Frequency Shift Of Radiation Research Articles

Theoretical calculation of “tune-out” wavelengths for clock states of Al<sup>+</sup>

In quantum optical experiments, the polarizabilities of atomic systems play a very important role, which can be used to describe the interactions of atomic systems with external electromagnetic fields. When subjected to a specific electric field such as a laser field with a particular frequency, the frequency-dependent electric-dipole (E1) dynamic polarizability of an atomic state can reach zero. The wavelength corresponding to such a frequency is referred to as the “turn-out” wavelength. In this work, the “turn-out” wavelengths for the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states of Al<sup>+</sup> are calculated by using the configuration interaction plus many-body perturbation theory (CI+MBPT) method. The values of energy and E1 reduced matrix elements of low-lying states of Al<sup>+</sup> are calculated. By combining these E1 reduced matrix elements with the experimental energy values, the E1 dynamic polarizabilities of the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states are determined in the angular frequency range of (0, 0.42 a.u.). The “turn-out” wavelengths are found at the zero-crossing points of the frequency-dependent dynamic polarizability curves for both the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> states. For the ground state 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub>, a single “turn-out” wavelength at 266.994(1) nm is observed. On the other hand, the excited state 3s3p <sup>3</sup>P<sub>0</sub> exhibits four distinct “turn-out” wavelengths, namely 184.56(1) nm, 174.433(1) nm, 121.52(2) nm, and 119.71(2) nm. The contributions of individual resonant transitions to the dynamic polarizabilities at the “turn-out” wavelengths are examined. It is observed that the resonant lines situated near a certain “turn-out” wavelength can provide dominant contributions to the polarizability, while the remaining resonant lines generally contribute minimally. When analyzing these data, we recommend accurately measuring these “turn-out” wavelengths to accurately determine the oscillator strengths or reduced matrix elements of the relevant transitions. This is crucial for minimizing the uncertainty of the blackbody radiation (BBR) frequency shift in Al<sup>+</sup> optical clock and suppressing the systematic uncertainty. Meanwhile, precisely measuring these “turn-out” wavelengths is also helpful for further exploring the atomic structure of Al<sup>+</sup>.

Multiple strategies for evaluating the uncertainty of blackbody radiation frequency shift in an optical clock

The Stark shift due to the blackbody radiation (BBR) is a crucial obstacle limiting the performance of optical clocks. Here five different methods are reported to evaluate an ytterbium (Yb) clock’s BBR shift in the same science chamber for the first time. The intercomparison shows that incorporating in-chamber temperature information can reduce the uncertainty by one order of magnitude. Notably, a simulation model is developed and optimized through calibration with in-chamber sensors, which can suppress the BBR uncertainty close to 1 × 10−18 at room temperature and provide more credible results. Moreover, the 10−19 level uncertainty is further identified by surrounding the atoms in the cryogenic environment. It is worth noting that the above results were obtained without BBR shield and external temperature control. These comprehensive evaluation results provide a valuable reference for different uncertainty requirements or building advanced optical clocks towards total uncertainty in the 10−19 region.

Conducting Polymer Switches Permit the Development of a Frequency-Reconfigurable Antenna

Conjugated polymers (CPs) undergo a wide range of reversible intrinsic property changes including electrical conductivity, electromagnetic absorption, volume, and charge mobility upon electrochemical oxidation/reduction, which has made them popular as ON/OFF organic-based switchable materials. Recent studies on the insulating-to-conductive transition within CPs have paved the way for a next generation of flexible switches that permit the creation of “dynamic” electric circuits. Here, we present an approach to a low-voltage, low-power electrochemically controllable, switchable, and printable CP-based conductive element that acts as a platform for the configuration of frequency-reconfigurable radiative antennas. We demonstrate that the DC conductivity of a soluble PEDOT derivative, PE2, film can be switched electrochemically by 4 orders of magnitude across large insulating gaps up to 15 mm within 20 s. Its integration in a DC switching element that is incorporated along the poles of a half-wave dipole antenna structure is able to generate an AC resonant frequency switch, and thus a radiation frequency shift, in the microwave (i.e., 1–2 GHz) range. This type of printable antenna fills an important need for the demand of bandwidth that is growing beyond the crowded frequency spectrum, by relying on the development of frequency-reconfigurable antenna systems capable of dynamically tuning their spectral properties when desired.

Spontaneous Frequency Shift and Phase Delay of Coupled Terahertz Radiation Mediated by the Josephson Plasmon in a Cuprate Superconductor

We examine coupling interactions used to synchronize macroscopic Josephson oscillations induced in intrinsic Josephson-junction (IJJ) mesa stacks made of a $\mathrm{Bi}2212$ single crystal. Synchronized radiations of terahertz electromagnetic (EM) waves are detected under common voltage and current bias operations of two connected mesas with close individual radiation frequencies, while uncoupled and bimodal radiations are frequently observed in two mesas with different individual radiation frequencies. Detailed observations of the polarizations of the EM waves emitted when two mesas are biased in parallel or series allow us to reveal the coupling matrix components, which include ratios of synchronized IJJs in the mesas and phase delay between the macroscopic Josephson oscillations. A frequency evolution of the phase delay implies that the coupling between the Josephson oscillations is mediated by the small amplitude Josephson plasmon inside the superconducting substrate. This finding stimulates systematic survey on polarization of EM wave emitted from synchronized multiple mesa devices in order to realize powerful terahertz emissions from superconductors.

PyCharge: An open-source Python package for self-consistent electrodynamics simulations of Lorentz oscillators and moving point charges

PyCharge is a computational electrodynamics Python simulator that can calculate the electromagnetic fields and potentials generated by moving point charges and can self-consistently simulate dipoles modeled as Lorentz oscillators. To calculate the total fields and potentials along a discretized spatial grid at a specified time, PyCharge computes the retarded time of the point charges at each grid point, which are subsequently used to compute the analytical solutions to Maxwell's equations for each point charge. The Lorentz oscillators are driven by the electric field in the system and PyCharge self-consistently determines the reaction of the radiation on the dipole moment at each time step. PyCharge treats the two opposite charges in the dipole as separate point charge sources and calculates their individual contributions to the total electromagnetic fields and potentials. The expected coupling that arises between dipoles is captured in the PyCharge simulation, and the modified radiative properties of the dipoles (radiative decay rate and frequency shift) can be extracted using the dipole's energy at each time step throughout the simulation. The modified radiative properties of two dipoles separated in the near-field, which require a full dipole response to yield the correct physics, are calculated by PyCharge and shown to be in excellent agreement with the analytical Green's function results (<0.2% relative error, over a wide range of spatial separations). Moving dipoles can also be modeled by specifying the dipole's origin position as a function of time. PyCharge includes a parallelized version of the dipole simulation method to enable the parallel execution of computationally demanding simulations on high performance computing environments to significantly improve run time. Program summaryProgram Title: PyChargeCPC Library link to program files:https://doi.org/10.17632/77d5vt43h9.1Developer's repository link:https://github.com/MatthewFilipovich/pychargeLicensing provisions: GPLv3Programming language: Python 3.7 or newerSupplementary material: Documentation is available at pycharge.readthedocs.io. The PyCharge package and its dependencies can be installed from PyPI: pypi.org/project/pychargeNature of problem: Calculating the electromagnetic fields and potentials generated by complex geometries of point charges, as well as the self-consistent simulation of Lorentz oscillators.Solution method: PyCharge calculates the individual contributions from each point charge in the system to calculate the total electromagnetic fields and potentials, and computes the dipole moment of the Lorentz oscillators at each time step by solving their governing equation of motion.Additional comments including restrictions and unusual features: The parallel simulation method is implemented using the mpi4py package [1].

Electromagnetic Scattering by Networks of High-Permittivity Thin Wires

The electromagnetic scattering from interconnections of high-permittivity dielectric thin wires with sizes smaller than (or almost equal to) the operating wavelength is investigated. A simple lumped element model for the polarization current intensities induced in the wires is proposed. The circuit elements are capacitances and inductances between the wires. An analytical expression for the induced polarization currents in terms of the magneto-quasistatic current modes is obtained. The connection between the spectral properties of the loop inductance matrix and the network's resonances is established. The number of the allowed current modes and resonances is deduced from the topology of the circuit's digraph. The coupling to radiation is also included, and the radiative frequency shifts and the quality factors are derived. The introduced concept and methods may find applications both at the microwaves and in nanophotonics.

Quantum theory of radiative decay rate and frequency shift of surface plasmon modes

In this paper we study, in the time domain, the interaction between localized surface plasmons and photons in arbitrarily shaped metal nanoparticles, by using the Hopfield approach to quantize the plasmon modes, where the electron oscillations are represented by a harmonic matter field linearly coupled to the electromagnetic radiation. The plasmon - photon coupling gives rise to dressed plasmon modes. We have found that the radiation does not induce a significant coupling among the different quasi-electrostatic plasmon modes for particles of size up to the plasma wavelength, but causes a frequency shift and an exponential decay in time of the modes. By solving the equations governing the expectation values of the plasmon creation and annihilation operators, we obtain a new closed-form full-wave expression for the decay rate and for the frequency shift of the plasmon modes. It is non-perturbative and it only depends on the surface charge distribution of the quasi-electrostatic plasmon modes. We validate the expression against the Mie theory for a nano-sphere of radius comparable to the plasma wavelength. Eventually, we investigate the decay rate and the frequency shift of the plasmon modes in isolated and interacting nanoparticle of non-canonical shape, as their size increases up to the plasma wavelength.

Plasmons in two-dimensional lattices of near-field coupled nanoparticles

We consider plasmonic metasurfaces constituted by an arbitrary periodic arrangement of spherical metallic nanoparticles. Each nanoparticle supports three degenerate dipolar localized surface plasmon (LSP) resonances. In the regime where the interparticle distance is much smaller than the optical or near-infrared wavelength associated with the LSPs, the latter couple through the dipole-dipole interaction and form collective plasmonic modes which extend over the whole metasurface. Within a Hamiltonian model which we solve exactly, we derive general expressions which enable us to extract analytically the quasistatic plasmonic dispersion for collective modes polarized within the plane and perpendicular to the plane of the metasurface. Importantly, our approach allows us not only to consider arbitrary Bravais lattices, but also non-Bravais two-dimensional metacrystals featuring nontrivial topological properties, such as, e.g., the honeycomb or Lieb lattices. Additionally, using an open quantum system approach, we consider perturbatively the coupling of the collective plasmons to both photonic and particle-hole environments, which lead, respectively, to radiative and nonradiative frequency shifts and damping rates, for which we provide closed-form expressions. The radiative frequency shift, when added to the quasistatic dispersion relation, provides an approximate analytical description of the fully retarded band structure of the collective plasmons. While it is tempting to make a direct analogy between the various systems which we consider and their electronic tight-binding equivalents, we critically examine how the long-range retarded and anisotropic nature of the dipole-dipole interaction may quantitatively and qualitatively modify the underlying band structures and discuss their experimental observability.

A Two-Channel High-Frequency Acousto-Optic Modulator

The design of a two-channel acousto-optic modulator transforming the frequency shift of optical radiation into the high-frequency amplitude modulation is presented. A large- aperture modulator with two orthogonally polarized output optical beams has been produced from a TeO2 single crystal for modulating radiation with a wavelength 0.63 µm and tested. The amplitudes of the beams are modulated at a frequency of approximately 100 MHz, and the beam modulations are in antiphase.

Static Limit and Penrose Effect in Rotating Reference Frames

We show that effects similar to those for a rotating black hole arise for an observer using a uniformly rotating reference frame in a flat space-time: a surface appears such that no body can be stationary beyond this surface, while the particle energy can be either zero or negative. Beyond this surface, which is similar to the static limit for a rotating black hole, an effect similar to the Penrose effect is possible. We consider the example where one of the fragments of a particle that has decayed into two particles beyond the static limit flies into the rotating reference frame inside the static limit and has an energy greater than the original particle energy. We obtain constraints on the relative velocity of the decay products during the Penrose process in the rotating reference frame. We consider the problem of defining energy in a noninertial reference frame. For a uniformly rotating reference frame, we consider the states of particles with minimum energy and show the relation of this quantity to the radiation frequency shift of the rotating body due to the transverse Doppler effect.

Evaluation of blackbody-radiation frequency shift in strontium optical lattice clock

The frequency shift caused by blackbody radiation is one of the dominant corrections to the evaluation of the optical lattice clock. The frequency shift of blackbody radiation is closely related to the dynamic and static correction factor, ambient temperature and atomic polarizability. The blackbody radiation shift is mainly affected by ambient temperature. During the normal operation of the strontium atom optical lattice clock, the experimental environment and other heat sources around the vacuum cavity have complicated the environment around the vacuum cavity, resulting in the fact that the external surface temperature of the vacuum cavity does not truly reflect the temperature change of the vacuum cavity. For the strontium atomic optical clock experimental apparatus of the National Time Service Center, the uncertainty and correctionof the blackbody radiation frequency shift are evaluated by the theoretical analysis, measurement of the temperature of the vacuum cavity outer surface, and software simulation. Among them, the frequency shift of black body radiation caused by strontium atom furnace, sapphire heating window, room temperature radiation entering into the vacuum cavity through the window plate, and the thermal radiation at the atomic group caused by Zeeman reducer are analyzed. Five temperature measuring points are set on the external surface of the vacuum chamber, and the temperature changes on the external surface of the vacuum chamber are monitored in real time by using the calibrated platinum resistance temperature sensor while the system is running normally. We obtain the average temperature of the five temperature measuring points. The model of vacuum cavity is established by using the SolidWorks. The method of finite element analysis is used to simulate the variation of the temperature around atom samples. We also obtain the temperature distribution around the atomic groups in the vacuum cavity. The result shows that the temperature around atoms varies with the temperature of the vacuum cavity. When the temperature of the ambient temperature changes 0.72 K, the fluctuation of the temperature around the atoms is 0.34 K. Finally, the total correction of blackbody radiation of the system is evaluated to be –2.13(1) Hz, and the correction uncertainty is about 2.4 × 10&lt;sup&gt;–17&lt;/sup&gt;.

Topological plasmons in dimerized chains of nanoparticles: robustness against long-range quasistatic interactions and retardation effects

We present a simple model of collective plasmons in a dimerized chain of spherical metallic nanoparticles, an elementary example of a topologically nontrivial nanoplasmonic system. Taking into account long-range quasistatic dipolar interactions throughout the chain, we provide an exact analytical expression for the full quasistatic bandstructure of the collective plasmons. An explicit calculation of the Zak phase proves the robustness of the topological physics of the system against the inclusion of long-range Coulomb interactions, despite the broken chiral symmetry. Using an open quantum systems approach, which includes retardation through the plasmon-photon coupling, we go on to analytically evaluate the resulting radiative frequency shifts of the plasmonic spectrum. The bright plasmonic bands experience size-dependent radiative shifts, while the dark bands are essentially unaffected by the light-matter coupling. Notably, the upper transverse-polarized band presents a logarithmic singularity where the quasistatic spectrum intersects the light cone. At wavevectors away from this intersection and for subwavelength nanoparticles, the plasmon-photon coupling only leads to a quantitative reconstruction of the bandstructure and the topologically-protected states at the edge of the first Brillouin zone are essentially unaffected.

Atomic fountain frequency standard: principle and development

The principle and development of fountain frequency standard are introduced in this paper. Fountain frequency standard is an atomic clock technology developed in recent 20 years. It is based on laser cooling technology, and realizes the trapping and projection of the cold atom medium with laser cooling technology. In the process of launching upward and falling back, the cold atom medium first completes the preparation of atomic state, then passes through the microwave cavity twice to achieve the Ramsey interaction; between the two interactions it undergoes free evolution, and finally the Ramsey interference fringes are obtained by detecting the atomic interference probability with the two-level fluorescence detection method in the detection region, and the frequency is locked with a line width of the central fringe being about 1 Hz. The stability and uncertainty of the frequency are two important indexes of the fountain frequency standard. The factors influencing the stability of the fountain clock frequency mainly are quantum projection noise and electronic noise. At present, the short term stability of the fountain clock is (10-13-10-14)τ-1/2, and the long term stability is (10-16-10-17). The frequency uncertainty of the fountain frequency standard is mainly influenced by the two-order Zeeman frequency shift, the blackbody radiation frequency shift, the cold atom collisional frequency shift, and the frequency shift relating to the microwave. The uncertainty of the fountain clock is around 10-16 currently. As a reference frequency standard, the working media of the fountain clock mainly are 133Cs and 87Rb. All international metrology institutions have been developing the fountain frequency standard, and it plays a more and more important role in establishing the coordinated universal time and the calibration of the international atomic time. In addition, the fountain frequency standards are also used to study high-precision time-frequency reference and time comparison chain, and verify basic physical theories.

Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell’s equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

Radiative frequency shifts in nanoplasmonic dimers

We study the effect of the electromagnetic environment on the resonance frequency of plasmonic excitations in dimers of interacting metallic nanoparticles. The coupling between plasmons and vacuum electromagnetic fluctuations induces a shift in the resonance frequencies (analogous to the Lamb shift in atomic physics) which is usually not measurable in an isolated nanoparticle. In contrast, we show that this shift leads to sizable corrections to the level splitting induced by dipolar interactions in nanoparticle dimers. For the system parameters which we consider in this work, the ratio between the level splitting for the longitudinal and transverse hybridized modes takes a universal form dependent only on the interparticle distance and thus is highly insensitive to the precise fabrication details of the two nanoparticles. We discuss the possibility to successfully perform the proposed measurement using state-of-the-art nanoplasmonic architectures.

An acousto-optic modulator of optical radiation at the double acoustic frequency

An acousto-optic (AO) modulator that converts a frequency shift of optical radiation into the amplitude modulation of light at the double acoustic frequency is proposed and described. A ТеО2 singlecrystal modulator mockup that was developed and tested provides the amplitude modulation of linearly polarized optical radiation at a wavelength of 0.63 μm at the double acoustic frequency, which is equal to ~82MHz.

Progress towards primary frequency standard

The cesium fountain clock as primary frequency standard is widely used in the areas, such as time-keeping system, satellite navigation, fundamental physics research, etc. The principle of operation of cesium fountain clock is introduced. The noise source and frequency shift term are ananlyzed. The major noise source influencing frequency stability are cold atom loading time, microwave phase noise related to Dick effect, and detection laser frequency noise. The major frequency bias influencing frequency uncertainty is blackbody radiation frequency shift,cold atom collision frequency shift,distributed cavity phase frequency shift and microwave leakage frequency shift.The key technique to achieve highperformance cesium fountain clock is sumerized. The application of cesium fountain clock is presented. The status of space cesium clock and future primary frequency standard of optical clock are shown.

High-accuracy measurement of the differential scalar polarizability of a 88Sr+ clock using the time-dilation effect.

We report a high-accuracy measurement of the differential static scalar polarizability Δα(0) of the 5s(2)S(1/2)-4d(2)D(5/2) transition of the (88)Sr(+) ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine Δα(0) without the need to determine the electric field. Δα(0) is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the (88)Sr(+) ion clock. The measured value of Δα(0) is -4.7938(71) × 10(-40) J m(2)/V(2). Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247,99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from 2 × 10(-17) to 8.3 × 10(-19). The revised total uncertainty of our reference standard is 1.2 × 10(-17), limited by the blackbody field evaluation. An additional benefit of the low uncertainty of Δα(0) is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

High-Accuracy Measurement of the Blackbody Radiation Frequency Shift of the Ground-State Hyperfine Transition inCs133

We report a high-accuracy direct measurement of the blackbody radiation shift of the 133Cs ground-state hyperfine transition. This frequency shift is one of the largest systematic frequency biases encountered in realizing the current definition of the International System of Units (SI) second. Uncertainty in the blackbody radiation frequency shift correction has led to its being the focus of intense theoretical effort by a variety of research groups. Our experimental measurement of the shift used three primary frequency standards operating at different temperatures. We achieved an uncertainty a factor of five smaller than the previous best direct measurement. These results tend to validate the claimed accuracy of the recently calculated values.

Hofmeister anionic effects on hydration electric fields around water and peptide

Specific ion effects on water dynamics and local solvation structure around a peptide are important in understanding the Hofmeister series of ions and their effects on protein stability in aqueous solution. Water dynamics is essentially governed by local hydrogen-bonding interactions with surrounding water molecules producing hydration electric field on each water molecule. Here, we show that the hydration electric field on the OD bond of HOD molecule in water can be directly estimated by measuring its OD stretch infrared (IR) radiation frequency shift upon increasing ion concentration. For a variety of electrolyte solutions containing Hofmeister anions, we measured the OD stretch IR bands and estimated the hydration electric field on the OD bond to be about a hundred MV∕cm with standard deviation of tens of MV∕cm. As anion concentration increases from 1 to 6 M, the hydration electric field on the OD bond decreases by about 10%, indicating that the local H-bond network is partially broken by dissolved ions. However, the measured hydration electric fields on the OD bond and its fluctuation amplitudes for varying anions are rather independent on whether the anion is a kosmotrope or a chaotrope. To further examine the Hofmeister effects on H-bond solvation structure around a peptide bond, we examined the amide I' and II' mode frequencies of N-methylacetamide in various electrolyte D(2)O solutions. It is found that the two amide vibrational frequencies are not affected by ions, indicating that the H-bond solvation structure in the vicinity of a peptide remains the same irrespective of the concentration and character of ions. The present experimental results suggest that the Hofmeister anionic effects are not caused by direct electrostatic interactions of ions with peptide bond or water molecules in its first solvation shell. Furthermore, even though the H-bond network of water is affected by ions, thus induced change of local hydration electric field on the OD bond of HOD is not in good correlation with the well-known Hofmeister series. We anticipate that the present experimental results provide an important clue about the Hofmeister effect on protein structure and present a discussion on possible alternative mechanisms.