Large Number Of Modes Research Articles

A general framework for multimode Gaussian quantum optics and photo-detection: Application to Hong–Ou–Mandel interference with filtered heralded single photon sources

The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involve maximizing the interference visibility while maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include a large number of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong–Ou–Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced.

High-fidelity spatial mode transmission through a 1-km-long multimode fiber via vectorial time reversal

The large number of spatial modes supported by standard multimode fibers is a promising platform for boosting the channel capacity of quantum and classical communications by orders of magnitude. However, the practical use of long multimode fibers is severely hampered by modal crosstalk and polarization mixing. To overcome these challenges, we develop and experimentally demonstrate a vectorial time reversal technique, which is accomplished by digitally pre-shaping the wavefront and polarization of the forward-propagating signal beam to be the phase conjugate of an auxiliary, backward-propagating probe beam. Here, we report an average modal fidelity above 80% for 210 Laguerre-Gauss and Hermite-Gauss modes by using vectorial time reversal over an unstabilized 1-km-long fiber. We also propose a practical and scalable spatial-mode-multiplexed quantum communication protocol over long multimode fibers to illustrate potential applications that can be enabled by our technique.

An efficient semi-analytical formulation for the Lamb-like waves in layered waveguides based on global discretization

Lamb-like waves are widely used in the health monitoring of layered structures. It is well known, however, that the semi-analytical finite element method, being capable to analyze the wave characteristics, requires a refined mesh, while the mode expansion technique requires a large number of modes in order to approximate the continuity conditions at the interfaces as well as the boundary conditions of the waveguide. In the present work, an efficient semi-analytical formulation is proposed based on the global discretization (GDSA), where all the continuity and boundary conditions can be exactly satisfied. First, the characteristic equation of an elementary layer is derived based on the wave structure described by the superposition of a polynomial and a series of sine basis functions, and the involved matrices are explicitly derived in form of the Kronecker product. Layered waveguides can then be modelled from the superposition of each layer. Based on this, a general transform, allowing to eliminate the imaginary parts of the eigenvalue problem, is proposed, and a reduced-order eigenvalue problem is developed which is capable to predict a majority of the cut-off frequencies. From the benchmarks on an aluminum plate and the plate covered by an ice layer, the convergence, accuracy and efficiency of the GDSA have been confirmed by comparing to existing methods. Lastly, the wave responses simulated from the spectral element analysis are taken for a case study. It is additionally found that the cut-off frequency of the A1 mode and the conversion between the symmetric and anti-symmetric modes are sensitive to the ice layer, having potential to the applications of ice detections.

Analysis of bath motion in MM-SQC dynamics via dimensionality reduction approach: Principal component analysis.

The system-plus-bath model is an important tool to understand the nonadiabatic dynamics of large molecular systems. Understanding the collective motion of a large number of bath modes is essential for revealing their key roles in the overall dynamics. Here, we applied principal component analysis (PCA) to investigate the bath motion in the basis of a large dataset generated from the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian nonadiabatic dynamics for the excited-state energy transfer in the Frenkel-exciton model. The PCA method clearly elucidated that two types of bath modes, which either display strong vibronic coupling or have frequencies close to that of the electronic transition, are important to the nonadiabatic dynamics. These observations were fully consistent with the physical insights. The conclusions were based on the PCA of the trajectory data and did not involve significant pre-defined physical knowledge. The results show that the PCA approach, which is one of the simplest unsupervised machine learning dimensionality reduction methods, is a powerful one for analyzing complicated nonadiabatic dynamics in the condensed phase with many degrees of freedom.

Parity-time symmetric frequency-tunable optoelectronic oscillator based on a Si3N4 microdisk resonator.

The optoelectronic oscillator (OEO) generates low-phase noise and high-frequency microwave signals thanks to a high Q-factor cavity with long and low-loss fiber delay. Traditionally, for the desired mode selection from the ultradense cavity modes, a narrowband electrical filter is needed, whose frequency tuning is very limited. On the other hand, for a tunable OEO offered by a microwave photonic filter (MPF), a paradox existed between the large number of cavity modes and the wide MPF bandwidth. Here, we achieve a tunable OEO using the mode-selection mechanism of parity-time symmetry, which overcomes the paradox. A high Q-factor silicon nitride microdisk resonator (Si3N4 MDR) is introduced to achieve frequency filtering and tuning. Moreover, the experimental results reveal that the tunable OEO generates a signal range from 3 GHz to 20 GHz with a phase noise about -120dBc/Hz at a 10 kHz offset frequency.

Pairwise Mode Locking in Dynamically Coupled Parametric Oscillators.

Mode locking in lasers is a collective effect, where due to a weak coupling a large number of frequency modes lock their phases to oscillate in unison, forming an ultrashort pulse in time. We demonstrate an analogous collective effect in coupled parametric oscillators, which we term "pairwise mode locking," where many pairs of modes with twin frequencies (symmetric around the center carrier) oscillate simultaneously with a locked phase sum, while the phases of individual modes remain undefined. Thus, despite being broadband and multimode, the emission is not pulsed and lacks first-order coherence, while possessing a very high degree of second-order coherence. Our configuration comprises two coupled parametric oscillators within identical multimode cavities, where the coupling between the oscillators is modulated in time at the repetition rate of the cavity modes, with some analogy to active mode locking in lasers. We demonstrate pairwise mode locking in a radio-frequency experiment, covering over an octave of bandwidth with approximately 20 resonant mode-locked pairs, filling most of the available bandwidth between dc and the pump frequency. We accompany our experiment with an analytic model that accounts for the properties of the coupled parametric oscillators near threshold.

Mode analysis of in-line Mach-Zehnder interferometer with offset splicing

Mode excitation of in-line Mach-Zehnder interferometer (MZI) with offset splicing between standard single-mode fiber (SMF) and thin-core fiber (TCF) is investigated. Based on the mode field profiles of high order modes in TCF, dependence of mode excitation on core offset is researched firstly. It is revealed that which modes can be significantly excited is strongly dependent on the mode fields matching between LP01 mode in SMF and LP1n mode in TCF, by which the dominant excited modes can be predicted and this method can be expanded to any two fibers with offset splicing. Based on the energy distributions of excited modes with/without considering interference among cladding modes, transmission spectra can be calculated by interference equations theoretically. By comparing with experimental results, it can be concluded that for kind of MZIs based on offset splicing, it is difficult to make the calculated results to be identical with experimental results due to the large number of modes excited, so an equivalent mode approach is proposed to solve this problem and verified by the temperature sensing experiment. In addition, dependence of mode excitation on probing wavelength or refractive index (RI) of surroundings, and effect of fiber parameters on signal shape are also studied. The MZI proposed here shows advantages of low cost, easy fabrication, no special splicing equipment required, and relative high sensitivity. Results shown here will provide valuable information for kind of MZIs based on core-offset splicing between TCF and SMF, and afford useful references for other kinds of in-line MZIs based on the interference between core and cladding modes.

A global eigenvalue reassignment method for the stabilization of nonlinear reduced‐order models

AbstractThe systematic and physics‐infused construction of a projection‐based reduced‐order model (ROM) shows the capability to replicate the original high‐dimensional system's dynamical evolution but with a fractional computational cost. However, certain nonlinear features and high‐frequency contributions may be lost throughout the aggressive order reduction. Thus, ROMs in a broad category of fluid dynamics applications require stabilization and closure methods to compensate for the key contributions missed through the model order reduction. A new stabilization method for nonlinear ROMs is proposed in this study that learns a linear control law to drive the nonlinear ROM toward maximum agreement with the full‐order model, where a total power constraint guarantees the stability of the nonlinear ROM. This new method achieves both stability and accuracy for nonlinear proper orthogonal decomposition‐Galerkin ROMs in two chosen applications with strong shock‐wake interactions and unsteady oscillations, which trigger strong instabilities in the original ROMs before stabilization. A multistage layout is designed to further enhance the proposed stabilization method for more efficient and robust stabilization of nonlinear ROMs with a large number of unstable modes.

Injection locking and pulling phenomena in an optoelectronic oscillator.

Injection locking and pulling characteristics of a long-loop optoelectronic oscillator (OEO) that has a large number of closely-spaced longitudinal modes are theoretically analyzed and experimentally evaluated. A differential phase equation that relates the phase difference between the OEO and the injected microwave signal to its instantaneous beat angular frequency is derived in the time domain. Based on the differential phase equation, both the locking and pulling characteristics of an injection-locked OEO are studied, and the phase noise performance is analyzed. It is found that the locking and pulling performance depends upon three parameters, the initial frequency difference between the frequency of the signal generated by the free-running OEO and frequency of the injected microwave signal, the voltage ratio between the signal generated by the free-running OEO and the injected microwave signal, and the Q factor of the free-running OEO. The phase noise performance depends upon the locking range, the phase noise performance of the free-running OEO as well as that of the injected microwave signal. The analysis is validated experimentally. Excellent agreement is found between the theoretical analysis and the experimental demonstration.

High-speed multimode fiber imaging system based on conditional generative adversarial network

The multimode fiber (MMF) has great potential to transmit high-resolution images with less invasive methods in endoscopy due to its large number of spatial modes and small core diameter. However, spatial modes crosstalk will inevitably occur in MMFs, which makes the received images become speckles. A conditional generative adversarial network (GAN) composed of a generator and a discriminator was utilized to reconstruct the received speckles. We conduct an MMF imaging experimental system of transmitting over 1 m MMF with a 50 µm core. Compared with the conventional method of U-net, this conditional GAN could reconstruct images with fewer training datasets to achieve the same performance and shows higher feature extraction capability.

Lower turning point convegence zone in deep water with an incomplete channel

In a deep sea sound channel, rays will bend due to the sound speed profile, and convergence zone will occur when the rays are intensive. Transmission loss in the convergence zone is smaller and it is conducive to acoustic detection and communication. Therefore the study of acoustic characteristics in convergence zone is always the focus of deep-sea acoustics. A long-range sound propagation experiment is conducted in the South China Sea. An equivalent broadband explosive sound source of 1 kg is placed at a depth of 200 m, and the hydrophone receives the data at 3146 m far. The processing and analysis of the experimental data indicate that there is a convergence zone below the sound channel axis in the incomplete deep channel. Compared with the upper turning point convergence zone near the surface, this convergence zone has a high convergence gain at a long distance. The caustic lines of refracted type and refracted surface-refleted type are determined by means of ray-normal mode theory. It is found that the location of the deep convergence zone observed in the experiment is consistent with the position of the refracted caustic line. It is proved that the convergence zone is a lower turning point convergence zone formed by the superposition of a large number of normal modes in the same phase, and it has a convergence effect at a certain depth below the sound channel axis in the deep sea. The formation conditions of the convergence zone and the influence of sound source depth on the caustic structure of the convergence zone are studied. The comparisons of the transmission loss and the width between the upper and lower turning point convergence zone at a long distance aremade. The analysis shows that the convergence gain in the seventh lower turning point convergence zone is still no less than 10 dB. The influence of the vertical structure of sound velocity on the lower turning point convergence zone is studied. The theoretical analysis results are in good agreement with the experimental data.

Optimization-Based Modal Decomposition for Systems with Multiple Transports

Mode-based model-reduction is used to reduce the degrees of freedom of high-dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and scientific applications, often require a large number of linear modes to obtain a small representation error. This difficulty, even for the most simple transports, originates from the inappropriateness of the decomposition structure in time dependent amplitudes of purely spatial modes. In this article an approach is discussed that decomposes a flow field into several fields of co-moving frames, where each one can be approximated by a few modes. The central aspect of this report is a transparent formulation of this decomposition as an optimization problem. Different singular-value-based objective functions are discussed and connected to former formulations. A boundary treatment is provided. The decomposition is applied to generic cases and to a technically relevant flow configuration of combustion physics.

Spectral Analysis of Optimal Disturbances of Stratified Turbulent Couette Flow

For a stratified turbulent Couette flow, the eigenmodes and optimal disturbances of corresponding simplified equations linearized around a steady state are considered. It is shown that the spectrum of these equations is symmetric with respect to the real axis and lies strictly in the left half-plane, i.e., all eigenmodes are stable, and the main part of an optimal disturbance is a linear combination of a large number of modes corresponding to eigenvalues with largest real parts. The number of the most significant modes in this linear combination grows with increasing Reynolds number.

Mode decomposition of multimode optical fiber beams by phase-only spatial light modulator

Multimode optical fibers (MMF) recently attracted a renewed attention, because of their potential for spatial division multiplexing, medical imaging and high-power fiber lasers, thanks to the discovery of new nonlinear optical effects, such as Kerr beam self-cleaning, spatiotemporal mode-locking, and geometric parametric instability, to name a few. The main feature of these effects is that many transverse modes are involved in nonlinear interactions. To advance our understanding, it is necessary to analyse the modal content of beams at the output of MMFs. In this work, based on a computer digital holography method using a phase-only spatial light modulator (SLM) as a correlation filter, we experimentally demonstrate a method of mode decomposition involving a large (≃80) number of fiber modes. To obtain this, we carried out a SLM calibration, and numerically investigated the most critical parameters which affect the fidelity of the decomposition, by comparing experimental and reconstructed beam patterns in both the linear (speckled structures) and in the nonlinear (self-cleaned beams) propagation regime.

Experimental observation of spectral super-broadening of backward stimulated Raman scattering in liquids

The spectral super-broadening of backward stimulated Raman scattering (SRS) in four liquid samples ( C C l 4 , dimethyl sulfoxide, acetone, and C H 2 C l 2 ) have been observed under the pump conditions of using 532-nm and ∼ 11 - n s pulsed laser beams from a frequency-doubled and multilongitudinal mode Pockels Q-switched Nd:YAG laser device. Under the same pump conditions, in acetone the observed maximum broadening range was ≥ 450 c m − 1 for the backward SRS, while it was ≤ 45 c m − 1 for the forward SRS. The physical origin of this observed effect is essentially related to the detailed temporal structure of the 532-nm pump pulse that consists of a series of subpulse of ∼ 50 p s width, owing to the randomly beating effect among a large number of longitudinal modes of the Pockels Q-switched laser source. Each backward SRS subpulse undergoes multiple cross-phase modulation (XPM) by interacting with a certain number of forward pump subpulses, and consequently manifests a super-broadened spectral distribution. In contrast, each forward SRS subpulse interacts only with a single pump subpulse and therefore experiences a much limited XPM influence, resulting in a much smaller spectral broadening. Furthermore, when the 532-nm pump beam was from a single-longitudinal mode-seeded Nd:YAG laser, there was no beating-effect-induced subpulse structure of the pump pulse, and thereby no noticeable spectral broadening for both backward and forward SRS could be observed.

Mechanism of stacking fault formation in metal(100) heteroepitaxial growth

Strain in metal(100) heteroepitaxial thin-film growth can lead to a variety of effects such as the formation of stacking faults (SFs). To gain a better understanding we have carried out temperature-accelerated dynamics (TAD) simulations of the submonolayer growth of Cu islands on a biaxially strained Cu substrate at 200 K. In the case of 4% compressive strain we find that SF formation occurs with a morphology very similar to the structures found experimentally in Cu/Ni(100) growth. We also find that islands play a key role by lowering the barrier for vacancy formation. In particular, once two substrate vacancies are formed and diffuse to form the appropriate configuration this leads to the formation of a SF in both the substrate and island. While the activation barrier for SF formation is very high, due to the presence of a large number of low-frequency vibrational modes, the saddle-point entropy is large while the corresponding Vineyard prefactor is more than 10 orders of magnitude larger than is typical of atomic processes in fcc metals. Similarly, an analysis of the entropy of the SF state indicates that the reverse prefactor is much smaller, while the free energy of this state is lower than that of the initial state.

Detectability of axion dark matter with phonon polaritons and magnons

Collective excitations in condensed matter systems, such as phonons and magnons, have recently been proposed as novel detection channels for light dark matter. We show that excitation of i) optical phonon polaritons in polar materials in an ${\mathcal O}$(1 T) magnetic field (via the axion-photon coupling), and ii) gapped magnons in magnetically ordered materials (via the axion wind coupling to the electron spin), can cover the difficult-to-reach ${\mathcal O}$(1-100) meV mass window of QCD axion dark matter with less than a kilogram-year exposure. Finding materials with a large number of optical phonon or magnon modes that can couple to the axion field is crucial, suggesting a program to search for a range of materials with different resonant energies and excitation selection rules; we outline the rules and discuss a few candidate targets, leaving a more exhaustive search for future work. Ongoing development of single photon, phonon and magnon detectors will provide the key for experimentally realizing the ideas presented here.

Magnetic and vibronic terahertz excitations in Zn-doped Fe2Mo3O8

We report on optical excitations in the magnetically ordered phases of multiferroic Fe$_{1.86}$Zn$_{0.14}$Mo$_3$O$_8$ in the frequency range from 10-130 cm$^{-1}$ (0.3-3.9 THz). In the collinear easy-axis antiferromagnetic phase below $T_N=50$~K eleven optically active modes have been observed in finite magnetic fields, assuming that the lowest-lying mode is doubly degenerate. The large number of modes reflects either a more complex magnetic structure than in pure Fe$_{2}$Mo$_3$O$_8$ or that spin stretching modes become active in addition to the usual spin precessional modes. Their magnetic field dependence, for fields applied along the easy axis, reflects the irreversible magnetic-field driven phase transition from the antiferromagnetic ground state to a ferrimagnetic state, while the number of modes remains unchanged in the covered frequency region. We determined selection rules for some of the AFM modes by investigating all polarization configurations and identified magnetic- and electric-dipole active modes as well. In addition to these sharp resonances, a broad electric-dipole active excitation band, which is not influenced by the external magnetic field, occurs below $T_N$ with an onset at 12 cm$^{-1}$. We are able to model this absorption band as a vibronic excitation related to the lowest-lying Fe$^{2+}$ electronic states in tetrahedral environment.

Coupling of lattice, spin, and intraconfigurational excitations of Eu3+ in Eu2ZnIrO6

In Eu2ZnIrO6, effectively two atoms are active i.e. Ir is magnetically active, which results in complex magnetic ordering within the Ir sublattice at low temperature. On the other hand, although Eu is a van-vleck paramagnet, it is active in the electronic channels involving 4f 6 crystal-field split levels. Phonons, quanta of lattice vibration, involving vibration of atoms in the unit cell, are intimately coupled with both magnetic and electronic degrees of freedom (DoF). Here, we report a comprehensive study focusing on the phonons as well as intra-configurational excitations in double-perovskite Eu2ZnIrO6. Our studies reveal strong coupling of phonons with the underlying magnetic DoF reflected in the renormalization of the phonon self-energy parameters well above the spin-solid phase (TN ~ 12 K) till temperature as high as ~ 3TN, evidences broken spin rotational symmetry deep into the paramagnetic phase. In particular, all the observed first-order phonon modes show softening of varying degree below ~3TN, and low-frequency phonons become sharper, while the high-frequency phonons show broadening attributed to the additional available magnetic damping channels. We also observed a large number of high-energy modes, 39 in total, attributed to the electronic transitions between 4f-levels of the rare-earth Eu3+ ion and these modes shows anomalous temperature evolution as well as mixing of the crystal-field split levels attributed to the strong coupling of electronic and lattice DoF.

Reduced order models for geometrically nonlinear structures: Assessment of implicit condensation in comparison with invariant manifold approach

A comparison between two methods to derive reduced-order models (ROM) for geometrically nonlinear structures is proposed. The implicit condensation and expansion (ICE) method relies on a series of applied static loadings. From this set, a stress manifold is constructed for building the ROM. On the other hand, nonlinear normal modes rely on invariant manifold theory in order to keep the key property of invariance for the reduced subspaces. When the model coefficients are fully known, the ICE method reduces to a static condensation. However, in the framework of finite element discretization, getting all these coefficients is generally too computationally expensive. The stress manifold is shown to tend to the invariant manifold only when a slow/fast decomposition between master and slave coordinates can be assumed. Another key problem in using the ICE method is related to the fitting procedure when a large number of modes need to be taken into account. A simplified procedure, relying on normal form theory and identification of only resonant monomial terms in the nonlinear stiffness, is proposed and contrasted with the current method. All the findings are illustrated on beams and plates examples.