Observation of Doppler sidebands of a laser-cooled Ca+ ion by using a low-temperature-operated laser diode

1/2 -D_5/2 electric-quadrupole-allowed transitions of a laser-cooled Ca⁺ ion in a small rf trap. The electron shelving method was used to measure the absorption spectrum of the electric-quadrupole-allowed transitions, and the motional sidebands due to the secular motion of the ion in the harmonic potential well of the rf trap were completely resolved. The effective temperature of the ion, estimated by comparing the observed sideband intensities with the theoretical ones, was less than 4.4 mK. This result is in good agreement with that obtained from the analysis of the linewidth measurement. Received: 18 March 1998     

Dual-frequency pulsed laser with an accurate gigahertz-beat note

We report a novel nanosecond pulsed laser with a highly accurate gigahertz beat that is realized by injection locking to gigahertz sidebands generated from a single-frequency cw laser radiation using a Mach-Zehnder type intensity modulator. It is shown from both the spectrum of the pulsed sidebands and their coherent beat in the time domain that the frequency accuracy of an rf oscillator driving the intensity modulator is reflected in the injection-locked nanosecond pulse with an intense peak power of the megawatt class.     

Radio frequencies in EPR: Conventional and advanced use

This mini-review focuses on various aspects of the application of radio frequency (rf) irradiation in electron paramagnetic resonance (EPR). The development of the electron-nuclear double resonance (ENDOR) technique is briefly described, and we highlight the use of circularly polarized rf fields and pulse ENDOR methodology in one- and two-dimensional experiments. The capability of pulse ENDOR at Q-band is illustrated with interesting experimental examples. Electron spin echo envelope modulation effects induced by an rf field in liquid samples demonstrate another role which rf fields can play. Technical achievements in the design of ENDOR resonators are illustrated by the example of a bridged loop-gap resonator. Finally, the influence of longitudinal rf fields on the dynamics of EPR transitions is explained using a dressed spin resonance treatment.     

59Co chemical shift anisotropy and quadrupole coupling for K3Co(CN)6 from MQMAS and MAS NMR spectroscopy

59Co triple-quantum (3Q) MAS and single-pulse MAS NMR spectra of K3Co(CN)6 have been obtained at 14.1 T and used in a comparison of these methods for determination of small chemical shift anisotropies for spin I = 7/2 nuclei. From the 3QMAS NMR spectrum a spinning sideband manifold in the isotropic dimension with high resolution is reconstructed from the intensities of all spinning sidebands in the 3QMAS spectrum. The chemical shift anisotropy (CSA) parameters determined from this spectrum are compared with those obtained from MAS NMR spectra of (i) the complete manifold of spinning sidebands for the central and satellite transitions and of (ii) the second-order quadrupolar lineshapes for the centerband and spinning sidebands from the central transition. A good agreement between the three data sets, all of high precision, is obtained for the shift anisotropy (delta(sigma) = delta(iso) - delta(zz)) whereas minor deviations are observed for the CSA asymmetry parameter (eta(sigma)). The temperature dependence of the isotropic 59Co chemical shift has been studied over a temperature range from -28 to +76 degrees C. A linear and positive temperature dependence of 0.97 ppm/degree C is observed.     

A low-cost implementation of EPR detection in a dissolution DNP setup

The implementation of electron paramagnetic resonance (EPR) detection in a low-temperature dissolution dynamic nuclear polarization (DNP) setup is presented. Using a coil oriented parallel to the static magnetic field, the change of the longitudinal magnetization of free radicals is measured upon resonant irradiation of an amplitude or frequency modulated microwave (mw) field. The absorption EPR spectrum is measured if the amplitude of the mw field is modulated, whilst the first derivative of the spectrum is obtained with frequency modulation. Using a burst of pulses, it is also possible to perform pump-probe experiments such as saturation-recovery or electron-electron double resonance experiments. Furthermore, the magnetization could be monitored in a time-resolved manner during amplitude modulation, thus making it possible to record its transient as it is approaching an equilibrium value. Experimental examples are shown with frozen solutions of trityl radical and TEMPO, two commonly used radicals for dissolution DNP experiments.     

贝塞尔函数的近似计算在调频制中的应用

一.引言 在近代通讯所用的讯号中,一般应进行某一定方式的调制,即在发送的高频电流瞬时值 i=Imsin(ω_1t+φ) (1)中,改变其中所包含的三个量(振幅Im,相角φ中或频率ω)之一;即是说要使发送的电流的振幅、相角或频率随着调制电流(所需要传送的低频讯号)而变,此三种方式分别称为调幅、调相及调频。     

High-frequency magnetic modulation of recoilless gamma radiation of57Fe

Radio-frequency (rf) magnetic modulation has been used to generate sidebands in⁵⁷Fe Mössbauer spectra of Fe_0.18Ni_0.82 Permalloy foils which have the smallest constant of magnetostriction among Fe?Ni alloys. Sidebands in Mössbauer spectra were observed at 30 MHz and 55 MHz. In addition to the generation of sidebands, the external rf magnetic field was found to alter the line positions of the original six line spectrum. An attempt was made to study acoustic vibrations in the foil by means of X-ray diffraction. The rf magnetic field caused changes in diffraction peak intensities and positions. It was found that X-ray diffraction can be used to study the amplitude of acoustic vibrations in Permalloy foils.     

The rf stimulation of amorphous metals

The effect of the rf modulation of the Mössbauer gamma radiation (rf sidebands) and the effect of the fast relaxation of the magnetic hyperfine field induced by the rf field (rf collapse) are described. The coexistence and separation of these effects is discussed. The rf collapse of the magnetic hyperfine structure allows a direct observation of the quadrupole interaction in ferromagnetic amorphous metals providing the method for studying the short range order. Examples of FeSiB, FeNiSiB, FeCoSiB and FeB are discussed with respect to structural models. The effect of radiofrequency enhanced crystallization of amorphous metals and its relation to rf sidebands is demonstrated.     

Mössbauer experiments in radio frequency magnetic fields: A method for investigations of nanostructured soft magnetic materials

We apply radio frequency (rf) effects, the sideband and the collapse effect, in the investigation of magnetic properties of nanostructured ferromagnetic alloys. We use the relative intensity of the sidebands in comparison to the central part of the spectrum to determine the relative samples' magnetostriction following successive preparation steps. Recent investigations of nanostructured soft ferromagnetic alloys in rf fields led to the discovery that the collapse in the Mössbauer spectra can become selective and partial. It means that the magnetisation reversal is not fast enough and varies differently in the various phases of the alloy. The application of rf magnetic fields then causes new kinds of rf forced relaxation‐type Mössbauer spectra. Experimental results and basic steps in the theoretical understanding are also presented.     

Two-photon nutation excited in a two-level spin system by microwave and RF fields

Two-photon transient nutation is observed in a two-level spin system (E′₁ centers in crystalline quartz) using a transverse microwave field and a linearly polarized rf field oriented along a static magnetic field in the electron paramagnetic resonance. Nutation is excited when the sum of the energies of a microwave photon and a rf photon is equal to the energy difference between two spin states. The two-photon nature of nutation is confirmed by measuring its frequency as a function of the amplitude and frequency of the rf field as well as the amplitude of the microwave field. The amplitude of the effective field of two-photon transitions is measured. It is shown that the decay rate of two-photon nutation is close to the decay rate for one-photon nutation and is determined by the spin-spin interaction between E′₁ centers.     

Frequency-octupled phase-coded signal generation based on carrier-suppressed high-order double sideband modulation

An approach for photonic generation of a frequency-octupled phase-coded signal based on carrier-suppressed high-order double sideband modulation is proposed and experimentally demonstrated. The key component of the scheme is an integrated dual-polarization quadrature phase shift keying modulator, which is used to achieve the carrier-suppressed high-order double sideband modulation. At the output of the modulator, two fourth-order optical sidebands are generated with the optical carrier suppressed. After that, a Sagnac loop incorporating a fiber Bragg grating and a phase modulator is employed to separate the two optical sidebands and phase modulate one sideband with a binary coding signal. The approach features large carrier frequency tuning range for the generated phase-coded signal from several megahertz to beyond the W-band. A proof-of-concept experiment is carried out. The 2 Gbit/s phase-coded signals with frequencies of 16.48, 21.92, and 29.76 GHz are generated.     

Applications of the CSA-amplified PASS experiment

The recently reported CSA-amplified PASS experiment correlates the spinning sidebands at the true spinning frequency omega(r) with the spinning sidebands that would be obtained at the effective spinning frequency omega(r)/N, where N is termed the scaling factor. The experiment is useful for the measurement of small chemical shift anisotropies, for which slow magic-angle spinning frequencies, required to measure several spinning sidebands, can be unstable. We have experimentally evaluated the reliability of this experiment for this application. In particular we have demonstrated that large scaling factors of the order of N=27 may be used, whilst still obtaining accurate chemical shift sideband intensities at the effective spinning frequency from the F(1) projection. Moreover, the sideband intensities are accurately obtained even in the presence of significant pulse imperfections. A second application of the CSA-amplified PASS experiment is the measurement of the chemical shift anisotropy of sites that experience homonuclear dipolar coupling, as may be found in uniformly labelled biological molecules, or for nuclei with a high natural abundance. The effects of homonuclear dipolar coupling on CSA-amplified PASS spectra has been investigated by numerical simulations and are demonstrated using uniformly (13)C enriched l-histidine monohydrochloride monohydrate.     

“Unusual” lines observed in low-frequency cw ENDOR of photoexcited triplet state molecules: the primary donor triplet in photosynthetic reaction centers as an example

The origin of frequently observed “negative” (opposite phase) ENDOR lines in the low-frequency region of triplet state ENDOR spectra is explained in terms of microwave hole burning and RF modulation phenomena. From this, a new method of detecting burnt side holes in EPR spectra is derived which is based on cw ENDOR instrumentation. The method uses the modulation satellites that are induced by a longitudinal RF field component and appear around any EPR line, including burnt holes (“negative” lines). The longitudinal RF field was generated by a coil oriented parallel to the external field, but a longitudinal component of the RF field also exists in most conventional ENDOR spectrometers because of slight misalignments of the ENDOR coil generating the transversal RF field. The lines it induces in the low-frequency part of ENDOR spectra are generally considered as artifacts. It is shown, however, that RF induced modulation satellites provide valuable information concerning the lines distant from the spectral position in the EPR spectrum chosen for ENDOR observation. This allows one to record the pattern of side holes burnt by microwave saturation through forbidden transitions that carries information about ENDOR frequencies comparable to what can be extracted from ESEEM experiments. Such comparability is demonstrated for examples of nitrogen ENDOR of photoexcited triplet states of the primary donor in photosynthetic reaction centers and related compounds.     

Multiplication of qubits in a doubly resonant bichromatic field

Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.     

The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers

This paper is concerned with modulation and beat detection for sinusoidal carriers. In the first experiment, temporal modulation transfer functions (TMTFs) were measured for carrier frequencies between 1 and 10 kHz. Modulation rates covered the range from 10 Hz to about the rate equaling the critical bandwidth at the carrier frequency. In experiment 2, TMTFs for three carrier frequencies were obtained as a function of the carrier level. In the final experiment, thresholds for the detection of either the lower or the upper modulation sideband (beat detection) were measured for "carrier" frequencies of 5 and 10 kHz, using the same range of modulation rates as in experiment 1. The TMTFs for carrier frequencies of 2 kHz and higher remained flat up to a modulation rate of about 100-130 Hz and had similar values across carrier frequencies. For higher rates, modulation thresholds initially increased and then decreased rapidly, reflecting the subjects' ability to resolve the sidebands spectrally. Detection thresholds generally improved with increasing carrier level, but large variations in the exact level dependence were observed, across subjects as well as across carrier frequencies. For beat rates up to about 70 Hz (at 5 kHz) and 100 Hz (at 10 kHz), beat detection thresholds were the same for the upper and the lower sidebands and were about 6 dB higher than the level per sideband at the modulation-detection threshold. At higher rates the threshold for both sidebands increased, but the increase was larger for the lower sideband. This reflects an asymmetry in masking with more masking towards lower frequencies. Only at rates well beyond the maximum of the TMTF did detection for the lower sideband start to be better than that for the upper sideband. The asymmetry at intermediate frequency separations can be explained by assuming that detection always takes place in filters centered above the stimulus spectrum. The shape of the TMTF and the beat-detection data reflects a limitation in resolving fast amplitude variations, which must occur central to the inner-ear filtering. Its characteristic resembles that of a first-order low-pass filter with a cutoff frequency of about 150 Hz.     

Photon Generation Scheme of 32-Fold Millimeter-Wave Signal Based on Mach-Zehnder Modulator

This paper proposes a 32-tupling frequency millimeter-wave (MMW) filter-free system based on four Mach-Zehnder Modulators (MZM) connected in parallel and cascaded with a simple radio-fiber (RoF) link structure. The four MZMs are all at the maximum transmission point (MATP), and the radio frequency (RF) driving voltage phase difference between MZMs is π /2. The center carrier is suppressed by using an optical attenuator (OATT) and an optical phase shifter (OPS). Two parallel MZMs can generate ±8th order and ±12th order optical sidebands, and the ±4th order optical sidebands can be suppressed by adjusting the modulation index m of the MZM, using cascaded two dual-parallel MZMS(DPMZM) and the phase difference of the RF signal source is π/4 to generate ±16th order optical sidebands. The theoretical analysis and simulation experiments are performed for the scheme proposed in this paper. The results show that the simulated and theoretical values of the optical sideband suppression ratio (OSSR) for ±16th order optical sideband signals are 60.02 and 59.96 dB, respectively, and the simulated and theoretical values of the RF sideband suppression ratio (RFSSR) for the 32-tupling MMW signal are 56.34 and 53.94 dB, respectively.     

Quantum photon emission from a moving mirror in the nonperturbative regime

We consider the coupling of the electromagnetic vacuum field with an oscillating perfectly-reflecting mirror in the nonrelativistic approximation. As a consequence of the frequency modulation associated to the motion of the mirror, low frequency photons are generated. We calculate the photon emission rate by following a nonperturbative approach, in which the coupling between the field sidebands is taken into account. We show that the usual perturbation theory fails to account correctly for the contribution of TM-polarized vacuum fluctuations that propagate along directions nearly parallel to the plane surface of the mirror. As a result of the modification of the field eigenfunctions, the resonance frequency for photon emission is shifted from its unperturbed value.     

Nonlinear ultrasonic wave modulation for online fatigue crack detection

This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a ‘pumping’ signal, and the higher frequency input is referred to as a ‘probing’ signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.     

Coherent Raman beats associated with superhyperfine structure in ruby

Coherent Raman beats associated with superhyperfine structure (shfs) due to Cr-Al interaction were observed in ruby. The rf modulated Stark field was used to create coherences between shfs sublevels under the irradiation with a cw ruby laser. From the beat frequencies high resolution spectra of shfs with width (HWHM) of about 10 kHz were obtained in the frequency range from about 4.5 to 6.5 MHz. The utility of phase sensitive detection technique combined with rf Stark modulation was demonstrated. The observed spectra were compared with the theoretical ones.     

Frequency modulation of the 6.2 keV Mössbauer states of181Ta

Mössbauer sidebands up to the first order from a single parent line have been produced by subjecting a non magnetic W(¹⁸¹W) Mössbauer source to a strong oscillating magnetic field of up to 230 Oe amplitude and a frequency of about one megahertz. The sidebands positions and intensities agree very well with theory, which is based on a periodic time-dependent interaction of the magnetic field with the nuclear magnetic moments of ground and excited states, respectively. From the sideband intensity ag-factor ratio ofg _e /g _g =1.75(6) was derived.