a blockade of collective synchronization that is not expected for classical oscillators. Additionally, the macroscopic ensemble shows emergent behavior not present at the level of two coupled quantum oscillators.

Enhancing quantum synchronization through homodyne measurement, noise, and squeezing

Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.

Cooperation and Competition in Synchronous Open Quantum Systems

Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.

Shortcut to synchronization in classical and quantum systems

Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.