Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization is blocked. We demon- strate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with super- conducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.
High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, t…
Dual Role of Squeezed-Reservoir in Quantum Phase Synchronization: Boosting and Blockade
School of Physics and Electronic Information, Gannan Normal University（赣南师范大学物理与电子信息学院）；School of Information Engineering, Jiangxi University of Science and Technology（江西理工大学信息工程学院）；Jiangxi Provincial Key Laboratory of Multidimensional Intelligent Perception and Control, Jiangxi University of Science and Technology（江西理工大学多维智能感知与控制江西省重点实验室）
Optically coupled optomechanical oscillators has turned out to be a versatile experimental resource for exploring optomechanical synchronizations and correlations. In this work, we investigate the phenomena of quantum synchronization and quantum correlations in two optically coupled optomechanical oscillators with two different topologies. In one case the oscillators are coupled with optical photons in a reversible manner, termed as bidirectional coupling, while in the other photons are allowed to enter to the other oscillator but not allowed to exchanged back in the opposite direction, termed…
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behaviour of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that due to the anharmonicity of the nonlinear interaction between the oscillators the system exhibits phonon blockade in the phase locking regime which is a pure non…
We report the first experimental demonstration of quantum synchronization. This is achieved by performing a digital simulation of a single spin-$1$ limit-cycle oscillator on the quantum computers of the IBM Q System. Applying an external signal to the oscillator, we verify typical features of quantum synchronization and demonstrate an interference-based quantum synchronization blockade. Our results show that state-of-the-art noisy intermediate-scale quantum computers are powerful enough to implement realistic dissipative quantum systems. Finally, we discuss limitations of current quantum hardw…
We study the quantum synchronization of a single spin driven by an external semiclassical signal for spin numbers larger than $S = 1$, the smallest system to host a quantum self-sustained oscillator. The occurrence of interference-based quantum synchronization blockade is found to be qualitatively different for integer vs. half-integer spin number $S$. We explain this phenomenon as the interplay between the external signal and the structure of the limit cycle in the generation of coherence in the system. Moreover, we show that the same dissipative limit-cycle stabilization mechanism leads to v…
With growing interest in quantum technologies, possibilities of synchronizing quantum systems has garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 $^{87}{Rb}$ atoms, we observe phase difference of spin coherences to synchronize with phases of external classical fields. An initial limit-cycle state of a spin-1 atom localizes in phase space due to dark-state-polaritons generated by classical two-photon tone fields. In particular, when the two couplings fields are out of phase, the limit-cycle state synchronizes only with two artificially engineere…
Mediated Transmission of Quantum Synchronization in Star Networks
Renmin University of China（中国人民大学）；School of Physics, Renmin University of China（中国人民大学物理学院）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学量子态构建与操控教育部重点实验室）
We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare quantitatively the synchronization behavior of different limit cycles and signals. We focus on the most elementary quantum system that is able to host a self-sustained oscillation, namely a single spin 1. Despite the spin having no classical analogue, we first show that it can realize the van der Pol limit cycle deep in the quantum regime, which allows us t…
Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The r…
College of Physics and Electronic Engineering, Sichuan Normal University（四川师范大学物理电子工程学院）；Microsystem and Terahertz Research Center, China Academy of Engineering Physics（中国工程物理研究院微系统与太赫兹研究中心）
