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arXiv:2112.06722

Quantum indirect synchronization

Guo Meitong, Niu Xiangyu, Yi Xue-Xi, Wei Wang

Published Dec 13, 2021• 0 citations
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Abstract

It is well known that a system with two or more levels exists a limit cycle and can be synchronized with an external drive when the system and the drive are directly coupled. One might wonder if a system can synchronize with the external drive when they are not coupled directly. In this paper, we examine this case by considering a composite system consisting of two coupled two-level quantum systems, one of which is driven by an external field, while another couples to the driven one. Due to the decoherence caused by environments, the composite system would stay in a mixed state, and an effective limit cycle is formed, so phase locking could occur. We find the phase locking phenomenon in the phase diagram characterized by Husimi $Q$ function, and the synchronization can be generated consequently that we will refer to indirect synchronization. The $S$ function defined in the earlier study can also be used to measure the strength of synchronization. We claim that indirect synchronization is possible. This result provides us with a method to synchronize a quantum system that coupled to its neighbour without interacting with external drive directly.

DOI
10.48550/arxiv.2112.06722

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It is well known that a system with two or more levels exists a limit cycle and can be synchronized with an external drive when the system and the drive are directly coupled. One might wonder if a system can synchronize with the external drive when they are not coupled directly. In this paper, we examine this case by considering a composite system consisting of two coupled two-level quantum systems, one of which is driven by an external field, while another couples to the driven one. Due to the decoherence caused by environments, the composite system would stay in a mixed state, and an effective limit cycle is formed, so phase locking could occur. We find the phase locking phenomenon in the phase diagram characterized by Husimi QQQ function, and the synchronization can be generated consequently that we will refer to indirect synchronization. The SSS function defined in the earlier study can also be used to measure the strength of synchronization. We claim that indirect synchronization is possible. This result provides us with a method to synchronize a quantum system that coupled to its neighbour without interacting with external drive directly.
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Quantum synchronization has been a subject of intensive research in the last decade. In this Letter, we propose a quantum Liénard system whose classical equivalent features two limit cycles to one of which the system will converge. In the quantum case, both limit cycles coexist in a single steady state. Each of these limit cycles localizes to a distinct phase if coupled to an external drive: one quantum state can thus be assigned two phases. Furthermore, coupling two such oscillators leads to the simultaneous appearance of synchronization and a synchronization blockade. To shed light on this apparent paradoxical result, we introduce finer measures of quantum synchronization.
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.
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.
Synchronization manifests itself in oscillators adjusting their frequencies and phases with respect to an external signal or another oscillator. In the quantum case, new features appear such as destructive interferences that can result in the suppression of phase locking. A three-level (spin-1) oscillator with equal gain and damping rates and subject to an external drive does not exhibit any 1:1 phase locking but 2:1 phase locking, i.e., its phase distribution features two maxima. This bistable locking at two opposite phases is a signature of the quantum interference synchronization blockade. An analogous behavior was found for two identical coupled spin-1 oscillators. In this work, we consider two coupled spin-1 oscillators and a drive applied to the first spin. This leads to two interference blockades between the drive and the first spin as well as between both spins. Although both interference blockades persist for strong drive and coupling strengths, remarkably, the undriven spin does show a 1:1 phase locking to the external drive. The magnitude of the locking is proportional to the drive strength if the drive strength is small. In other words, the undriven oscillator synchronizes to the external drive through both interference blockades while the blockades persist. For a chain of three coupled spin-1 oscillators, we find synchronization between the first and third spins mediated via the blockaded, second spin.
We consider a cavity quantum electrodynamics (CQED) setup where an ensemble of spin-1 atoms driven by a classical field interacts with two driven cavity field modes. We show that the two sub-systems - the atoms and the two-mode cavity field, exhibit limit-cycle or quantum synchronization depending on the cavity drive strengths and other system parameters. In order to visualize the limit cycle and synchronization in the field, we introduce generalized two-mode field Husimi-Q function using SU(2) coherent states. For atomic spin states, we make use of spin-1 Husimi-Q function to visualize the same. We further corroborate the occurrence of field synchronization and limit cycle by analyzing U(1)U(1)U(1) symmetry breaking, Wigner quasi-probability distribution, coherence properties of reduced field density matrix. Our results reveal intriguing interplay between the limit-cycle and quantum synchronization behavior, highlighting emergent quantum phenomena in driven dissipative interacting quantum systems. Additionally, we calculate Wehrl mutual information between the two modes and find that the field synchronization and Wehrl mutual information are mutually exclusive. Our study would be important to extract quantum advantages in quantum metrology using coupled atom-cavity systems.