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arXiv:2511.19697

Synergistic Effects of Detuning and Auxiliary Qubits on Quantum Synchronization

Amir Hossein Houshmand Almani, Ali Mortezapour, Alireza Nourmandipour

quant-phSubmitted Nov 24, 2025• Announced Nov 26, 2025• 0 citations
v1 · Nov 24, 2025v2 · Nov 26, 2025
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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.

Comments
10 pages, 7 figures

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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.
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.
Abstract We investigate forced quantum phase synchronization and transient relaxation dynamics of a driven two-level system (TLS) coupled to a hierarchical structured environment arranged in a wheel-graph, where a primary cavity directly couples to the TLS and interacts uniformly with a closed ring of N nearest-neighbor-coupled auxiliary cavities. Employing the dressed-state secular representation and conditional non-Hermitian Hamiltonian in the dressed-state subspace, we characterize the phase-locking behavior using the Husimi Q -function and the synchronization measure S . In the steady-state regime, the TLS exhibits anti-phase locking relative to the coherent drive, governed by the dynamic competition between detuning-induced phase drift and drive-induced phase torque, which naturally delineates a quantum analogue of the classical Arnold tongue. Crucially, we identify an environmental dimensionality decoupling effect, wherein the steady-state phase synchronization remains invariant to the auxiliary reservoir size N . In contrast, the transient relaxation time toward synchronization displays a non-monotonic dependence on the primary–auxiliary coupling strength κ . Below a critical threshold κ crit , the auxiliary array acts as a broadband Markovian reservoir, accelerating phase locking via Purcell-like dissipation. Above this threshold, mode hybridization triggers non-Markovian information backflow, which prolongs transient oscillations and delays synchronization. Finally, we discuss an experimentally feasible implementation based on superconducting circuit quantum electrodynamics. These results provide insights into the mechanism governing steady-state quantum phase synchronization in structured environments and offer practical guidance for reservoir engineering in quantum technologies.
Abstract Quantum phase synchronization is studied in a dissipative model via an analytic approach. It is found that a robust phase preference using the Husimi Q-function against decoherence for both the Markovian and non-Markovian regimes can be obtained by manipulating auxiliary qubits in a reservoir. Specifically, we show that quantum phase synchronization can be significantly improved by adding a number of auxiliary qubits for both the Markovian and non-Markovian regimes. We also find that a steady quantum phase synchronization can be obtained in the long-time limit, which is only dependent on the number of auxiliary qubits regardless of the Markovian or non-Markovian regimes. We give some intuitive interpretations of the obtained results. Overall, our results are of theoretical interest in the enhancement of quantum phase synchronization in noisy environments, and may have potential applications in quantum information science.
Synchronizing a few-level quantum system is of fundamental importance to the understanding of synchronization in the deep quantum regime. We investigate quantum phase synchronization of a two-level system (qubit) driven by a semiclassical laser field, in the presence of a general non-Markovian dissipative environment. The phase preference of the qubit is demonstrated through Husimi Q-function, and the existence of a limit cycle is also shown in our system. Synchronization of the qubit is quantified using the shifted phase distribution. The signature of quantum phase synchronization viz the Arnold tongue is obtained from the maximal value of the shifted phase distribution. Two distinct types of qubit dynamics is considered depending on the reservoir correlation time being very short and a situation when bath correlation time is finite. In the Markov regime of the environment, the phase preference of the qubit goes away in the long time limit, whereas the long-time phase localization persists in the non-Markovian regime. We also plot the maximum of the shifted phase distribution in two ways: (a) by varying the detuning and laser driving strength, and (b) by varying the system-bath coupling and laser driving strength. Various system-environment parameters determine the synchronization regions and the qubit phase synchronization is shown to be enhanced in the non-Markov regime.
We study the quantum phase synchronization of a driven two-level system (TLS) coupled to a structured environment and demonstrate that quantum synchronization can be enhanced by the classical driving field. We use the Husimi QQQ function to characterize the phase preference and find the in-phase and anti-phase locking phenomenon in the phase diagram. Remarkably, we show that the in-phase classical driving enables a TLS to reach stable anti-phase locking in the Markovian regime. However, we find that the synergistic action of classical driving and non-Markovian effects significantly enhances the initial in-phase locking. By introducing the SSS function and its maximal value to quantify the strength of synchronization and sketch the synchronization regions, we observe the typical signatures of the hollowed Arnold tongue in the parameter regions of synchronization. In the hollowed Arnold tongue, the synchronization regions exist both inside and outside the tongue while unsynchronized regions only lie on the boundary line. We also provide an intuitive interpretation of the above results by using the quasimode theory.
We investigate a two-qubit quantum battery where coherent charger-battery coupling competes with non-Markovian environmental interactions. By tuning the coupling strengths and detuning, we identify regimes in which environmental memory enhances energy storage and charging power, while strong dissipation suppresses ergotropy by driving the battery into passive states. We show that detuning plays a dual role: reducing dissipation and inducing a phase shift in the memory kernel that controls the interference between coherent energy exchange and environment-induced backflow. As a result, although the stored energy varies smoothly, the extractable work exhibits a discontinuous onset at a critical detuning, signaling a first-order phase transition in ergotropy. The corresponding phase diagram in the coupling-detuning plane reveals a sharp boundary between thermodynamically inactive and work-producing regimes. Our results demonstrate that phase-controlled coherence and non-Markovianity provide a powerful mechanism for optimizing work extraction in open quantum batteries, offering practical strategies for noise-resilient quantum energy storage.