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arXiv:2412.14114 · Annalen der Physik

Enhancing Quantum Synchronization in a Driven Qubit System Coupled to a Structured Environment

Amir Hossein Houshmand Almani, Ali Mortezapour, Alireza Nourmandipour

Published Jul 10, 2025• 1 citation
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Abstract

Abstract In this paper, the issue of Quantum Synchronization in a driven two‐level (qubit) system situated within a structured environment is examined. The findings have practical implications as it is discovered that adding a time‐dependent periodic modulation to the transition frequency of the qubit can significantly enhance quantum synchronization. The phase preference and, consequently, the phase locking conditions in the system is first discovered using the Husimi ‐function. It is revealed that combining frequency modulation and non‐Markovian effects enables us to achieve a stable phase‐locking for the system. It is shown that tuning the amplitude‐to‐frequency ratio of the modulation process on the zeros of the zeroth‐order Bessel function led to phase locking and, thus, surprisingly enhances quantum synchronization in the system. These results provide new insights into efficiently understanding phase dynamics in quantum environments.

DOI
10.1002/andp.202400441

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Abstract In this paper, the issue of Quantum Synchronization in a driven two‐level (qubit) system situated within a structured environment is examined. The findings have practical implications as it is discovered that adding a time‐dependent periodic modulation to the transition frequency of the qubit can significantly enhance quantum synchronization. The phase preference and, consequently, the phase locking conditions in the system is first discovered using the Husimi ‐function. It is revealed that combining frequency modulation and non‐Markovian effects enables us to achieve a stable phase‐locking for the system. It is shown that tuning the amplitude‐to‐frequency ratio of the modulation process on the zeros of the zeroth‐order Bessel function led to phase locking and, thus, surprisingly enhances quantum synchronization in the system. These results provide new insights into efficiently understanding phase dynamics in quantum environments.
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.
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 dissipative environment having finite bath correlation. The phase preference of the qubit is demonstrated through the 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 are considered depending on the reservoir correlation time being very short and a situation when bath correlation time is finite. When the reservoir’s frequency spectrum is broad and the bath correlation time is short, the qubit’s phase preference vanishes in the long-time limit. In contrast, a finite bath correlation time and narrow spectral density result in persistent long-time phase localization. The synchronization regions are governed by system–environment parameters, with qubit phase synchronization being enhanced when the reservoir exhibits a narrow frequency spectrum.
We study phase-synchronization in a driven two-level system coupled to a non-Markovian bosonic reservoir. The dynamics is described by treating the system-bath coupling and the coherent drive without invoking the rotating-wave approximation, and simulated using the numerically exact hierarchical equations of motion. We observe that a robust phase-locking develops and that the corresponding synchronization measure rapidly acquires a finite value when the system is tuned to what we identify as a resonant-ratio condition, namely when the ratio between the drive amplitude and its frequency coincides with a zero of the Bessel function J0J_0J0​. We provide an explanation for this phenomenon by means of a static approximation derived from a Fourier analysis of the periodically driven Hamiltonian.
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.