In this paper, we study the synchronization of dissipative quantum harmonic oscillators in the framework of a quantum open system via the active-passive decomposition (APD) configuration. We show that two or more quantum systems may be synchronized when the quantum systems of interest are embedded in dissipative environments and influenced by a common classical system. Such a classical system is typically termed a controller, which (1) can drive quantum systems to cross different regimes (e.g., from periodic to chaotic motions) and (2) constructs the so-called active-passive decomposition configuration, such that all the quantum objects under consideration may be synchronized. The main finding of this paper is that we demonstrate that the complete synchronizations measured using the standard quantum deviation may be achieved for both stable regimes (quantum limit circles) and unstable regimes (quantum chaotic motions). As an example, we numerically show in an optomechanical setup that complete synchronization can be realized in quantum mechanical resonators.
In this paper, we study the synchronization of dissipative quantum harmonic oscillators in the framework of a quantum open system via the active-passive decomposition (APD) configuration. We show that two or more quantum systems may be synchronized when the quantum systems of interest are embedded in dissipative environments and influenced by a common classical system. Such a classical system is typically termed a controller, which (1) can drive quantum systems to cross different regimes (e.g., from periodic to chaotic motions) and (2) constructs the so-called active-passive decomposition configuration, such that all the quantum objects under consideration may be synchronized. The main finding of this paper is that we demonstrate that the complete synchronizations measured using the standard quantum deviation may be achieved for both stable regimes (quantum limit circles) and unstable regimes (quantum chaotic motions). As an example, we numerically show in an optomechanical setup that complete synchronization can be realized in quantum mechanical resonators.
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously synchronize when they are strongly coupled to a common bosonic quantum dissipative environment at zero temperature, in the absence of any driving mechanism. To do so, we compute the dynamics of the oscillators with an exact master equation obtained from a path integral formalism. Above some value of the system-environment coupling strength, we observe numerically a strongly reduced damping and a frequency locking in the dynamics of the oscillators. Beyond the synchronization mechanism, we also describe the rich phenomenology of the dynamics in the model and notably identify the additional emergence of a regime with long-lived oscillations.
In a dissipative regime, we study the properties of several qubits coupled to a driven resonator in the framework of a Jaynes-Cummings model. The time evolution and the steady state of the system are numerically analyzed within the Lindblad master equation, with up to several million components. Two semi-analytical approaches, at weak and strong (semiclassical) dissipations, are developed to describe the steady state of this system and determine its validity by comparing it with the Lindblad equation results. We show that the synchronization of several qubits with the driving phase can be obtained due to their coupling to the resonator. We establish the existence of two different qubit synchronization regimes: In the first one, the semiclassical approach describes well the dynamics of qubits and, thus, their quantum features and entanglement are suppressed by dissipation and the synchronization is essentially classical. In the second one, the entangled steady state of a pair of qubits remains synchronized in the presence of dissipation and decoherence, corresponding to the regime non-existent in classical synchronization.
In this work, we study the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization of two mechanical oscillators in a coupled optomechanical system. The oscillators are coupled to an optical cavity filled with a Kerr nonlinear medium and subjected to periodic modulation of the cavity detunings and driving amplitudes by a common driving field. Our results show that the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization in nonlinear systems exhibit more favorable behaviors than in linear systems. In addition, we have investigated the performances of two synchronization measurements to various parameters by analyzing the sensitivity of $\ensuremath{\phi}$. Accordingly, perfect synchronization can be achieved under specific parameters by periodically modulating the cavity and driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations.
In recent years, significant progress has been made to push micro-, nano-, and optomechanical systems into the quantum regime. The common goal is to demonstrate and control quantum effects in these systems, which enable applications in quantum metrology and quantum information processing. This process is hampered by dissipation, i.e., the interaction of these systems with their environment. \n \n \nIn this thesis, we focus on two different aspects of dissipative nonlinear systems in the quantum regime. In the first part, we study how states with genuinely quantum properties can be generated by a continuous measurement of the interaction between the quantum system and its environment. This approach turns dissipation into a useful tool to generate nonclassical states of light and matter, which have been identified as important resources for quantum-enhanced sensing, quantum communication, and quantum error processing. We discuss the generation of mechanical states with a sub-Poissonian phonon-number distribution in an optomechanical phonon laser beyond the resolved-sideband regime, and we propose a heralded protocol to generate nonclassical states by photon-counting measurements. We apply this protocol to a Kerr nonlinear oscillator and show that it enables the creation of states with a negative Wigner function although the steady-state Wigner function of this system is strictly positive. \n \n \nIn the second part of this thesis, we focus on self-sustained oscillators in the quantum regime. If a weak perturbation is applied to a self-sustained oscillator, the oscillator can adjust its frequency of oscillation. This effect is called synchronization and has been identified as a universal feature of many different complex classical systems, e.g., electrical circuits, biological systems, and power grids. In recent years, several theoretical proposals have been put forward to study synchronization in the quantum regime. However, an experimental demonstration of quantum effects in synchronization has still been missing. \n \n \nWe develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. This framework establishes a unified description of the above-mentioned proposals and allows us to identify the quantum-mechanical resource of synchronization. Based on these findings, we discover a novel interference-based quantum synchronization blockade effect and we derive a bound on the maximum degree of synchronization that can be achieved in the quantum regime. The framework also reveals a large freedom in tailoring a quantum system that is able to synchronize. Taking advantage of this freedom, we propose alternative implementations of quantum self-sustained oscillators that reduce the experimental challenges. \n \n \nFinally, we use digital quantum simulation to implement a quantum self-sustained oscillator on a current quantum computer. Applying an external signal to the oscillator, we verify typical features of quantum synchronization, and we demonstrate interference-based quantum synchronization blockade. Our results are the first experimental demonstration of genuinely quantum effects in synchronization and they show that state-of-the-art noisy intermediate-scale quantum computers are powerful enough to implement and study realistic dissipative quantum systems. \n
The phenomenon of spontaneous synchronization arises in a broad range of systems when the mutual interaction strength among components overcomes the effect of detuning. Recently it has been studied also in the quantum regime with a variety of approaches and in different dynamical contexts. We review here transient synchronization arising during the relaxation of open quantum systems, describing the common enabling mechanism in presence of either local or global dissipation. We address both networks of harmonic oscillators and spins and compare different synchronization measures.
In this work, we investigate the dynamics of quantum synchronization in a four-mode optomechanical system, focusing on the influence of the Coulomb interaction between two mechanical resonators. We analyze the effect of the Coulomb coupling on three distinct synchronization regimes, i.e., complete quantum synchronization, φ-synchronization, and quantum phase synchronization. Our results show that while the Coulomb interaction plays a pivotal role in significantly enhancing quantum phase synchronization by facilitating energy exchange and phase coherence, it has little impact on complete and φ-synchronization. This indicates that amplitude and frequency locking are primarily determined by the optical driving, whereas phase alignment depends critically on inter-resonator coupling. We also demonstrate that the oscillations of the two optical cavities, which are indirectly coupled via the mechanical resonators, can become aligned over time, resulting in classical synchronization. These findings provide a robust mechanism for controlling collective quantum dynamics and offer a foundation for applications in quantum communication, precision sensing, and the development of synchronized quantum networks.