Degenerate Modes Research Articles

Entangling free electrons and optical excitations.

The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with momentum changes in the former. Specifically, free-electron entanglement with nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the achievable degree of entanglement is currently limited by the lack of control over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical-cavity excitations and separable free-electron states. We shape the electron wave function profile to select the accessible cavity modes and simultaneously associate them with targeted electron scattering directions. This concept is exemplified through theoretical calculations of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles and atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond existing protocols.

Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains.

Some quantum critical states cannot be smoothly deformed into each other without either crossing some multicritical points or explicitly breaking certain symmetries even if they belong to the same universality class. This brings up the notion of "symmetry-enriched" quantum criticality. While recent works in the literature focused on critical states with robust degenerate edge modes, we propose that the conformal boundary condition (B.C.) is a more generic characteristic of such quantum critical states. We show that in two families of quantum spin chains, which generalize the Ising and the three-state Potts models, the quantum critical point between a symmetry-protected topological phase and a symmetry-breaking order realizes a conformal B.C. distinct from the simple Ising and Potts chains. Furthermore, we argue that the conformal B.C. can be derived from the bulk effective field theory, which realizes a novel bulk-boundary correspondence in symmetry-enriched quantum critical states.

A novel mode-division (de)multiplexer with degenerate modes output for MIMO-FREE applications

In this study, we propose a novel three-dimensional architecture mode (de)multiplexer with degenerate modes output using a pure silica FMF ring core transmission channel, which solves the problem caused by random mode rotation and can be used in multiple-input multiple-output free (MIMO-FREE) applications such as data center application in the future. By using the pure silica FMF ring core transmission channel and larger effective refractive index difference, the performance with low loss, high extinction ratio (ER) and low crosstalk is achieved. The main channel with a few-mode fiber (FMF) ring-core structure supports the modes LP01, LP11, and LP21, and the large effective refractive index difference between each mode in the core ensures low crosstalk characteristics between the modes. Using the pure silica core channel can effectively reduce propagation attenuation and fusion loss. Our proposed MUX/DEMUX with degenerate modes output is achieved when the degenerate modes LP11a/LP11b and LP21a/LP21b are transmitted as two independent mode signals, which can be used in MIMO-FREE applications. The extinction ratios (ERs) of the degenerate modes LP11 and LP21 are kept above 31.66 dB and 24.43 dB, respectively, and the ER of mode LP01 is kept above 38.72 dB in the C band. The coupling efficiency of mode LP01 is approximately 0 dB, which is almost unchanged with the increase of the wavelength. The coupling efficiency of LP11 is higher than −3.49 dB and that of LP21 is higher than −7.24 dB in the whole C-band. At 1550 nm, the coupling efficiencies of modes LP01, LP11, and LP21 are −0.002 dB, −0.052 dB, and −0.178 dB, respectively. The coupling efficiency and ER of LP01 mode are the best, and those of the degenerate mode LP11 are always better than those of mode LP21. Our proposed MUX/DEMUX achieves low crosstalk and high ER performance and solves the problem caused by the degenerate modes rotations during transmission.

General Framework of Bound States in the Continuum in an Open Acoustic Resonator

Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we propose a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrate that FW BICs can be achieved with arbitrary two degenerate resonances in a closed resonator, regardless of whether they have the same or opposite parity. Moreover, their eigenmode profiles can be arbitrarily engineered by adjusting the position of the attached waveguide. This suggests an effective way of continuously switching the nature of the BICs from FW BICs to symmetry-protected BICs or accidental BICs. Also, such BICs are sustained in the coupled waveguide-resonator system with shapes such as rectangles, ellipses, and rhomboids. These interesting phenomena are well explained by the two-level effective non-Hermitian Hamiltonian, where two strongly coupled degenerate modes play a major role in forming such FW BICs. Additionally, we find that such an open system also supports accidental BICs in geometry space instead of momentum space via tuning the position of the attached waveguide, which is attributed to the quenched coupling between the waveguide and eigenmodes of the closed cavity. Finally, we fabricate a series of three-dimensional coupled resonator waveguides and experimentally verify the existence of FW BICs and accidental BICs by measuring the transmission spectra. Our results complement the current BIC library in acoustics and provide nice routes for designing acoustic devices, such as acoustic absorbers, filters, and sensors.

Degenerate line modes in the surface and bulk phonon spectra of orthorhombic NaMgF3 perovskite

Degenerate bulk-line phonon modes have been widely reported in various crystal system types; however, degenerate surface-line phonon modes have only been reported in monoclinic crystal systems, such as SnIP with space group P2/c (No. 13). Herein, we propose that degenerate surface-line phonon modes can also emerge in solids with orthorhombic structures. Based on first-principle calculations and symmetry analysis, we propose that orthorhombic NaMgF3 fluoroperovskite with space group Pnma (No. 62) is a material candidate with degenerate line states in both the bulk phonon mode and the (010) surface phonon mode. We discovered four closed nodal loops (two type-I and two hybrid-type) on the ky = 0 plane in the bulk phonon mode, all of which coexisted with Dirac points on the Z–U and X–U paths. Moreover, we discovered symmetry-projected doubly degenerate nodal lines along the X¯–U¯ surface path in the (010) surface phonon mode. The proposed degenerate surface-line phonons in NaMgF3 is quite clean and protected by symmetries, which will aid future experimental detection.

Vibrational resonance analysis of linear molecules using resummation of divergent Rayleigh–Schrödinger perturbation theory series

The large order Rayleigh–Schrödinger perturbation theory (RSPT) was applied for calculating vibrational states of linear molecules. Two molecules (CO2 and C2H2) were used as test cases with using of isomorphic Watson Hamiltonian and quartic force fields. For CO2 the Sayvetz condition can remove all degeneracies for purely vibrational states and the non-degenerate perturbation theory can be applied. However, an existence of two degenerate modes in C2H2 requires using the upgraded degenerate version of RSPT that was employed in this context for the first time. The dominating divergent behavior of such series requires the resummation technique that mimics the multivalued nature of the underlying solutions, and the applied quartic Padé–Hermite approximants (QPHA) provided full solution of the problem. Moreover, some mathematical properties of QPHA proved to be an efficient tool for studying resonance effects through the Katz theorem that controls the singular points of the eigenvalues on the complex plane. In the case of C2H2, not only all earlier observed classical resonances were confirmed and quantified, but also subtle interpolyad resonances (K2/55,K3/4555), proposed recently by Herman (2011) were described as well. Following the analysis, we found several novel resonances, of which we proposed one independent interpolyad resonance K2/4444. The complete analysis of such critical points provided the full resonance picture of all studied molecules.

Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals.

Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong interactions between photonic modes of the same energy, where the level repulsion and the hybridization between modes causes the emergence of photonic bandgaps. However, most often this phenomenon does not lead to a complete and inverted bandgap formation over the entire Brillouin zone. Here, by systematically breaking the symmetry of a two-dimensional square photonic crystal, we investigate the formation of Dirac points, line node singularities, and inverted bandgaps. The formation of this complete bandgap is due to the level repulsion between degenerate modes along the line nodes of a semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical experiments are performed by a home-build numerical framework based on a multigrid finite element method. The developed numerical toolbox and our observations pave the way towards designing complete bandgap photonic crystals and exploring the role of symmetry on the optical behaviour of even more complicated orders in photonic crystal systems.

Electric field enhancement effect on Raman spectra in two-dimensional MoSi[formula omitted]N[formula omitted], TiSi[formula omitted]N[formula omitted] and MoGe[formula omitted]As[formula omitted] monolayers

Characterizing two-dimensional (2D) layered materials in the monolayer limit is key to discovering their new phenomena and unusual properties. We theoretically predict the electric field modulated Raman spectra of 2D MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, with two kinds of laser lines (532 and 633 nm). Based on the Raman tensor, we have calculated the angle-dependent Raman intensities of the major Raman peak (A1′1) in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, locating at 1029 cm−1, 993 cm−1 and 317 cm−1, respectively. Applying the external electric field to MoSi2N4 monolayer, the symmetry of D3h reduces to C3v, which results in more peaks of Raman-active modes found in the Raman spectra. As a result, besides E′ and A1′ modes, three other major Raman peaks (A1′1, A1′2 and A1′3) are found in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, which can help us to distinguish the 2D MA2Z4 materials. We find that the enhancement factor by external electric field can be up to 10 times. Moreover, the non-resonant Raman spectra peaks of doubly degenerate mode (E′) and one-dimensional modes A1′ and A2″ in MoSi2N4, TiSi2N4 and MoGe2As4 monolayer are calculated. These theoretical results of Raman spectra of MoSi2N4 monolayer may provide theoretical guidelines for its utilization in crystal structure characterizations and optoelectric devices.

Helicity exchange and symmetry breaking of in-plane phonon scattering of h-BN probed by polarized Raman spectroscopy

Due to its atomic thickness and insulating nature, hexagonal boron nitride (h-BN) is considered to be one of the most promising substrates and gate insulating materials for two-dimensional electronic devices. In this study, polarized Raman spectroscopy was employed to uncover the effects of polarized incident light on the optical properties of h-BN phonon modes. Our measured polarization-resolved Raman spectra indicate that the symmetrical nature and the broken symmetry of degenerate phonon modes from h-BN are induced by linearly and elliptically polarized light, respectively. Moreover, a helicity exchange was observed between the excitation of circularly polarized light and the resulting opposite circular polarization of scattered light from h-BN. The measured phenomena were modeled on the basis of Raman tensors and Jones calculus to eventually calculate the amplitude coefficients of two orthogonal in-plane phonon modes. Hence, our experimental study provides a holistic understanding of the vibrational modes in h-BN, which is expected to enhance the knowledge of physical mechanisms such as heat capacity and thermal and electrical conductivities of this layered material.

A Novel Insight into the Strain Effect of T2g Mode Splitting and Bandgap in Diamond

Herein, a comprehensive analysis of the change in the bandgap and Raman frequency of diamond under the uniaxial strain along the [100], [110] and [111] directions using first‐principles calculation is presented. The results demonstrate that the triple degenerate T2g mode splitting occurs spontaneously, owing to the strain‐induced symmetry breaking. Phonon splitting into two or three different modes demonstrates its anisotropy characteristics. The tensile softening and compressive stiffening of Raman frequencies depend on the bond length, bond angle, and bond strength response to the uniaxial strain. The bandgap decreases with increasing whether the tensile or compressive strain, which is attributed to the strain‐induced change of bond identities. These findings demonstrate that the uniaxial strain engineering has potential application in future diamond electronic devices.

Simultaneous ground-state cooling of multiple degenerate mechanical modes through the cross-Kerr effect.

Simultaneous ground-state cooling of multiple degenerate mechanical modes is a difficult issue in optomechanical systems, owing to the existence of the dark mode effect. Here we propose a universal and scalable method to break the dark mode effect of two degenerate mechanical modes by introducing cross-Kerr (CK) nonlinearity. At most, four stable steady states can be achieved in our scheme in the presence of the CK effect, unlike the bistable behavior of the standard optomechanical system. Under a constant input laser power, the effective detuning and mechanical resonant frequency can be modulated by the CK nonlinearity, resulting in an optimal CK coupling strength for cooling. Similarly, there will be an optimal input laser power for cooling when the CK coupling strength stays fixed. Our scheme can be extended to break the dark mode effect of multiple degenerate mechanical modes by introducing more than one CK effect. To fulfill the requirement of the simultaneous ground-state cooling of N multiple degenerate mechanical modes, N - 1 CK effects with different strengths are needed. Our proposal provides new, to the best of our knowledge. insights into dark mode control and might pave the way to manipulating multiple quantum states in a macroscopic system.

Dual-Mode Dielectric Waveguide Monoblock Filter Design

This paper presents a design of dielectric waveguide filter using dual-mode dielectric waveguide resonators (DWRs). The filter is formed by a ceramic monoblock, thus it is compact and ease of fabrication. The employed degenerate modes of DWR are TE101 and TE011 mode, which can be coupled by a slot on the dielectric block. The coupling between a dual-mode DWR and a single-mode DWR is realized by aperture and slot. The external coupling is realized by a silver-coated blind hole that aligns to the mode for excitation. Transmission zero (TZ) can be flexibly generated above or below passband, by changing the relative position of coupling slot. A sixth order bandpass filter working at 4.9 GHz is designed using dual- and single-mode DWRs. The filter is fabricated and measured, agreeing well with simulation. This filter has compact size, low insertion loss, good selectivity and wide spurious-free response, which is applicable to 5G base stations.

Influence of birefringence- and core ellipticity-induced mode coupling on the gain statistics of forward-pumped Raman amplified few-mode fiber links.

The equations describing light propagation in a few-mode fiber for space-division multiplexing are derived under the presence of linear mode coupling and both Kerr- and Raman-induced nonlinearity. By considering physical models of stress birefringence and core ellipticity, the effect of such fiber imperfections on the gain of a forward-pumped Raman-amplified link is assessed through numerical simulations. The average gain and the variation of signal power at the output of the amplified fiber span is numerically evaluated for different levels of coupling strength in fibers supporting 2 and 4 groups of LP modes, identifying three main propagation regimes and assessing the effect of coupling between different groups of degenerate modes.

Quantum Optics Parity Effect on Generalized NOON States and Its Implications for Quantum Metrology

AbstractNOON states are entangled states of great interest in the development of quantum technologies, because they enable high‐precision phase measurements in interferometric schemes relevant to quantum metrology and sensing. This study shows that two degenerate modes of a cavity field coupled to an atom or molecule that can be modeled as a two‐level system through two‐photon interactions, initially prepared in a (generalized) NOON state, experience a dynamical evolution that distinctly depends on the parity of the photon number. When the total photon number is even, the system dynamics is characterized by a time range in which the state of the system evolves near maximally entangled states that may be fed to an optical interferometer to make phase measurements essentially at the Heisenberg limit. Such entangled states cannot be achieved for odd photon numbers instead. The parity effect thus emerges as a potential control factor in quantum metrology, sensing, and lithography.

Design of the optical system for the gamma factory proof of principle experiment at the CERN Super Proton Synchrotron

The Gamma Factory proof of principle experiment aims at colliding laser pulses with ultrarelativistic partially stripped ion beams at the CERN Super Proton Synchrotron. Its goals include the first demonstration of fast cooling of ultrarelativistic ion beams and opening up many possibilities for new physics measurements in various domains from atomic physics to particle physics. A high average-power, pulsed laser system delivering approximately 200 kW needs to be implemented for this aim. This is possible thanks to state-of-the-art optical systems that recently demonstrated similar performances in the laboratory environment. Challenges lie in the implementation of this kind of laser system in the harsh environment of hadronic machines including their robust and fully remote operation. The design of this laser system, involving a high quality factor enhancement cavity, is drawn and described in this article. Mitigation procedures are proposed to overcome limitations imposed by the occurrence of degenerate high-order mode at high average power in such optical resonators. We show that the operation at average power above 200 kW is feasible.

Large Thermal Conductivity Switching in Ferroelectrics by Electric Field-Triggered Crystal Symmetry Engineering

A convenient, reversible, fast, and wide-range switching of thermal conductivity is desired for efficient heat energy management. However, traditional methods, such as temperature-induced phase transition and chemical doping, have many limitations, e.g., the lack of continuous tunability over a wide temperature range and low switching speed. In this work, a strategy of electric field-driven crystal symmetry engineering to efficiently modulate thermal conductivity is reported with first-principles calculations. By simply changing the direction of an external electric field loaded in ferroelectric PbZr0.5Ti0.5O3, near the morphotropic phase boundary composition, we obtain the largest switching of thermal conductivity for ferroelectric materials at room temperature based on the dual-phonon theory, i.e., normal and diffuson-like phonons, with three different criteria. The calculation results indicate that with decreasing crystal symmetry, the degeneracy of phonon modes reduces and the avoid-crossing behavior of phonon branches enhances, leading to the increase of diffuson-like phonons and weighted phonon-phonon scattering phase space. A thermal switch prototype based on PbZr0.5Ti0.5O3 is further shown that can protect the Li-ion battery by modulating its temperature up to 17.5 °C. Our studies would pave the way for designing next-generation thermal switch with high speed, a wide temperature range, and a large switching ratio.

Degenerate Lattice-Instability-Driven Amorphization under Compression in Metal Halide Perovskite CsPbI3.

Halide perovskites have been intensively investigated for photovoltaic applications because of their good optoelectronic properties and low cost. Various high-pressure experiments have shown that these materials generally undergo reversible phase transitions between different crystalline phases as well as between crystalline and amorphous phases under external pressure. Herein, using first-principles density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations, we investigate the origin of the pressure-induced amorphization in CsPbI3. We find that the amorphous-like structures obtained from AIMD calculations become more stable than the orthorhombic Pbnm phase above 6.66 GPa, in good agreement with the experimental value (4.44 GPa). We further find that an imaginary flat band appears in the phonon dispersion of the orthorhombic CsPbI3 phase across the Brillouin zone at 10 GPa, leading to degenerate lattice instabilities. These energetically degenerate phonon modes are related to PbI6 octahedral tilting modes and provide random local distortions, leading to amorphization.

Manipulating electromagnetic waves in a cavity-waveguide system with nontrivial and trivial modes.

The coupled cavity-waveguide approach provides a flexible platform to design integrated photonic devices that are widely applied in optical communications and information processing. Topological photonic crystals that can excite the nontrivial edge state (ES) and corner state (CS) have an unprecedented capability to manipulate electromagnetic (EM) waves, leading to a variety of unusual functionalities that are impossible to achieve with conventional cavity-waveguide systems. In this Letter, two-dimensional photonic crystals consisting of an ES waveguide, a CS cavity, and a trivial cavity are proposed as a means to robustly control the transmission characteristics of electromagnetic waves. As a proof-of-principle example, the analog of electromagnetically induced transparency (EIT) that is tolerated in disorders due to the robustness of the CS is numerically demonstrated. In addition, the analog of multi-EIT is also verified by introducing a trivial cavity with two degenerate orthogonal modes. This unique approach for robustly manipulating EM waves may open an avenue to the design of high-performance filters, modulators, and on-chip processors.

Optical Transparency Induced by a Largely Purcell Enhanced Quantum Dot in a Polarization-Degenerate Cavity.

Optically active spin systems coupled to photonic cavities with high cooperativity can generate strong light-matter interactions, a key ingredient in quantum networks. However, obtaining high cooperativities for quantum information processing often involves the use of photonic crystal cavities that feature a poor optical access from the free space, especially to circularly polarized light required for the coherent control of the spin. Here, we demonstrate coupling with a cooperativity as high as 8 of an InAs/GaAs quantum dot to a fabricated bullseye cavity that provides nearly degenerate and Gaussian polarization modes for efficient optical accessing. We observe spontaneous emission lifetimes of the quantum dot as short as 80 ps (an ∼15 Purcell enhancement) and a ∼80% transparency of light reflected from the cavity. Leveraging the induced transparency for photon switching while coherently controlling the quantum dot spin could contribute to ongoing efforts of establishing quantum networks.

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices.

We investigate the discrete Talbot self-imaging effect in Floquet superlattices based on a mesh of directional couplers with periodically varying separation between waveguides, both theoretically and numerically. The modulated discreteness of the lattices sets strong constraints to ensure the Talbot effect generation. We show that discrete Talbot effect occurs only if the incident periods are N = 1, 2, and 4 in dispersive regimes of the Hermitian superlattices. In both dynamic localized and rectification regimes, self-imaging effect can occur for arbitrary input period N. For the rectification case, Talbot distance equals the input period. In the regime of dynamical localization, the Talbot distance remains unchanged irrespective of the pattern period. For non-Hermitian Floquet superlattices, due to the non-zero imaginary part of quasi-energy spectrum arising at the center of the Brillouin zone, where the mode degeneracy occurs, Talbot revival is not preserved when the input period is an even number, and exists only as N = 1 in the dispersive regime. The theoretical calculations and numerical simulations verify each other completely.