We study the phenomenon of quantum synchronization from the viewpoint of quantum metrology. By interpreting quantum self-sustained oscillators as dissipative quantum sensors, we develop a framework to characterize several aspects of quantum synchronization. We show that the quantum Fisher information (QFI) serves as a system-agnostic measure of quantum synchronization that also carries a clear operational meaning, viz., it quantifies the precision with which the amplitude of a weak synchronizing drive can be measured. We extend our analysis to study many-body oscillators subjected to multiple drives. We show how the QFI matrix can be used to determine the optimal drive that maximizes quantum synchronization, and also to quantitatively differentiate the synchronization responses induced by different drives. Our work highlights multiple connections between quantum synchronization and quantum metrology, paving a route toward finding quantum technological applications of quantum synchronization.
We study the phenomenon of quantum synchronization from the viewpoint of quantum metrology. By interpreting quantum self-sustained oscillators as dissipative quantum sensors, we develop a framework to characterize several aspects of quantum synchronization. We show that the quantum Fisher information (QFI) serves as a system-agnostic measure of quantum synchronization that also carries a clear operational meaning, viz., it quantifies the precision with which the amplitude of a weak synchronizing drive can be measured. We extend our analysis to study many-body oscillators subjected to multiple drives. We show how the QFI matrix can be used to determine the optimal drive that maximizes quantum synchronization, and also to quantitatively differentiate the synchronization responses induced by different drives. Our work highlights multiple connections between quantum synchronization and quantum metrology, paving a route toward finding quantum technological applications of quantum synchronization.
Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of a weak external perturbation. General expressions for the QFI in the nonequilibrium steady-state are derived, which hold for arbitrary interacting many-body systems at finite or zero temperature, and can be related to susceptibilities or linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to *exponential* scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical measurements. In particular, we show that current-based metrology in quantum circuits can leverage many-body effects for enhanced sensing.
Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is currently no widely agreed metric that is universally adopted. In this paper, we propose using classical and quantum Fisher information (FI) as alternative metrics to detect and measure quantum synchronization. We establish the connection between FI and quantum synchronization, demonstrating that both classical and quantum FI can be deployed as more general indicators of quantum phase synchronization in some regimes where all other existing measures fail to provide reliable results. We show advantages in FI-based measures, especially in 2-to-1 synchronization. Furthermore, we analyze the impact of noise on the synchronization measures, revealing the robustness and susceptibility of each method in the presence of dissipation and decoherence. Our results open up new avenues for understanding and exploiting quantum synchronization.
Synchronization is a collective phenomenon in which interacting nonlinear oscillators develop a persistent relation between their phases and frequencies. In quantum systems, its description requires connecting the classical dynamics of limit-cycle oscillators with quantum fluctuations, dissipation, and the notion of phase. In this tutorial review, we offer a systematic framework for analyzing synchronization in classical and quantum dynamical systems. Starting from amplitude-phase dynamics, we introduce successively topics of relevance, such as phase locking, the Adler equation, Arnold tongues, and the Kuramoto model, and use these concepts to analyze coupled oscillators and their stability. We then formulate the corresponding description for quantum limit-cycle oscillators using Lindblad master equations and phase-space methods, with explicit examples of two and many coupled oscillators. We further discuss noise, synchronization measures, and the extreme quantum regime, including synchronization in spin systems. The emphasis throughout is on analytical derivations and a practical methodology for identifying synchronized states, determining their stability, and characterizing synchronization in quantum systems. The review is designed as a self-contained guide from which we hope that students can learn the essential concepts and techniques, while researchers can readily find the analytical tools and methodological insights needed to approach new synchronization problems.
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
Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy FM(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼10−2 of the available QFI, while the degree required to recover 90% of it grows to k90≃28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.
Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative phase distribution. In particular, we identify the subset of coherence elements in the joint density matrix that serve as key resources for enabling quantum phase synchronization. Our theory is validated against the previously proposed interaction models known to induce synchronization between the self-sustained oscillators. Moreover, our approach offers valuable insights into the relationship between phase synchronization and various information-theoretic measures.