Universal Manipulation of Quantum Synchronization in Spin Oscillator Networks

TL;DR

The paper proposes a universal, dissipation-agnostic method to control quantum synchronization in spin oscillator networks by tuning XYZ interaction anisotropy, enabling continuous passage from maximal QS to synchronization blockade (QSB). Through a perturbative analysis, QS is shown to originate from spin flip-flop channels and higher-order correlators $\\langle (\\hat J_1^+ \\hat J_2^-)^p + h.c. \\ angle$, with the isotropic part $(u^x+u^y)$ enabling phase locking while the anisotropic component does not contribute to QS; a macroscopic QSB is demonstrated in the thermodynamic limit via a geometric measure $S_{\\\infty}^{\\text{MF}}$. The framework is validated with two-spin-1 examples and extended to arbitrary spin $J$, and is argued to be implementable with XYZ interactions and optical pumping, e.g., using Rydberg-dressed neutral atoms. This universal, scalable approach provides a programmable route to QS and dynamical phases in large quantum networks, with potential applications in quantum thermodynamics and metrology.

Abstract

Quantum synchronization (QS) in open many-body systems offers a promising route for controlling collective quantum dynamics, yet existing manipulation schemes often rely on dissipation engineering, which distorts limit cycles, lacks scalability, and is strongly system-dependent. Here, we propose a universal and scalable method for continuously tuning QS from maximal synchronization under isotropic interactions to complete synchronization blockade (QSB) under fully anisotropic coupling in spin oscillator networks. Our approach preserves intrinsic limit cycles and applies to both few-body and macroscopic systems. We analytically show that QS arises solely from spin flip-flop processes and their higher-order correlations, while anisotropic interactions induce non-synchronizing coherence. A geometric QS measure reveals a macroscopic QSB effect in the thermodynamic limit. The proposed mechanism is experimentally feasible using XYZ interactions and optical pumping, and provides a general framework for programmable synchronization control in complex quantum networks and dynamical phases of matter.

Figures (5)

• Figure 1: (a) Illustration of the universal interaction-based control of spin networks, each spin is subject to both damping ($\gamma^{-}_{j}$) and gain ($\gamma^{+}_{j}$) dissipations. Without interaction (I, IV), each spin independently evolves into a limit cycle state (II). When interactions are isotropic ($u^{x}/u^{y}=1$), the system reaches maximum synchronization (III); when anisotropic ($u^{x}/u^{y}=-1$), synchronization is blocked (IV). (b) Two spin-1 oscillator example. Synchronization $S_{2}^{\text{max}}$, entanglement $C$ and discord $D$, exhibits similar behavior across stages I, II, and IV. However, at stage III, neither $C$ and $D$ displays the quantum blockade effect as $S_{2}^{\text{max}}$ does. Notably, $C$ experiences a sudden-death followed by a revival to a nonzero value. Parameters: $\gamma^{+}_{2}=\gamma^{-}_{1},\gamma^{+}_{1}=\gamma^{-}_{2}=100\gamma^{-}_{1},\epsilon=0.1\gamma^{-}_{1},u^{z}=0,\Delta_{12}=\omega_{1}-\omega_{2}=0$
• Figure 2: (a) Synchronization measure $S^{\text{max}}_{2}$ for two resonant spin-1 oscillators with imbalanced gain and damping. Synchronization is suppressed when $u^{x}/u^{y} = -1$, indicating a blockade. Insets show phase locking at $-\pi/2$ and $\pi/2$, corresponding to repulsive (black lines, circles) and attractive (red lines, stars) couplings, respectively. (b) Control of synchronization $S^{\text{max}}_{2}$, entanglement $C$, and mutual information $I$ by tuning the anisotropy ratio $u^{x}/u^{y}$. The shaded region highlights the regime where only synchronization can be linearly tuned from full blockade to its maximum. (c) Arnold tongues for synchronization (c1, c3) and entanglement (c2, c4) under $u^{x}/u^{y} \neq -1$ (c1-c2) and $u^{x}/u^{y} = -1$ (c3-c4). Synchronization vanishes under purely anisotropic interaction (c3), whereas entanglement persists with a visible tongue structure(c4). Parameters: (a-c) $u^z = 0$; (a-b) $\epsilon = 0.1\gamma^{-}_{1}$; (a,c) $\gamma^{+}_{1} = \gamma^{-}_{2} = 100\gamma^{-}_{1} = 100\gamma^{+}_{2}$; (b) $|u^{x}+u^{y}|+|u^{x}-u^{y}|=1$.
• Figure 3: Synchronization in spin-1 networks for $N = 3$ (a) and $N=\infty$ (b,c). (a) Synchronization measure $S^{\mathrm{max}}_{12}$ between 1th and 2nd spins. The inset compares the universal control scenario along the red dashed line and the black diagonal, showing that the synchronization behavior is insensitive to the presence of spin 3. (b) Dynamics of a large-scale network in the thermodynamic limit for three representative cases: fully anisotropic (b1), partially isotropic (b2), and fully isotropic (b3). Symbols indicate the initial states, which correspond to the representative cases shown in (c). (c) Synchronization measure $S_\infty^{\mathrm{MF}}$, defined as the area enclosed by the limit-cycle trajectory. The inset (c1) corresponds to the red solid line and illustrates how increasing anisotropy suppresses synchronization even when the total isotropic strength is held fixed. Parameters: (a) $\epsilon = 0.1\gamma^{-}_{1}$, $|u_{1,2,3}^{x}+u_{1,2,3}^{y}|+|u_{1,2,3}^{x}-u_{1,2,3}^{y}|=1$,$\gamma^{+}_{1} = \gamma^{-}_{2} = 10\gamma^{+}_{3} = 5\gamma^{-}_{3} = 100\gamma^{-}_{1} = 100\gamma^{+}_{2}$, $\Delta_{12}=\Delta_{23}=0$; (b) $\epsilon = 6\gamma^{+}$, $\gamma^{-}= 10\gamma^{+}$.
• Figure S1: Quantum synchronization measures for two-body systems with different spin values under anisotropic interactions. Parameters: $\epsilon = 0.1\gamma_1^d$, $\gamma_1^g = \gamma_2^d = 2\gamma_1^d = 2\gamma_2^g$.
• Figure S2: Experimental setup and level schemes. (a) On the single-atom level, we couple the electronic ground states ($|m_F=-1,+1\rangle$) to distinct Rydberg states ($|r_{-1}\rangle, |r_{+1}\rangle$) using polarization-resolved dressing lasers with Rabi frequencies $\Omega_{-}, \Omega_{+}$ and detunings $\Delta_{-}, \Delta_{+}$. Dissipative transitions between $|m_F = +1\rangle$ and $|m_F = -1\rangle$ are implemented via optical pumping through short-lived excited states, with tunable rates $\sigma_+$ and $\sigma_-$, respectively. The excited state $|e\rangle$ decays spontaneously to the opposite ground state with decay rates $\kappa_+$ and $\kappa_-$. (b) Schematic for the flop-flop interaction $u_{kl}^{++}$ between two atoms $k$ and $l$. Pairs of ground-state atoms in $|+1,+1\rangle$ or $|-1,-1\rangle$ are off-resonantly coupled to interacting Rydberg pair states $|\Psi_\alpha^{(2)}\rangle$ with effective two-body Rabi frequencies $\Omega_{++}^{(\alpha)}$ and $\Omega_{--}^{(\alpha)}$. The effective two-photon detuning $\Delta_\alpha^{(2)}$ to each molecular state $|\Psi_\alpha^{(2)}\rangle$ includes interaction-induced energy shifts between the Rydberg levels. (c) Schematic for the flip-flop interaction $u_{kl}^{+-}$ between two atoms $k$ and $l$. Ground-state atom pairs in $|+1,-1\rangle$ or $|-1,+1\rangle$ are virtually coupled to interacting Rydberg pair states $|\Psi_\alpha^{(2)}\rangle$ via polarization-resolved laser dressing, with effective two-body Rabi frequencies $\Omega_{+-}^{(\alpha)}$ and $\Omega_{-+}^{(\alpha)}$. The associated detuning $\Delta_\alpha^{(2)}$ includes the interaction-induced energy shift of the molecular state $|\Psi_\alpha^{(2)}\rangle$.