Research
Research interests
Nonlinear dynamics and mathematical engineering My research focuses on real-world physical systems that exhibit nonlinear phenomena. My goal is to elucidate the simple, universal mathematical structures underlying nonlinear phenomena and develop engineering methods for nonlinear systems based on these structures. My approach to these problems is based on concepts from physics as well as mathematical engineering; e.g. system modeling, dynamic analysis, signal processing, and controller design. Nonlinear dynamics of open quantum systems I am currently working on nonlinear dynamics of open quantum systems. In recent years, with the development of experimental techniques for realizing quantum nonlinear phenomena, there has been a growing demand for theoretical studies of quantum nonlinear dynamics to unveil new features of these phenomena. In particular, the nonlinear dynamics of open quantum systems have recently been studied. For example, there has been a lot of theoretical work on quantum synchronization, and recently the first experimental realization of phase synchronization in quantum spin systems was reported. Besides, data science approaches to nonlinear dynamics in open quantum systems have been developed based on machine learning and system identification.
Keywords
Nonlinear Dynamics, Quantum Mechanics, Control Theory, Synchronization, Quantum Control, Quantum Optics, Reduction Theory, Stochastic Processes
Selected works
Selected previous works are briefly summarized below. For more information, please see "Publications" section.
Turing instability in quantum activator-inhibitor systems
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study, we show that Turing instability can occur in a quantum dissipative system and analyze its quantum features such as entanglement and the effect of measurement. We propose a degenerate parametric oscillator with nonlinear damping in quantum optics as a quantum activator-inhibitor unit and demonstrate that a system of two activator-inhibitor units can undergo Turing instability when diffusively coupled with each other. The Turing instability induces nonuniformity and entanglement between the two units and gives rise to a pair of nonuniform states that are mixed due to quantum noise. Further performing continuous measurement on the coupled system reveals the nonuniformity caused by the Turing instability. Our results extend the universality of the Turing mechanism to the quantum realm and may provide a novel perspective on the possibility of quantum nonequilibrium self-organization and its application in quantum technologies.
"Turing instability in quantum activator-inhibitor systems"
Yuzuru Kato, Hiroya Nakao, Sci. Rep. 12,15573 (2022)
[Journal(Open Access)]
[arxiv]
Quantum asymptotic phase reveals signatures of quantum synchronization
We introduce a fully quantum mechanical asymptotic phase variable, which is the fundamental phase variable for quantum nonlinear oscillators, beyond the semiclassical regime. This extends the applicability of this phase variable to the strong quantum regime, allowing the analysis of non-trivial quantum synchronization phenomena. We analyze a quantum van der Pol oscillator with Kerr effect and show that our quantum asymptotic phase yields appropriate results in the strong quantum regime and reproduces the conventional asymptotic phase in the semiclassical regime. Using this quantum asymptotic phase, the multiple phase locking of the system with a harmonic drive at several different frequencies, an explicit quantum effect observed only in the strong quantum regime, can be understood as synchronization of the system on a torus rather than a simple limit cycle.
"A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint" Yuzuru Kato, Hiroya Nakao, Chaos 32, 063133 (2022) (Featured) [Journal] [arxiv]
"Quantum asymptotic phase reveals signatures of quantum synchronization"
Yuzuru Kato, Hiroya Nakao, New J. Phys. 25 023012 (2023)
[Journal(Open Access)]
[arxiv v1]
[arxiv v2]
Semiclassical Phase Reduction Theory for Quantum Synchronization
We formulate the phase-reduction theory for quantum limit-cycle oscillators in the semiclassical regime.
The phase-reduction theory has played a central role in analyzing the rhythmic dynamics of classical limit-cycle oscillators. This theory enables us to quantitatively approximate the dynamics of a nonlinear multi-dimensional limit-cycle oscillator by a simple one-dimensional phase equation, which has greatly facilitated systematic analysis of universal properties of limit-cycle oscillators, such as synchronization of oscillators with external periodic forcing, mutual synchronization between coupled oscillators, and the collective synchronization transition in a system of globally coupled phase oscillators. In this study, we generalize the conventional phase-reduction theory to quantum limit-cycle oscillators in the semiclassical regime where the quantum dynamics can be approximately described by a stochastic differential equation representing a system state in the phase space fluctuating along a deterministic classical trajectory due to small quantum noise. The developed semiclassical phase-reduction theory enables us to quantitatively approximate a quantum oscillator exhibiting stable limit-cycle oscillations by a simple one-dimensional phase equation, facilitating a systematic analysis of quantum synchronization in this regime. As a simple example, we analyze synchronization properties of a typical model of quantum limit-cycle oscillators, known as the quantum van der Pol oscillator, subjected to a harmonic driving and squeezing, including the case that the squeezing is strong and the oscillation is asymmetric. In comparison with the previous results of deriving a phase equation for quantum oscillator having asymmetric limit-cycle in the classical limit, the proposed semiclassical phase-reduction theory provides a systematic analysis tool for quantum synchronization in a general class of asymmetric limit-cycle oscillators. Using the formulated semiclassical phase-reduction theory, we also consider optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive in the semiclassical regime.
"Semiclassical Phase Reduction Theory for Quantum Synchronization"
Yuzuru Kato, Naoki Yamamoto, Hiroya Nakao, Phys. Rev. Research 1, 033012 (2019).
[Journal(Open Access)]
[arxiv]
"Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators"
Yuzuru Kato, Hiroya Nakao, Physical Review E. 101.012210 (2020).
[Journal]
[arxiv]
Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases.
"Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators"
Yuzuru Kato, Anatoly Zlotnik, Jr-Shin Li, Hiroya Nakao, Nonlinear dynamics (2021)
[Journal]
[arxiv]
Continuous Measurement and Feedback Control for Enhancement of Quantum Synchronization
Recent theoretical studies on quantum synchronization have revealed that quantum fluctuations generally induce phase diffusion of quantum limit-cycle oscillators and disturb strict synchronization. In this study, to overcome this drawback of quantum effects in synchronization, we propose continuous measurement and feedback control for enhancement of quantum synchronization. We consider synchronization of a quantum van der Pol oscillator driven by a harmonic signal and demonstrate that performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator can enhance quantum synchronization. We argue that the phase coherence of the oscillator is increased by the reduction of quantum fluctuations due to the continuous measurement and that a simple feedback policy can suppress the measurement-induced fluctuations by adjusting the external frequency of the driving signal.
"Enhancement of quantum synchronization via continuous measurement and feedback control"
Yuzuru Kato, Hiroya Nakao, New Journal of Physics, IOP Publishing, 23 013007 (2021).
[Journal(Open Access)]
[arxiv]
Quantum coherence resonance
In this study, we demonstrate that coherence resonance occurs in quantum dissipative systems. Stochastic resonance is a well-known phenomenon of noise-induced order where the response of a system to a subthreshold signal is maximized at a certain optimal noise intensity. It universally occurs in various systems, ranging from lasers and electric circuits to biological cells and climate systems, and recently the first experimental observation of quantum stochastic resonance has been achieved using an a.c.-driven single-electron quantum dot. Coherence resonance one of the noise-induced phenomenon closely related to stochastic resonance, in which regularity of the oscillatory response of a nonlinear system is maximized at a certain optimal noise intensity. It has been theoretically analyzed for regular and chaotic dynamical systems in detail and experimentally observed in various systems such as electrical circuits, laser diodes, and chemical reactions; its biological functions in living cells have also been discussed. However, coherence resonance in quantum systems has not been explicitly studied in the literature. In this study, we numerically demonstrate that quantum coherence resonance occurs in a quantum van der Pol system subjected to squeezing. We first demonstrate that quantum coherence resonance occurs in the semiclassical regime, namely, the regularity of the system's oscillatory response is maximized at an optimal intensity of quantum fluctuations, and interpret this phenomenon by analogy with classical noisy excitable systems using semiclassical stochastic differential equations. We further investigate the stronger quantum regimes and demonstrate that the regularity of the system's response can exhibit the second peak as the intensity of the quantum fluctuations is further increased. We show that this second peak of resonance is a strong quantum effect that cannot be interpreted by a semiclassical picture, in which only a few energy states participate in the system dynamics.
"Quantum coherence resonance"
Yuzuru Kato, Hiroya Nakao, New Journal of Physics, IOP Publishing, 23 043018 (2021)
[Journal(Open Access)]
[arxiv]
Structure identification and state initialization of spin networks with limited access
We provide two methods for structure identification and state initialization of spin networks accessible by only a single node. For reliable and consistent quantum information processing on quantum networks, the network structure must be fully known and a desired initial state must be accurately prepared on it. In this paper, we provide two continuous measurement-based methods to achieve the above requirements for spin networks accessible by only a single node.
First, we identify an unknown network graph structure based on continuous-time Bayesian updates. We numerically demonstrate that our graph estimator correctly identifies the true graph structure from five possible nominal graphs for three spin cases.
Second, we propose a feedback control that deterministically drives an arbitrary mixed state to a spin-coherent state for network initialization. We numerically demonstrate that our feedback control can deterministically stabilize the spin-coherent states of the five spin networks.
"Structure identification and state initialization of spin network with limited access"
Yuzuru Kato, Naoki Yamamoto, New Journal of Physics, IOP Publishing, 16, 023024, (2014).
[Journal(Open Access)]
[arxiv]
