Ensemble Of Resonators Research Articles

A parametrically programmable delay line for microwave photons

Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line’s properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon.

A New Signature for Strong Light-Matter Coupling Using Spectroscopic Ellipsometry.

Light–matter interactions can occur when an ensemble of molecular resonators is placed in a confined electromagnetic field. In the strong coupling regime the rapid exchange of energy between the molecules and the electromagnetic field results in the emergence of hybrid light–matter states called polaritons. Multiple criteria exist to define the strong coupling regime, usually by comparing the splitting of the polariton bands with the line widths of the uncoupled modes. Here, we highlight the limitations of these criteria and study strong coupling using spectroscopic ellipsometry, a commonly used optical characterization technique. We identify a new signature of strong coupling in ellipsometric phase spectra. The combination of ellipsometric amplitude and phase spectra yields a distinct topological feature that we suggest could serve as a new criterion for strong coupling. Our results introduce the idea of ellipsometric topology and could provide further insight into the transition from the weak to strong coupling regime.

Generalized Maxwell projections for multi-mode network Photonics

The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. While describing the dynamics of few resonances is a relatively well understood problem, controlling the behavior of systems with many overlapping states is considerably more difficult. In this work, we use the theory of generalized operators to formulate an exact form of spatio-temporal coupled mode theory, which retains the simplicity of traditional coupled mode theory developed for optical waveguides. We developed a fast computational method that extracts all the characteristics of optical resonators, including the full density of states, the modes quality factors, and the mode resonances and linewidths, by employing a single first principle simulation. This approach can facilitate the analytical and numerical study of complex dynamics arising from the interactions of many overlapping resonances, defined in ensembles of resonators of any geometrical shape and in materials with arbitrary responses.

Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions

We propose a system that exploits the fundamental features of topological photonics and synthetic dimensions to force many semiconductor laser resonators to synchronize, mutually lock, and under suitable modulation emit a train of transform-limited mode-locked pulses. These lasers exploit the Floquet topological edge states in a 1D array of ring resonators, which corresponds to a 2D topological system with one spatial dimension and one synthetic frequency dimension. We show that the lasing state of the multi-element laser system possesses the distinct characteristics of spatial topological edge states while exhibiting topologically protected transport. The topological synthetic-space edge mode imposes a constant-phase difference between the multi-frequency modes on the edges, and together with modulation of the individual elements forces the ensemble of resonators to mode-lock and emit short pulses, robust to disorder in the multi-resonator system. Our results offer a proof-of-concept mechanism to actively mode-lock a laser diode array of many lasing elements, which is otherwise extremely difficult due to the presence of many spatial modes of the array. The topological synthetic-space concepts proposed here offer an avenue to overcome this major technological challenge, and open new opportunities in laser physics.

Quantum Theory of the Wannier Phenomenon

We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation [1] to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e- + He(1s ns)→He-** for n ≫ 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by . The coupling constant g has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.

Multiple scattering enabled superdirectivity from a subwavelength ensemble of resonators

An ensemble of resonators arranged on a subwavelength scale is usually considered as a bulk effective medium, known as a metamaterial, and can offer unusual macroscopic properties. Here, we take a different approach and limit ourselves to the study of only a few number of such elementary components and demonstrate that they still offer uncommon opportunities. Typically, owing to the multiple scattering and the phase shift that the resonances offer, we observe fields that vary at scales completely independent of the wavelength in free space. By smartly tuning the resonance frequencies, we can design at will the complex current distribution in those resonators. This way, we design a superdirective antenna, i.e., an antenna that is surprisingly more directive than its size would foreshadow. This approach is verified numerically and experimentally in the context of microwaves, but this applies to any wave field where subwavelength resonators exist.

Stationary multi-wave resonant ensembles in a microtubule

Stationary energy distribution between nonlinearity coupled modes of oscillations in microtubules is investigated using standard asymptotic approaches in the framework of classical mechanics. The first–order approximation analysis reveals three various types of triple–mode resonant ensembles consisting of one longitudinal wave and a pair of transverse modes being in phase. In turn, the nonlinear coupling between triads of various types and spectral states creates stationary multi-mode resonant ensembles. The corresponding stationary multi-mode solutions exhibit Lyapunov–stable quasiperiodic orbits in contrast to chaotic motions inherent in the same system. It is found that the energy distribution in microtubules being in thermal equilibrium is described by a recursive function that cannot be reduced to well-known classical statistical laws. Also, multi-frequency envelope solitons, taking place far from the thermal equilibrium of a microtubule, are possible when getting some portion of energy from the environment. The mechanical momentum of such solitons can propagate along microtubules without dispersion in long distances that can help for efficient heat exchange as well as in providing coherent movement of motor organelles.

Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as Δϕ∝1/N2 under quadratic phase accumulation, which is 1/N times smaller than the linear counterpart, where N is probe number. Here, we experimentally demonstrate the nonlinear quantum metrology by using a spin-I (I>1/2) nuclear magnetic resonance (NMR) ensemble that can be mapped into a system of N=2I spin-1/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as Δϕ∝1/(N2-1) by optimizing the input states, when N is an odd number. In addition, the interferometric measurement with quadratic interaction provides a new way for estimating the quadrupolar coupling strength in an NMR system. Our system may be further extended to exotic nonlinear quantum metrology with higher order many-body interactions.

Point dipole and quadrupole scattering approximation to collectively responding resonator systems

We develop a theoretical formalism for collectively responding point scatterers where the radiating electromagnetic fields from each emitter are considered in the electric dipole, magnetic dipole, and electric quadrupole approximation. The contributions of the electric quadrupole moment to electromagnetically-mediated interactions between the scatterers are derived in detail for a system where each scatterer represents a linear $RLC$ circuit resonator, representing common metamaterial resonators in radiofrequency, microwave, and optical regimes. The resulting theory includes a closed set of equations for an ensemble of discrete resonators that are radiatively coupled to each other by propagating electromagnetic fields, incorporating potentially strong interactions and recurrent scattering processes. The effective model is illustrated and tested for examples of pairs of interacting point electric dipoles, where each pair can be qualitatively replaced by a model point emitter with different multipole radiation moments.

Scalable high-precision tuning of photonic resonators by resonant cavity-enhanced photoelectrochemical etching

Photonic lattices of mutually interacting indistinguishable cavities represent a cornerstone of collective phenomena in optics and could become important in advanced sensing or communication devices. The disorder induced by fabrication technologies has so far hindered the development of such resonant cavity architectures, while post-fabrication tuning methods have been limited by complexity and poor scalability. Here we present a new simple and scalable tuning method for ensembles of microphotonic and nanophotonic resonators, which enables their permanent collective spectral alignment. The method introduces an approach of cavity-enhanced photoelectrochemical etching in a fluid, a resonant process triggered by sub-bandgap light that allows for high selectivity and precision. The technique is presented on a gallium arsenide nanophotonic platform and illustrated by finely tuning one, two and up to five resonators. It opens the way to applications requiring large networks of identical resonators and their spectral referencing to external etalons.

Split-loop resonator array for microwave energy harvesting

In this paper, we propose a three-dimensional split-loop resonator composed of a bended wire, a metallic ground slab, and a coaxial line loaded with a lumped matching resistor to mimic the input impedance of a rectifier. An ensemble of such resonators can function as an efficient energy harvester. The energy capture mechanism is explained by an equivalent circuit model. A 20 × 20 resonator array is fabricated to resonate around 2.45 GHz. The simulated and measured results indicate that the proposed resonator array has nearly unity energy conversion efficiency at the resonant frequency and is quite promising as an energy harvester in the microwave wireless power transmission system.

Resonant ensembles of stationary quasi-harmonic waves in one-dimensional crystals

Using a simple mathematical model, built on geometric representations of central and noncentral interactions between material particles in a one-dimensional anharmonic chain, nonlinear resonant interactions between quasi-harmonic waves are investigated in the so-called harmonic approximation. The investigation is carried out with standard asymptotic nonlinear dynamics methods. In the first-order approximation, resonant wave triads are established that are formed at a characteristic quadratic nonlinearity of the system provided that the phase-matching conditions are satisfied. It is demonstrated that the resonant triads can be of only three different types and each resonant triad can consist of only one longitudinal and two transverse oscillation modes. In the general case, a nontrivial interaction between different resonant triplets of three different types and spectral scales is implemented in a chain. Cascade processes of the energy exchange between oscillation modes are characterized by both the complicated dynamics typical of Hamiltonian nonintegrable dynamic systems and the presence of Lyapunov-stable multiwave steady-state motions. In ideal crystalline structures, such steady-state coherent wave ensembles can significantly affect the specific heat and other phenomenological parameters of a system, especially at low temperatures. Therefore, the theoretical and experimental study of these ensembles is of great importance.

Cooperative resonance linewidth narrowing in a planar metamaterial

We theoretically analyse the experimental observations of a spectral line collapse in a metamaterial array of asymmetric split ring resonators (Fedotov et al 2010 Phys. Rev. Lett.104 223901). We show that the ensemble of closely-spaced resonators exhibits a cooperative response, explaining the observed system-size dependent narrowing of the transmission resonance linewidth. We further show that this cooperative narrowing depends sensitively on the lattice spacing and that significantly stronger narrowing could be achieved in media with suppressed ohmic losses.

Cooperative emission from nuclei: The collective Lamb shift and electromagnetically induced transparency

AbstractThe narrow nuclear resonances of Mössbauer isotopes constitute almost ideal two‐level systems to study cooperative effects in the interaction of x‐rays with matter. Embedding an ensemble of resonant Mössbauer nuclei into a planar cavity facilitates the excitation of superradiant oscillatory eigenmodes via pulses of synchrotron radiation. These modes exhibit a large collective Lamb shift that can be controlled via the excitation conditions and the cavity geometry. Cooperative emission in connection with the radiative coupling of two resonant ensembles in a cavity leads to electromagnetically induced transparency (EIT). This contribution gives a review on cooperative effects in nuclear resonant scattering of synchrotron radiation. Special emphasis is given to the basic principles of recent experiments that led to the observation of the collective Lamb shift and EIT with nuclear resonances in the regime of hard x‐rays.

Photon echo quantum random access memory integration in a quantum computer

We have analysed an efficient integration of multi-qubit echo quantum memory (QM) into the quantum computer scheme based on squids, quantum dots or atomic resonant ensembles in a quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the QM node and other nodes characterized by the homogeneously broadened resonant line are used for processing. We have found the optimal conditions for the efficient integration of the multi-qubit QM modified for the analysed scheme, and we have determined the self-temporal modes providing a perfect reversible transfer of the photon qubits between the QM node and arbitrary processing nodes. The obtained results open the way for realization of a full-scale solid state quantum computing based on the efficient multi-qubit QM.

Investigation of the Leggett-Garg Inequality for Precessing Nuclear Spins

We report experimental implementation of a protocol for testing the Leggett-Garg inequality (LGI) for nuclear spins precessing in an external magnetic field. The implementation involves certain controlled operations, performed in parallel on pairs of spin-1/2 nuclei (target and probe) from molecules of a nuclear magnetic resonance ensemble, which enable evaluation of temporal correlations from an LG string. Our experiment demonstrates violation of the LGI for time intervals between successive measurements, over which the effects of relaxation on the quantum state of target spin are negligible. Further, it is observed that the temporal correlations decay, and the same target spin appears to display macrorealistic behavior consistent with LGI.

Single Molecule Fluorescence Resonance Energy Transfer and Ensemble Biophysical Characterization of a G-quadruplex Formed in the Promoter of Human Myocyte Enhancer Factor 2D

DNA G-quadruplexes (G4s) are believed to be involved in many biological processes,including the gene expression regulation and the maintenance of telomere.However,the kinetics of G4,in particular how G4 forms in the double-stranded genomic DNA is an underexplored issue.We found that a very stable G4 can form in the promoter of human myocyte enhancer factor 2D (MEF2D),the gene encodes a transcription factor belonging to the MEF2 (myocyte enhancer factor-2) family which regulates the response of heart to cardiac stress signals.Biophysical characterizations,in particular single molecule fluorescence resonance energy transfer (smFRET) measurements,suggest that this G4 is more stable than its duplex form in near physiological conditions.Two major G4 structures were identified based on single molecule conformational analysis on the end and internal labeled DNA systems.A free energy landscape for the G4 hybridization was established in light of the smFRET G4/duplex competition assay.In addition,the G4 hybridization and unfolding rate constants were obtained.

Quantum demonstration of a bio-molecular solution of the satisfiability problem on spin-based ensemble

DNA computation (DNAC) has been proposed to solve the satisfiability (SAT) problem due to operations in parallel on extremely large numbers of strands. This paper attempts to treat the DNA-based bio-molecular solution for the SAT problem from the quantum mechanical perspective with a purpose to explore the relationship between DNAC and quantum computation (QC). To achieve this goal, it first builds up the correspondence of operations between QC and DNAC. Then it gives an example for the case of two variables and three clauses for details of this theory. It also demonstrates a three-qubit experiment for solving the simplest SAT problem with a single variable on a liquid-state nuclear magnetic resonance ensemble to verify this theory. Some discussions are made for the potential application and for further exploration of the present work.

Computational identification of slow conformational fluctuations in proteins.

Conformational flexibility of proteins has been linked to their designated functions. Slow conformational fluctuations occurring at the microsecond to millisecond time scale, in particular, have recently attracted considerable interest in connection to the mechanism of enzyme catalysis. Computational methods are providing valuable insights into the connection between protein structure, flexibility, and function. In this report, we present studies on identification and characterization of microsecond flexibility of ubiquitin, based on quasi-harmonic analysis (QHA) and normal-mode analysis (NMA). The results indicate that the slowest 10 QHA modes, computed from the 0.5 mus molecular dynamics ensemble, contribute over 78% of all motions. The identified slow movements show over 75% similarity with the conformational fluctuations observed in nuclear magnetic resonance ensemble and also agree with displacements in the set of X-ray structures. The slowest modes show high flexibility in the beta1-beta2, alpha1-beta3, and beta3-beta4 loop regions, with functional implications in the mechanism of binding other proteins. NMA of ubiquitin structures was not able to reproduce the long time scale fluctuations, as they were found to strongly depend on the reference structures. Further, conformational fluctuations coupled to the cis/trans isomerization reaction catalyzed by the enzyme cyclophilin A (CypA), occurring at the microsecond to millisecond time scale, have also been identified and characterized on the basis of QHA of conformations sampled along the reaction pathway. The results indicate that QHA covers the same conformational landscape as the experimentally observed CypA flexibility. Overall, the identified slow conformational fluctuations in ubiquitin and CypA indicate that the intrinsic flexibility of these proteins is closely linked to their designated functions.

Simulation of general three-body interactions in a nuclear magnetic resonance ensemble quantum computer

Three-body interaction plays an important role in many-body physics, and quantum computer is efficient in simulating many-body interactions. We have experimentally demonstrated the general three-body interactions in a three-qubit nuclear magnetic resonance ensemble quantum computer. Using a nuclear magnetic resonance computer we implemented general forms of three-body interactions including σ 1 x σ 2 z σ 3 x and σ 1 x σ 2 z σ 3 y The results show good agreement between theory and experiment. We have also given a concise and practical formula for a general n-body interaction in terms of one-and two-body interactions.