Synergistic Effects of Detuning and Auxiliary Qubits on Quantum Synchronization

TL;DR

This work addresses quantum phase synchronization in a dissipative, multi-qubit system coupled to a structured (Lorentzian) reservoir. By treating detuning Δ as an active control parameter and introducing non-interacting auxiliary qubits to strengthen memory, the authors derive an exact single-excitation solution with a decay function h(t) dependent on d = λ - iΔ and D = \sqrt{d^2 - 2N γ_0 λ}. The key finding is that detuning is ineffective in Markovian environments but promotes robust, long-lived phase locking in non-Markovian regimes where environmental memory sustains coherence, with auxiliary qubits amplifying memory through collective coupling; this is demonstrated via Husimi Q-function analysis, a synchronization measure S(φ,t), Arnold tongue structures, and Bloch-sphere trajectories. The results propose a cooperative, resource-efficient strategy for engineered quantum phase control with potential applications in quantum communications, metrology, and synchronized quantum energy technologies.

Abstract

We investigate how detuning and auxiliary qubits collaboratively enhance quantum synchronization in a dissipative multi-qubit system that is coupled to a structured reservoir. Our findings indicate that while detuning is ineffective in Markovian environments, it emerges as a powerful control parameter in the non-Markovian regime, where environmental memory facilitates long-lived phase coherence. It is shown that adding more auxiliary qubits amplifies this effect by strengthening the collective coupling and enhancing memory, resulting in robust phase locking within the system. Analysis using the Husimi Q-function, synchronization measures, and Arnold tongue structures reveals a detuning-induced enhancement of phase locking, which significantly improves stability compared to the resonance case. These results establish a cooperative control strategy where detuning actively engineers phases, while auxiliary qubits provide the necessary memory for sustained synchronization.

Figures (7)

• Figure 1: Husimi $Q$-function $Q(\theta, \phi, t)$ for various numbers of ancillary qubits ($N$) in the Markovian regime ($\lambda = 5\gamma_0$). The top row shows resonance condition ($\Delta = 0$), while the bottom row correspond to $\Delta = \gamma_0$.
• Figure 2: Husimi $Q$-function $Q(\theta, \phi, t)$ for various numbers of ancillary qubits ($N$) in the non-Markovian regime ($\lambda = 0.01\gamma_0$). The top row shows resonance condition ($\Delta = 0$), while the bottom row correspond to $\Delta = \gamma_0$.
• Figure 3: Synchronization measure $S(\phi=0,t)$ in the non-Markovian regime ( $\lambda = 0.01\gamma_0$ ) and several values of $N$ and $\Delta = 0$. Panels corresponds to (a) $\Delta = 0$ , (b) $\Delta = 0.5\gamma_0$, (c) $\Delta = \gamma_0$, and (d) $\Delta = 2\gamma_0$.
• Figure 4: Maximum synchronization measure $S_m(t)$ as a function of the detuning $\Delta$ and coupling strength $\gamma$ (in units of $\gamma_0$) at time $\gamma_0t=1000$ for $\lambda=0.01\gamma_0$. Panels show (a) $N=1$, (b) $N=3$, (c) $N=6$, and (d) $N=10$.
• Figure 5: Maximum synchronization measure $S_m(t)$ as a function of detuning $\Delta$ and spectral width $\lambda$ (in units of $\gamma_0$) at time $\gamma_0t=1000$ for (a) $N=1$, (b) $N=3$, (c) $N=6$, and (d) $N=10$.