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arXiv:2608.28808

Quantum synchronization of spin-1 system: Enhanced synchronization due to additive Lindblad operators

Tran Duong Anh-Tai, S. Zhong, X. Molenda, A. M. Marino, D. Blume

quant-phcond-mat.quant-gasSubmitted Aug 28, 2026• Announced Sep 1, 2026• 0 citations
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Abstract

We experimentally investigate quantum synchronization for one of the simplest possible quantum systems, namely an externally driven few-level system with equally spaced energy levels effectively acting as a spin-1 system. Coupling to excited auxiliary states, we realize additive effective Lindblad operators that are associated with non-conventional dissipative pathways, which are shown to enhance, in certain parameter regimes, quantum synchronization. The experimental set-up, which utilizes cold $^{87}$Rb atoms in a MOT, and associated synchronization extraction protocol are benchmarked carefully through dedicated simulations. Convincing agreement is found between experiment and simulations. The dissipation engineering approach established in our work can be readily extended to systems with more energy levels, such as effective spin-$3/2$ or spin-$2$ systems, and has implications for quantum synchronization studies in higher-spin systems as well as for a wide range of quantum science studies and technology applications.

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We experimentally investigate quantum synchronization for one of the simplest possible quantum systems, namely an externally driven few-level system with equally spaced energy levels effectively acting as a spin-1 system. Coupling to excited auxiliary states, we realize additive effective Lindblad operators that are associated with non-conventional dissipative pathways, which are shown to enhance, in certain parameter regimes, quantum synchronization. The experimental set-up, which utilizes cold 87^{87}87Rb atoms in a MOT, and associated synchronization extraction protocol are benchmarked carefully through dedicated simulations. Convincing agreement is found between experiment and simulations. The dissipation engineering approach established in our work can be readily extended to systems with more energy levels, such as effective spin-3/23/23/2 or spin-222 systems, and has implications for quantum synchronization studies in higher-spin systems as well as for a wide range of quantum science studies and technology applications.
Extending classical synchronization to the quantum domain is of great interest both from the fundamental physics point of view and with a view toward quantum technology applications. This work characterizes phase synchronization of an effective spin-1 system, which is realized by coupling three quantum states with infinite lifetime to auxiliary excited states that have a finite lifetime. Integrating out the excited states, the effective spin-1 model features coherent and incoherent effective couplings. Our key findings are: (i) Phase synchronization can be controlled by adjusting the phases of the couplings to the excited states. (ii) Unlike in the paradigmatic spin-1 system studied in the literature, where the dissipative couplings describe decay into the limit cycle state, the effective spin-1 model investigated in this work is governed by a competition between dissipative decay into and out of the limit cycle state, with the dissipative decay out of the limit cycle state playing a critical role. (iii) We identify a parameter regime where phase synchronization of the effective spin-1 system is -- in the absence of coherent effective couplings -- governed entirely by the effective dissipators. The effective spin-1 model is benchmarked through comparisons with master equation calculations for the full Hilbert space. Physical insights are gained through analytical perturbation theory calculations. Our findings, which are expected to hold for a broad class of energy level and coupling schemes, are demonstrated using hyperfine states of 87^{87}87Rb.
Synchronization has recently been explored deep in the quantum regime with elementary few-level quantum oscillators such as qudits and weakly pumped quantum van der Pol oscillators. To engineer more complex quantum synchronizing systems, it is practically relevant to study composite oscillators built from basic quantum units that are commonly available and offer high controllability. Here we consider a minimal model for a composite oscillator consisting of two interacting qubits coupled to separate baths and show that this system exhibits a wide variety of synchronizing behaviors. We study the phase response of the constituent qubits as well as the system as a whole, when one of the qubits is weakly driven. We consider the thermal baths to have positive as well as effective negative temperatures and discover effects that occur only when the temperatures of the baths for the two qubits are of opposite signs. We propose and analyze a circuit quantum electrodynamics implementation of this model, which exploits recent advances in dissipation engineering to realize effective negative temperature baths. Our work demonstrates the potential for assembling complex quantum synchronizing systems from basic building units, which is of pragmatic importance for advancing the field of quantum synchronization.
With growing interest in quantum technologies, possibilities of synchronizing quantum systems have 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 engineered, anisotropic decay rates. Furthermore, we observe a blockade of synchronization due to quantum interference and emergence of Arnold-tongue-like features. Such anisotropic decay induced synchronization of spin-1 systems with no classical analog can provide insights in open quantum systems and find applications in synchronized quantum networks.
In a dissipative regime, we study the properties of several qubits coupled to a driven resonator in the framework of a Jaynes-Cummings model. The time evolution and the steady state of the system are numerically analyzed within the Lindblad master equation, with up to several million components. Two semi-analytical approaches, at weak and strong (semiclassical) dissipations, are developed to describe the steady state of this system and determine its validity by comparing it with the Lindblad equation results. We show that the synchronization of several qubits with the driving phase can be obtained due to their coupling to the resonator. We establish the existence of two different qubit synchronization regimes: In the first one, the semiclassical approach describes well the dynamics of qubits and, thus, their quantum features and entanglement are suppressed by dissipation and the synchronization is essentially classical. In the second one, the entangled steady state of a pair of qubits remains synchronized in the presence of dissipation and decoherence, corresponding to the regime non-existent in classical synchronization.
The robustness of quantum synchronization induced by the dynamical Casimir effect (DCE) is analyzed within a circuit quantum electrodynamics (cQED) architecture consisting of two superconducting qubits coupled to a shared, parametrically driven cavity. Using a Lindblad master equation approach, this study evaluates the impact of various decoherence channels (including photon loss, relaxation, thermal excitation, and pure dephasing) on the resulting synchronization dynamics. The results demonstrate that DCE-induced synchronization persists under dissipation rates achievable in state-of-the-art superconducting platforms, confirming its experimental feasibility. Among the studied mechanisms, pure dephasing is identified as the dominant factor limiting the fidelity of the synchronized state. Furthermore, it is shown that in strongly dissipative regimes, the Pearson correlation coefficient may overestimate the degree of quantum synchronization, as environmental relaxation can generate classical correlations that mimic synchronized behavior. These findings establish the parameter regimes necessary for observing genuine DCE-induced quantum synchronization and provide practical guidelines for future cQED experiments.
Classical self-sustained oscillators, which generate periodic motion without periodic external forcing, are ubiquitous in science and technology. The realization of nonclassical self-oscillators is an important goal of quantum physics. We here present the experimental implementation of a quantum van der Pol oscillator, a paradigmatic autonomous quantum driven-dissipative system with nonlinear damping, using a single trapped atom. We demonstrate the existence of a quantum limit cycle in phase space in the absence of a drive and the occurrence of quantum synchronization when the nonlinear oscillator is externally driven. We additionally show that synchronization can be enhanced with the help of squeezing perpendicular to the direction of the drive and, counterintuitively, linear dissipation. We also observe the bifurcation to a bistable phase-space distribution for large squeezing. Our results pave the way for the exploration of self-sustained quantum oscillators and their application to quantum technology.