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arXiv:2205.08822

Quantum synchronization due to information backflow

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

Published May 18, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2205.08822

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The phase synchronization of a single qubit in a dissipative bath in the absence of driving field is demonstrated. Using the Husimi QQQ-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.
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 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 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.
Synchronization, a ubiquitous phenomenon in classical systems, has recently been extended to the quantum domain. Here, we show quantum synchronization of a bosonic mode exhibiting a Fock state-like limit cycle, manifesting as a steady state with a negative Wigner function. We demonstrate that this non-classical state can be phase-locked to an external drive, achieving synchronization within an Arnold tongue regime. We argue that synchronization is a dynamical property and fundamentally tied to the suppression of phase slips, which we show to occur with exponentially decreasing probability. We introduce a novel method to extract the phase slip rate from the Lindblad time evolution of the system. This work opens new avenues for understanding and manipulating non-classical synchronization dynamics.
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.
Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.