Phase-locked Regimes Research Articles

Particle-in-Cell Simulations on High-Efficiency Phase-Locking Millimeter-Wave Magnetrons with Unsynchronized High-Voltage Pulses

Phase locking is an essential choice for building a coherent array, and a system of phase-locked magnetrons is relatively compact and cheaper than other microwave sources. Previous theoretical and experimental studies on phase locking are conducted using synchronized high-voltage pulses. Here, we investigate the characteristics of two phase-locked magnetrons using particle-in-cell (PIC) simulation software (CST STUDIO SUITE 2020) when two high-voltage pulses have delays. The results show that the magnetrons produced two-level RF signals because the operation could be divided into two stages. The first stage happened when one cathode emitted electrons; then, the electrons formed one spoke, traveling in synchronism with the 0-phase difference mode. Two output ports both produced half the output power of a free-running magnetron. The second stage happened after another cathode started to emit electrons, which were instantly pre-modulated by the electromagnetic field of the 0-phase difference mode produced during the first stage. In the second stage, simulations showed that pre-modulation accelerated the process of electron bunching. Eventually, two magnetrons were phase-locked, and the total output power of the two identical magnetrons nearly doubled the output power of the free-running magnetron, which demonstrated that the magnetrons were phase-locked in the high-efficiency phase-locking regime.

Quantum synchronization in quadratically coupled quantum van der Pol oscillators

We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behavior of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der Pol oscillators and anharmonic self-oscillators. We demonstrate that the considered systems exhibit a high-order synchronization through coupling in both classical and quantum domains. We show that, due to the anharmonicity of the nonlinear interaction between the oscillators, the system exhibits phonon blockade in the phase-locking regime, which is a pure nonclassical effect and has not been observed in the classical domain. We also demonstrate that, for coupled anharmonic oscillators, the system shows a multiple resonance phase-locking behavior due to nonlinear interaction. We point out that the synchronization blockade arises due to strong anticorrelation between the oscillators, which leads to phonon antibunching in the same parametric regime. In the anharmonic oscillator case we illustrate the simultaneous occurrence of bunching and antibunching effects as a consequence of simultaneous negative and positive correlation between the anharmonic oscillators. We examine the aforementioned characteristic features in the frequency entrainment of the oscillators using a power spectrum where one can observe normal mode splitting and the Mollow triplet in the strong coupling regime. Finally, we propose a possible experimental realization for the considered system in the trapped ion and optomechanical setting.

Self-Induced Phase Locking of Terahertz Frequency Combs in a Phase-Sensitive Hyperspectral Near-Field Nanoscope.

Chip‐scale, electrically‐pumped terahertz (THz) frequency‐combs (FCs) rely on nonlinear four‐wave‐mixing processes, and have a nontrivial phase relationship between the evenly spaced set of emitted modes. Simultaneous monitoring and manipulation of the intermode phase coherence, without any external seeding or active modulation, is a very demanding task for which there has hitherto been no technological solution. Here, a self‐mixing intermode‐beatnote spectroscopy system is demonstrated, based on THz quantum cascade laser FCs, in which light is back‐scattered from the tip of a scanning near‐field optical‐microscope (SNOM) and the intracavity reinjection monitored. This enables to exploit the sensitivity of FC phase‐coherence to optical feedback and, for the first time, manipulate the amplitude, linewidth and frequency of the intermode THz FC beatnote using the feedback itself. Stable phase‐locked regimes are used to construct a FC‐based hyperspectral, THz s‐SNOM nanoscope. This nanoscope provides 160 nm spatial resolution, coherent detection of multiple phase‐locked modes, and mapping of the THz optical response of nanoscale materials up to 3.5 THz, with noise‐equivalent‐power (NEP) ≈400 pW √Hz−1. This technique can be applied to the entire infrared range, opening up a new approach to hyper‐spectral near‐field imaging with wide‐scale applications in the study of plasmonics and quantum science, inter alia.

Domain-wall motion driven by a rotating field in a ferrimagnet

We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find that, depending on the magnitude and the frequency of the rotating field, the dynamics of a ferrimagnetic domain wall can be classified into two regimes. First, when the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain wall via the gyrotropic coupling between the domain-wall angle and position. In this so-called phase-locking regime, a domain-wall velocity increases as the frequency increases. Second, when the frequency exceeds the critical frequency, a domain-wall angle precession is not synchronous with the applied field. In this phase-unlocking regime, a domain wall velocity decreases as the frequency increases. Moreover, the direction of the domain-wall motion is found to be reversed across the angular compensation point where the net spin density of the ferrimagnet changes its sign. Our work suggests that the dynamics of magnetic solitons under time-varying biases may serve as platform to study critical phenomena.

Acoustically induced transparency for synchrotron hard x-ray photons

The induced transparency of opaque medium for resonant electromagnetic radiation is a powerful tool for manipulating the field-matter interaction. Various techniques to make different physical systems transparent for radiation from microwaves to x-rays were implemented. Most of them are based on the modification of the quantum-optical properties of the medium under the action of an external coherent electromagnetic field. Recently, an observation of acoustically induced transparency (AIT) of the 57Fe absorber for resonant 14.4-keV photons from the radioactive 57Co source was reported. About 150-fold suppression of the resonant absorption of photons due to collective acoustic oscillations of the nuclei was demonstrated. In this paper, we extend the AIT phenomenon to a novel phase-locked regime, when the transmitted photons are synchronized with the absorber vibration. We show that the advantages of synchrotron Mössbauer sources such as the deterministic periodic emission of radiation and controlled spectral-temporal characteristics of the emitted photons along with high-intensity photon flux in a tightly focused beam, make it possible to efficiently implement this regime, paving the way for the development of the acoustically controlled interface between hard x-ray photons and nuclear ensembles.

Dissipative Josephson effect in coupled nanolasers

Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker–Planck equation and show that it exhibits an interesting non-equilibrium phase diagram as a function of the coherent coupling between nanolasers. As we increase that coupling, we find a non-equilibrium phase transition between a phase-locked (PL) and a non-phase-locked (NPL) steady-state, in which phase coherence is destroyed by the photon tunneling process. In the coherent, PL regime, an imbalanced photon number population appears if there is a phase difference between the nanolasers, which appears in the steady-state as a result of the competition between competing local dissipative dynamics and the Josephson photo-current. The latter is amplified for large incoherent pumping rates and it is also enchanced close to the lasing phase transition. We show that the Josephson photocurrent can be used to measure optical phase differences. In the quantum limit, the accuracy of the two nanolaser interferometer grows with the square of the photon number and, thus, it can be enhanced by increasing the rate of incoherent pumping of photons into the nanolasers.

Self-Stimulated Capillary Jet

Inspired by Savart's pioneering work, we study the self-stimulated dynamics of a capillary jet. The feedback loop is realized by extracting surface perturbations from a section of the jet itself via a laser-photodiode pair, whose amplified signal drives an electromechanical actuator that, in turn, produces pressure perturbations at the exit chamber. Under specific conditions, this loop establishes phase-locked stimulation regimes that overcome the otherwise random natural breakup. For each laser position along the jet, the gain of the amplifier acts as a selector across a discrete set of observable frequencies. The main observed features are explained by a linear theory that combines the transfer function of each stage in the loop. Our findings are relevant to continuous inkjet technologies for the production of equally sized droplets.

Noise Properties of Two Mutually Coupled Spin-Transfer Nanooscillators in the Phase Locking Regime

Introduction. Today, many research endeavors are devoted to the miniaturization of microwave sources. One of the promising approaches is the use of magnetic nanostructures (spintronics elements), providing a wide range of frequency tuning and low power consumption. The main disadvantage of spintronics generators (spintransfer nanoscillators ‒ STNO) is a low output power of generated oscillations (tens of nanowatts and less). A possible solution is to sum up the power of many STNOs in a mutual synchronization mode.Aim. The investigation of noise properties of two connected STNOs with identical and non-identical parameters in a phase synchronization mode.Materials and methods. A model was developed of two STNOs interconnected by spin waves taking into account thermal noises. Spectral power densities of the amplitude and phase noise were obtained by the method of effective linearization.Results. Dependencies were obtained in a general form for attenuation coefficients of the amplitude and phase fluctuations of noise sources for each STNO. Three cases of synchronization were considered: completely identical STNOs, two identical STNOs but with different oscillation frequencies, and two non-identical STNOs, differing in an allowance of self-excitation by frequencies and amplitudes of the oscillations. It was possible to obtain a gain in the amplitude and phase noise for two identical STNOs. In this case, an increase in the allowance of self-excitation led to a decrease in the level of phase and amplitude noise.Conclusion. This analysis of the attenuation coefficients for non-identical STNOs demonstrates the possibility of improving the noise properties of each of the generators. In this case, the best noise value is obtained for an STNO with greater stability in a stand-alone mode.

Phase-locked states in oscillating neural networks and their role in neural communication

The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on the strength of the signal emitted but also on the relative phases between them. More precisely, effective communication occurs when the emitting and receiving populations are properly phase locked so the inputs sent by the emitting population arrive at the phases of maximal excitability of the receiving population. To study this setting, we consider a population rate model consisting of excitatory and inhibitory cells modelling the receiving population, and we perturb it with a time-dependent periodic function modelling the input from the emitting population. We consider the stroboscopic map for this system and compute numerically the fixed and periodic points of this map and their bifurcations as the amplitude and the frequency of the perturbation are varied. From the bifurcation diagram, we identify the phase-locked states as well as different regions of bistability. We explore carefully the dynamics of particular phase-locking regimes emphasizing its implications for the CTC theory. In particular, we study how the input gain depends on the timing between the input and the inhibitory action of the receiving population. Our results show that naturally an optimal phase locking for CTC emerges, and provide a mechanism by which the receiving population can implement selective communication. Moreover, the presence of bistable regions, suggests a mechanism by which different communication regimes between brain areas can be established without changing the structure of the network.

Flux-flow Josephson oscillator as the broadband tunable terahertz source to open space

The flux-flow oscillator (FFO) based on a long Josephson junction has been implemented as a broadband tunable terahertz (THz) source to open space. For this purpose, the transmitting slot antenna has been coupled to the oscillator. Additionally, an elliptical lens with a diameter of 10 mm has been matched to the antenna, forming a narrow output beam of the THz emission. Two designs for the antenna, integrated with the oscillator and developed for operation at different frequency ranges of 0.32–0.55 THz and 0.4–0.7 THz, have been investigated. The FFO has been phase locked to an external reference oscillator by utilizing a harmonic mixer. Its linewidth in the phase-locking regime is determined by the phase noise of the reference oscillator and the number of harmonics used and has been measured to be less than 0.1 MHz. A free-running FFO linewidth from about 2 MHz to several MHz, depending on the operating point, has been obtained. Output emission to open space has been measured by a superconducting integrated spectrometer located in a separate cryostat. The FFO operation as an external source with the achieved emission power and spectral characteristics has demonstrated its applicability for different tasks and purposes where tunable THz sources are required.

Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques

We study dynamics of antiferromagnets induced by simultaneous application of dc spin current and ac charge current, motivated by the requirement of all-electrically controlled devices in THz gap (0.1-30 THz). We show that ac electric current, via N\'eel spin orbit torques, can lock the phase of a steady rotating N\'eel vector whose precession is controlled by a dc spin current. In the phase-locking regime the frequency of the incoming ac signal coincides with the frequency of autooscillations which for typical antiferromagnets fall into the THz range. The frequency of autooscillations is proportional to the precession-induced tilting of the magnetic sublattices related to the so-called dynamical magnetization. We show how the incoming ac signal can be detected from the measurement of the dc-current dependencies of the constant dynamical magnetization. We formulate the conditions of phase-locking based on relations between parameters of an antiferromagnet and the characteristics of the incoming signal (frequency, amplitude, bandwidth, duration). We also show that the rotating N\'eel vector can generate ac electrical current via inverse N\'eel spin-orbit torque. Hence, antiferromagnets driven by dc spin current can be used as tunable detectors and emitters of narrow-band signals operating in the THz range.

Characterization of Superparamagnetic Particles Mobility by On-Chip Micromagnets

We fabricate on-chip micromagnets using Ni80Fe20 and Co70Fe30 materials for the characterization of mobility of superparamagnetic particles. The maximum velocity of the particles around the periphery of the micromagnets is determined by the critical frequency, which indicates that the particle enters the phase-slipping regime from the phase-locked regime. The maximum velocity of NiFe micromagnets is approximately 3 times larger than that of CoFe micromagnets measured at the low field regions. Moreover, the maximum velocity of the particles is decreasing with increasing the thickness of Teflon coating on the micromagnets, which is in a good agreement with the variation of the magnetostatic potential energy evaluated numerically from micromagnetic simulations.

Спектральный анализ сигналов с использованием спин-трансферного наноосциллятора в режиме синхронизации (в порядке дискуссии)

The spectral analysis of signals with the use of a spin-transfer nanooscillator operating in the external phase-locking regime is investigated. The study is motivated by investigations carried out in the field of spintronics, spin-transfer nanooscillators (STNO) and neuromorphic computing. Currently, active research is underway on developing miniature oscillation sources in the microwave band. STNOs, which have dimensions of tens and hundreds of nanometers and retuned in the range of fractions to tens of gigahertz are among the promising candidates for this role. The main disadvantage of such generators is the low output power of generated oscillations, making a few hundred nanowatt. One possible way to increase the power of STNO-based devices is to combine them into ensembles in order to synchronize and add their capacities. Various mechanisms of external and mutual synchronization of STNO are known, for example, by means of phase-locked circuits. Despite a large number of works in the field of STNO synchronization, many problems have not been solved as yet. It is proposed to use an STNO as a detector of microwave signals operating in the phase locking regime. This would make it possible to construct a spectrum analyzer operating at low power of the input (analyzed) signal (as low as a few picowatt). The main operating modes of this analyzer have been numerically simulated, and its main operating characteristics (the limiting sensitivity and maximum scanning rate) have been determined. The mathematical model of an STNO-based synthesizing device has been investigated, and its main performance characteristics have analytically been determined using the oscillation theory methods, which have been compared with the similar parameters obtained using numerical methods. The obtained results can be used in experimental investigations of STNO- based spectrum analyzers and various spintronic devices.

Anticipated and zero-lag synchronization in motifs of delay-coupled systems.

Anticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators.

Anticipated synchronization in neuronal circuits unveiled by a phase-response-curve analysis.

Anticipated synchronization (AS) is a counterintuitive behavior that has been observed in several systems. When AS occurs in a sender-receiver configuration, the latter can predict the future dynamics of the former for certain parameter values. In particular, in neuroscience AS was proposed to explain the apparent discrepancy between information flow and time lag in the cortical activity recorded in monkeys. Despite its success, a clear understanding of the mechanisms yielding AS in neuronal circuits is still missing. Here we use the well-known phase-response-curve (PRC) approach to study the prototypical sender-receiver-interneuron neuronal motif. Our aim is to better understand how the transitions between delayed to anticipated synchronization and anticipated synchronization to phase-drift regimes occur. We construct a map based on the PRC method to predict the phase-locking regimes and their stability. We find that a PRC function of two variables, accounting simultaneously for the inputs from sender and interneuron into the receiver, is essential to reproduce the numerical results obtained using a Hodgkin-Huxley model for the neurons. On the contrary, the typical approximation that considers a sum of two independent single-variable PRCs fails for intermediate to high values of the inhibitory coupling strength of the interneuron. In particular, it loses the delayed-synchronization to anticipated-synchronization transition.

Pulse train uniformity and nonlinear dynamics of soliton crystals in mode-locked fiber ring lasers

The evolution of soliton crystal structures is analytically and numerically investigated in passively mode-locked fiber lasers by means of the nonlinear rotation of polarization. Four parameters are considered as fluctuating canonical variables of the light propagating along the fiber ring: the polarization, the phase, the amplitude, and the chirp. The stability criteria define pulse train uniformity in the soliton crystal via stable phase-locking regimes at 0 and π/2, with polarization-locked regimes prohibited due to strong amplitude polarization coupling and the bounded nature of the pumped signal. Numerical investigations of the phase-locked regimes also reveal a novel phenomenon that is the generation of spatial soliton lattices. We suggest this remarkable phenomenon results from the amplitude-chirp interplay that transfers the elliptic soliton profile of temporal pumps into spatially localized excitations upon round-trip tours in the fiber ring.

Pulse train uniformity and nonlinear dynamics of soliton crystals in mode-locked fiber ring lasers

The evolution of soliton crystal structures is analytically and numerically investigated in passively mode-locked fiber lasers by means of the nonlinear rotation of polarization. Four parameters are considered as fluctuating canonical variables of the light propagating along the fiber ring: the polarization, the phase, the amplitude, and the chirp. The stability criteria define pulse train uniformity in the soliton crystal via stable phase-locking regimes at 0 and π/2, with polarization-locked regimes prohibited due to strong amplitude polarization coupling and the bounded nature of the pumped signal. Numerical investigations of the phase-locked regimes also reveal a novel phenomenon that is the generation of spatial soliton lattices. We suggest this remarkable phenomenon results from the amplitude-chirp interplay that transfers the elliptic soliton profile of temporal pumps into spatially localized excitations upon round-trip tours in the fiber ring.

Dynamical phase transitions and pattern formation induced by a pulse pumping of excitons to a system near a thermodynamic instability

We suggest a phenomenological theory of dynamical phase transitions and the subsequent spaciotemporal evolution induced by a short optical pulse in a system which is already prone to a thermodynamic instability. We address the case of pumping to excitons whose density contributes additively to the thermodynamic order parameter like for charge-transfer excitons in electronic charge-ordering transitions. To describe both thermodynamic and dynamical effects on equal footing, we adopt for the phase transition a view of the ``excitonic insulator'' (EI) and suggest a formation of the macroscopic quantum state for the pumped excitons. The double nature of the ensemble of excitons leads to an intricate time evolution: the dynamical transition between number-preserved and phase-locked regimes, macroscopic quantum oscillations from interference between the Bose condensate of excitons, and the ground state of the EI. Modeling for an extended sample shows also stratification in domains of low and high densities which evolve through local dynamical phase transitions and a sequence of domain merges.

Frequency-locked chaotic opto-RF oscillator.

A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is experimentally and numerically studied in a chaotic regime. Precise control of the reinjection strength and detuning permits isolation of a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found, and phase noise spectra allow us to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator, even in the chaotic regime.

Micromagnet Conductors for High-Resolution Separation of Magnetically Driven Beads and Cells at Multiple Frequencies

We demonstrate a separation method for complex mixture of superparamagnetic beads using half-disk pathways, under an in-plane rotating magnetic field, which is highly sensitive to the bead size and magnetic susceptibility. The non-linear dynamics of the beads moving along the half-disk pathways at multiple frequencies can be divided into three regimes: a phase-locked regime at low driving frequencies, a phase-slipping regime above the first critical frequency f c1 , and a phase-insulated regime above the second critical frequency f c2 in which the beads just hop at the gaps between two half-disks. Hence, based on the dynamical motions, the beads with varied sizes or heterogenic magnetic properties can be separated efficiently. Furthermore, a bio-selective separation of bead plus human monocytic leukemia (THP-1) cell complexes from bare beads has been achieved due to the increased drag force on the complexes, resulting in a decreased critical frequency.