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.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.

arXiv:2311.05664Nov 9, 20230 citations

Quantum synchronization due to information backflow

Md. Manirul Ali, Po‐Wen Chen, Chandrashekar Radhakrishnan

The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi $Q$ -function we show that the phase preference is present in the long time limit only during non-Markovian evolution with a finite detuning. This happens due to the information backflow signifying that non-Markovianity is a resource for quantum synchronization. To quantify synchronization we use the shifted phase distribution as well as its maximal value. From the maximal value of the shifted phase distribution we observe the signatures of quantum synchronization {\it viz} the Arnold tongue. In our case the region ofsynchronization is outside the tongue region and the region inside the tongue is the desynchronized region. This is in contrast to the results in the literature, where the synchronization is within the tongue region.The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi $Q$-function we show that the phase preference is present in the long time limit only during non-Markovian evolution with a finite detuning. This happens due to the information backflow signifying that non-Markovianity is a resource for quantum synchronization. To quantify synchronization we use the shifted phase distribution as well as its maximal value. From the maximal value of the shifted phase distribution we observe the signatures of quantum synchronization {\it viz} the Arnold tongue. In our case the region ofsynchronization is outside the tongue region and the region inside the tongue is the desynchronized region. This is in contrast to the results in the literature, where the synchronization is within the tongue region.

arXiv:2205.08822May 18, 20220 citations

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

Amir Hossein Houshmand Almani, Ali Mortezapour, Alireza Nourmandipour

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.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.

arXiv:2412.14114Annalen der PhysikJul 10, 20251 citation

Classical-driving-assisted quantum synchronization in non-Markovian environments

Xing Mao Xiao, Tian-Xiang Lu, Wo-Jun Zhong +1 more

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 $Q$ 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 $S$ 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 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 $Q$ 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 $S$ 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.

arXiv:2209.05960Physical Review AFeb 21, 202311 citations

Improving quantum synchronization by manipulating auxiliary qubits in a dissipative model

Jia-Tao Luo, Li Li, He Wei +2 more

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.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.

Laser Physics LettersDec 18, 20243 citations

Quantum phase synchronization and non-Markovian relaxation dynamics of a driven two-level system in a hierarchical environment

Yan‐Ling Li, Duo Huang, Xing Mao Xiao

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 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.

Physica ScriptaSep 28, 20260 citations

The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi

Q

-function we show that the phase preference is present in the long time limit only during non-Markovian evolution with a finite detuning. This happens due to the information backflow signifying that non-Markovianity is a resource for quantum synchronization. To quantify synchronization we use the shifted phase distribution as well as its maximal value. From the maximal value of the shifted phase distribution we observe the signatures of quantum synchronization {\it viz} the Arnold tongue. In our case the region ofsynchronization is outside the tongue region and the region inside the tongue is the desynchronized region. This is in contrast to the results in the literature, where the synchronization is within the tongue region.

Q

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

S

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.