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arXiv:2302.13465 · Physical review. E

Enhancing quantum synchronization through homodyne measurement, noise, and squeezing

Yuan Shen, Hong Yi Soh, W. J. Fan, L. C. Kwek

Published Aug 4, 2023• 10 citations
arXivHTMLPDF

Abstract

Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.

DOI
10.1103/physreve.108.024204

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Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.
It is desirable to observe synchronization of quantum systems in the quantum regime, defined by the low number of excitations and a highly nonclassical steady state of the self-sustained oscillator. Several existing proposals of observing synchronization in the quantum regime suffer from the fact that the noise statistics overwhelm synchronization in this regime. Here, we resolve this issue by driving a self-sustained oscillator with a squeezing Hamiltonian instead of a harmonic drive and analyze this system in the classical and quantum regime. We demonstrate that strong entrainment is possible for small values of squeezing, and in this regime, the states are nonclassical. Furthermore, we show that the quality of synchronization measured by the FWHM of the power spectrum is enhanced with squeezing.
Abstract We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator. The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization. We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information on the oscillator phase is extracted.
We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator. The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization. We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information of the oscillator phase is extracted.
We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator.The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point.We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization.We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information on the oscillator phase is extracted.
We analyze synchronization of a quantum van der Pol (vdP) oscillator driven by a harmonic signal and demonstrate that performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying a feedback control to the oscillator can enhance quantum synchronization. We show that the phase coherence of the oscillator is increased by the reduction of quantum fluctuations due to the continuous measurement, but also that the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy that can suppress the measurement-induced fluctuations by adjusting the frequency detuning between the oscillator and the driving signal, which leads to enhancement of quantum synchronization. We further demonstrate that the maximum phase coherence can be achieved by performing the quantum measurement on the quadrature angle at which the phase diffusion of the oscillator takes the largest value and the maximum information of the oscillator phase is attained.
In this thesis we investigate two different aspects of nonlinear dynamical behaviour: First, we study quantum synchronization which is based on nonlinear, so-called limit-cycle oscillators. Second, we investigate the influence of nonlinear interactions on topological transport in bosonic systems. We begin with the investigation of the synchronization of two optomechanical systems in the presence of quantum noise. With numerical simulations of the full quantum and a semiclassical model, we identify different phase synchronization regimes, although exact phase locking is prevented due to the inevitable quantum noise. Our main results are noise-induced transitions between different synchronization states, as well as noise-induced bistability, i.e., the appearance of a second synchronization state in the quantumregime, even if in the classical, noiseless limit only a single stable synchronization state exists. We give an overview about the classical-to-quantumtransition and also compare our findings to synchronization in the presence of classical, thermal noise. Subsequently, we study the quantum synchronization dynamics of a quantum Van der Pol oscillator coupled to an external periodic driving. This paradigm system for limit-cycle oscillators allows us to derive an effective, analytical quantum model and identify the different dynamical regimes, like overdamped, underdamped, and notably also quantum-coherent phase motion. We explore the distinct signatures of these different dynamical regimes, e.g., in the spectrum or the squeezing. Moreover, we show that in the remarkable regime of quantum-coherent phase dynamics quantum states with negative Wigner densities (like Schrödinger cat states) are preserved for many oscillations of the system. Our effective model gives insight into how to achieve quantum coherence in synchronization dynamics, while numerical simulations of the full model confirm the predicted behaviour. Finally, we turn to the classical dynamics of a Chern topological insulator in a nonlinear bosonic system. To this end, we study the half Bernevig-Hughes-Zhang model on a square lattice in the presence of a local Kerr nonlinearity. We investigate the stability of a linear edge state in the nonlinear model and present a linear stability analysis to gain insight into the unstable scattering processes enabled by the nonlinearity. In a time evolution of the full nonlinear model, we can show that these processes lead to a spatially periodic modulation of the edge channel on an intermediate timescale. However, eventually we observe that strong nonlinear processes lead to more complicated behaviour and a significant radiation into the bulk.