First-order Doppler Research Articles

Preliminary sensitivity study for a gravitational redshift measurement with China’s Lunar exploration project

General relativity (GR) is a highly successful theory that describes gravity as a geometric phenomenon. The gravitational redshift, a classic test of GR, can potentially be violated in alternative gravity theories, and experimental tests on this effect are crucial for our understanding of gravity. In this paper, considering the space-ground clock comparisons with free-space links, we discuss a high-precision Doppler cancellation-based measurement model for testing gravitational redshift. This model can effectively reduce various sources of error and noise, reducing the influences of the first-order Doppler effect, atmospheric delay, Shapiro delay, etc. China’s Lunar Exploration Project (CLEP) is proposed to equip the deep-space H maser with a daily stability of 2×10−15 , which provides an approach for testing gravitational redshift. Based on the simulation, we analyze the space-ground clock comparison experiments of the CLEP experiment, and simulation analysis demonstrates that under ideal condition of high-precision measurement of the onboard H-maser frequency offset and drift, the CLEP experiment may reach the uncertainty of 3.7×10−6 after a measurement session of 60 days. Our results demonstrate that if the issue of frequency offset and drift is solved, CLEP missions have a potential of testing the gravitational redshift with high accuracy.

Doppler-free spectroscopy of an atomic beam probed in traveling-wave fields

The authors propose and demonstrate a method for precision spectroscopy of atoms in a beam using two sequential rather than simultaneous laser pulses, thereby overcoming systematic challenges associated with standing-wave beams that plague other methods. Their results show that this method can effectively suppress the first-order Doppler effect and reduce systematic uncertainty.

Improved ionization potential of calcium using frequency-comb-based Rydberg spectroscopy

We report new frequency-comb-based measurements of Ca Rydberg energy levels. Counter-propagating laser beams at 390 nm and 423 nm excite Ca atoms from the $4s^2~^1\mbox{S}_0$ ground state to $4sns~^1\mbox{S}_0$ Rydberg levels with $n$ ranging from 40 to 110. Near-resonant two-photon two-color excitation of atoms in a thermal beam makes it possible to eliminate the first-order Doppler shift. The resulting lineshapes are symmetric and Gaussian. We verify laser metrology and absolute accuracy by reproducing measurements of well-known transitions in Cs, close to the fundamental wavelengths of our frequency-doubled ti:sapphire lasers. From the measured transition energies we derive the ionization potential of Ca, $E_{\rm IP} = 1, 478, 154, 283.42 \pm 0.08 \mbox{(statistical)} \pm 0.07 \mbox{(systematic)}$ MHz, improving the previous best determination by a factor of 11.

First-Order Ocean Surface Cross Section for Shipborne Bistatic HFSWR: Derivation and Simulation

A bistatic high-frequency surface wave radar (HFSWR) with both receiving and transmitting stations placed on different ships (platforms) is a new radar system and referred to as shipborne bistatic HFSWR. In this paper, a first-order ocean surface cross section of shipborne bistatic HFSWR was derived. The first-order cross-section models for three different cases, i.e., ships moving with uniform, periodic, and hybrid motion states, respectively, are presented. The corresponding first-order Doppler spectra were simulated, and the spread width of the first-order spectrum was investigated. The simulation results show that the characteristics of the first-order spectrum are similar to those of a shore-based bistatic HFSWR when the transmitting and receiving platforms move in opposite directions. The first-order spectral spread width in the case of platforms with opposite directions is much smaller than that in the case of platforms with the same direction. This finding is useful for reducing HFSWR first-order spectrum spread due to platform motion, thus improving the target detection performance of the shipborne bistatic HFSWR. In addition, periodic oscillation motion of both platforms will cause complex motion-induced peaks in the first-order spectrum, which may be detrimental to target detection and ocean remote sensing. These results have important implications for the application of shipborne bistatic HFSWR.

Continuous operation of a bicolor thulium optical lattice clock

We discuss the extension of a recently proposed method based on continuous spectroscopy of 88Sr atoms trapped in a moving optical lattice [Appl. Phys. Express, 14, 072 006 (2021)] to the operation of bicolor thulium optical clocks. Simultaneous interrogation of two clock transitions at 1.14 μm and build-up of a synthetic frequency provides a straightforward way to significantly suppress the first-order Doppler shift and cancel out the second-order Zeeman shift, the latter being one of the major sources of uncertainty in the originally proposed 88Sr setup. In our configuration, the total systematic frequency shift is 4 × 10−16 and instability is at or lower than 10−18 after 1 h of integration.

Wideband Generalized Beamspace Modulation (wGBM) for mmWave Massive MIMO Over Doubly-Selective Channels

Generalized beam modulation (GBM) is a recently proposed spectrum efficiency (SE)-enhanced index modulation (IM) scheme for narrowband millimeter wave (mmWave) massive multiple-input multiple-output (mMIMO) systems with hybrid transceivers. Unlike most existing fully-digital IM techniques whose application to wideband channels is straightforward after adopting the orthogonal frequency division multiplexing (OFDM) technique, extending GBM from the narrowband to wideband channels is quite challenging. The reason is that the per-subcarrier process in hybrid OFDM systems is no longer independent across individuals as all subcarriers share a common analog beamformer. Hence, the designed wideband GBM (wGBM) has to be compatible with hybrid OFDM systems while maintaining the SE-enhanced merit of GBM. Towards this objective, a symbol-based instead of the prevalent subcarrier-based paradigm is applied to guide wGBM design. To avoid the high detection complexity in large-scale OFDM systems, we devise a low-complexity detector by transforming the complicated symbol (block) detection into the manageable subcarrier (sub-block) detection. Finally, a simple first-order Doppler compensator is carefully designed to enhance the robustness of wGBM against Doppler. Both theoretical analyses and numerical simulations have been carried out to demonstrate the superiority of wGBM over existing alternatives in terms of error performance and energy efficiency.

Proton–electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime

Optical spectroscopy in the gas phase is a key tool to elucidate the structure of atoms and molecules and of their interaction with external fields. The line resolution is usually limited by a combination of first-order Doppler broadening due to particle thermal motion and of a short transit time through the excitation beam. For trapped particles, suitable laser cooling techniques can lead to strong confinement (Lamb-Dicke regime, LDR) and thus to optical spectroscopy free of these effects. For non-laser coolable spectroscopy ions, this has so far only been achieved when trapping one or two atomic ions, together with a single laser-coolable atomic ion [1,2]. Here we show that one-photon optical spectroscopy free of Doppler and transit broadening can also be obtained with more easily prepared ensembles of ions, if performed with mid-infrared radiation. We demonstrate the method on molecular ions. We trap approximately 100 molecular hydrogen ions (HD$^{+}$) within a Coulomb cluster of a few thousand laser-cooled atomic ions and perform laser spectroscopy of the fundamental vibrational transition. Transition frequencies were determined with lowest uncertainty of 3.3$\times$10$^{-12}$ fractionally. As an application, we determine the proton-electron mass ratio by matching a precise ab initio calculation with the measured vibrational frequency.

Detecting High-Speed Maneuvering Targets by Exploiting Range-Doppler Relationship for LFM Radar

This paper considers the problem of high-speed maneuvering target detection, which involves the processing of complex range migration (RM) and Doppler frequency migration (DFM) within the coherent processing interval (CPI). By exploiting the coupling relationship between the range frequency and the Doppler frequency, a detection algorithm is proposed for high-speed maneuvering targets. After the range compression, approximate 2-D range-frequency and Doppler-frequency expressions are derived according to the principle of stationary phase (POSP) and series inversion extension. The mathematical range-Doppler frequency relationships are then exploited to search the target's first-order motion parameters and Doppler ambiguity numbers within a predetermined parameter range, and formulate the corresponding new data from the original 2-D data matrix. Finally, Fourier transform and constant false-alarm rate (CFAR) detector are further applied to detect the targets. Simulation results show that the proposed algorithm has low complexity requirements and is suitable for low signal-to-noise ratio (SNR) scenarios. Moreover, it is not sensitive to the motion order of targets.

Apsidal Precession Effects on the Lunar-Based Synthetic Aperture Radar Imaging Performance

There have been considerable interests in the lunar-based synthetic aperture radar (LBSAR) for monitoring large-scale geoscience phenomena. However, the signal distortions given rise by lunar orbital perturbations, especially the apsidal precession, are particularly severe in the LBSAR. The apsidal precession effects can induce a coordinate drift of the LBSAR, which can further lead to the variation in the range history of the LBSAR. As a result, LBSAR’s image performance might be affected. In this letter, we thoroughly investigate whether the apsidal precession effects cause the phase decorrelation in the signal of the LBSAR, and how such effects impact the LBSAR imaging. The theoretical result shows that the impact of the lunar apsidal precession mainly results in the first-order and second-order Doppler errors, which further influence the geometric location and focusing quality along the azimuth direction. Numerical simulations using the point target response show good consistency with the theoretical analysis. To this end, the lunar apsidal precession effects deserve special care in the LBSAR for high imaging quality.

Pre-Compensation-Assisted Generalized Beam Index Modulation (PC-GBIM) for mmWave Massive MIMO Over Doubly Selective Channels

To better serve future vehicular network, we judiciously design an anti-Doppler index modulation termed as pre-compensation assisted generalized beam index modulation (PC-GBIM) for wideband mmWave massive multiple-input multiple-output (mMIMO) systems. The proposed PC-GBIM design comprises two key elements. First, we generalize the existing beam index modulation (BIM) from the hybrid narrowband to hybrid wideband systems and from activating single beam to activating multiple beams. Secondly, an effective first-order Doppler pre-compensator is introduced to assist index modulation, such that the originally complicated block-based maximum likelihood (ML) detection degenerates into the simple subcarrier-based ML detection. Both the theoretical analyses and numerical simulations have been made and demonstrate the superiority over existing alternatives in doubly-selective channels.

Sub-ppb Measurement of a Fundamental Band Rovibrational Transition in HD.

We report a direct measurement of the 1-0 R(0) vibrational transition frequency in ground-state hydrogen deuteride (HD) using infrared-ultraviolet double resonance spectroscopy in a molecular beam. Ground-state molecules are vibrationally excited using a frequency comb referenced continuous-wave infrared laser, and the excited molecules are detected via state-selective ionization with a pulsed ultraviolet laser. We determine an absolute transition frequency of 111 448 815 477(13)kHz. The 0.12 parts-per-billion (ppb) uncertainty is limited primarily by the residual first-order Doppler shift.

Rabi spectroscopy of the clock transition in thulium atoms in a one-dimensional optical lattice

The clock transition at a wavelength of 1.14 μm in thulium atoms in an optical lattice in the Lamb – Dick regime is studied. The capture of thulium atoms makes it possible to suppress completely both the transition broadening due to the first-order Doppler effect and the shift of the transition frequency caused by the recoil effect. The excitation spectra of sideband oscillation frequencies and Rabi oscillations of population between the clock transition levels upon resonance excitation are investigated.

Wave Height Field Extraction From First-Order Doppler Spectra of a Dual-Frequency Wide-Beam High-Frequency Surface Wave Radar

Ocean wave height measurement using a wide-beam high-frequency surface wave radar (HFSWR) remains challenging due to its poor spatial resolution, which significantly limits the application of such compact systems. In this article, a novel method for wave height field extraction from the first-order Doppler spectra of a dual-frequency wide-beam radar is proposed. A model relating significant wave height to the ratio of the first-order spectral powers associated with two radar frequencies is put forward and studied numerically. Through theoretical analysis and experimental validation, it is confirmed that the first-order Doppler peaks of two radar frequencies have arisen from an approximately same direction of arrival (DOA), and their amplitudes are also affected by a similar wave directional spreading. Hereby, an algorithm combining beamforming and direction finding is developed to determine the spatial distribution of the first-order spectral power ratio and derive the significant wave height field. Finally, experimental results are given to verify the algorithm. The radar-derived wave height field agrees well with that obtained using a numerical wave model. Furthermore, the radar-measured wave heights are compared with the data collected by two buoys at the distances of 12.7 and 73 km, respectively. The comparison shows that the corresponding root-mean-square errors are 0.3 and 0.5 m and the correlation coefficients are 0.85 and 0.88, respectively.

Measuring Ocean Surface Wind Field Using Shipborne High-Frequency Surface Wave Radar

Extraction of ocean surface wind field from data collected by shipborne high-frequency surface wave radar (HFSWR) is an ongoing challenge because of the inherent directional ambiguity and the effect of complicated platform motion on radar Doppler spectra. Here, a method for extracting the wind direction and speed from the spreading first-order radar Doppler spectra is first presented. First, the mathematical model of the wind direction versus a variable spreading parameter is developed. Moreover, based on the spreading characteristic of the first-order spectra, an approach for simultaneously determining the unambiguous wind direction and the unique spreading parameter with a single receiving antenna is presented. Furthermore, the relationship between the wind speed and the spreading parameter is derived on the basis of the relationship between the drag coefficient and the spreading parameter, and the wind speed can be determined. Therefore, the wind field of ocean area covered by shipborne HFSWR can be measured by sequentially exploiting the presented method, which is more beneficial for shipborne HFSWR because of smaller installation space and less cost. Simulation results and discussions of basic applications show the feasibility of wind field measurement in shipborne HFSWR. Experimental results validate the presented method and evaluate the detection accuracy and distance limit. The range for wind field measurement is up to 120 km, which is the range for which the signal-to-noise ratio typically exceeds about 11 dB in the relevant first-order portions of the backscatter spectra. Comparisons between the radar-measured and forecasting or buoy-measured results show good agreement.

Joint parameter estimation method for multiple manoeuvring targets with high speed

In this study, a joint parameter estimation method is proposed to realise the long-time coherent integration and estimate the motion parameters for multiple weak manoeuvring targets with high speed and acceleration, involving the first-order range migration (FRM), second-order RM (SRM) and Doppler frequency migration. In the proposed method, the effect of the target's Doppler spectrum spanning over two neighbouring pulse repetition frequency bounds on first-order keystone transform (FKT) is first analysed and a Doppler shifting function is constructed to solve this problem. Then, FKT and the velocity ambiguity factor searching are performed to eliminate the FRM. After that, SRM is removed through the phase compensation function related to acceleration. Finally, the Lv's distribution is applied to realise the coherent integration and obtain the estimates of velocity and acceleration. The numerical experiments using both simulated and real data demonstrate that the proposed method can achieve close detection and estimation performance with much lower computational complexity, compared with the generalised radon-Fourier transform. Moreover, it can estimate the motion parameters of the targets without knowing any prior knowledge of targets and obtain good coherent integration performance in low signal-to-noise ratio scenarios.

Simulation study of first-order sea clutter Doppler spectra for shipborne high frequency radar via hybrid sky-surface wave propagation

The Doppler spectra of first-order sea echo are studied in a high frequency radar system for hybrid sky-surface wave propagation when the receiving antenna array is mounted on a shipborne platform. Here, the platform motion and ionosphere perturbed phases are assumed to be the key factors resulting in the sea clutter spectral fluctuation. Based on the received first-order electric field equation, a closed form of cross sections is derived to account for the ship motion influence. It is shown numerically that the resultant clutter spectra exhibit significant discrepancies with different system operating parameters and platform motion states. In addition, the phase path variations along the inhomogeneous ionosphere are considered by dividing the ionosphere into the quiescent and distorted components. Such manipulation makes it feasible to simulate the phase fluctuations with a method associated with deterministic and stochastic models. Eventually, simulation results for a composite modulation taking account of both effects are provided. Compared with the spread Doppler spectra due to the platform motion, the attached ionosphere perturbed phases will further split and leak the spectral energy, which may bring in difficulties for the applications in remote sensing and target detection.

Spectroscopy of the hydrogen1S−3Stransition with chirped laser pulses

We identify a systematic present in two-photon direct frequency comb spectroscopy (DFCS) which is a result of chirped laser pulses and is amanifestation of the first-order Doppler effect. We carefully analyze this systematic and propose methods for its mitigation within the context of our measurement of the hydrogen 1S-3S transition. We also report on our determination of the absolute frequency of this transition, which is comparable to a previous measurement using continuous-wave spectroscopy [O. Arnoult et al., Eur. Phys. J. D 60, 243 (2010)], but was obtained with a different experimental method.

Polarization dependence of n = 2 positronium transition rates to Stark-split n = 30 levels via crossed-beam spectroscopy

We produce Rydberg Ps by a two-step laser excitation from and from to states of principal quantum level that are Stark split by a motionally induced electric field. Our measurements are largely free of first-order Doppler shifts such that we are able to investigate the impact of laser polarization on the population of the closely spaced Stark levels. We find a variation in the distribution that is primarily dependent on the IR laser polarization with respect to the direction of the motionally induced electric field. With the IR light polarized parallel to the electric field F, the ratio of excitation probability to the levels of maximal Stark splitting compared to that of excitation to the states of minimal Stark splitting is found to be 3.37 ± 0.51, whereas with the IR light polarized perpendicular to F, the excitation ratio is 0.87 ± 0.64. Our results agree with those of Wall et al (2015 Phys. Rev. Lett. 114 173001) obtained with n = 11 and will be useful in the preparation of high-n states of Ps for a variety of experiments, including measuring the interaction of Ps with gravity, in precision time-of-flight (TOF) energy spectroscopy, and precision optical spectroscopy of Ps.

Doppler-corrected Balmer spectroscopy of Rydberg positronium

The production of long-lived Rydberg positronium (Ps) and correction for Doppler shifts in the excitation laser frequencies are crucial elements of proposed measurements of the gravitational freefall of antimatter and for precision measurements of the optical spectrum of Ps. Using a two-step optical transition via $2P$ levels, we have prepared Ps atoms in Rydberg states up to the term limit. The spectra are corrected for the first-order Doppler shift using measured velocities, and the Balmer transitions are resolved for $15\ensuremath{\le}n\ensuremath{\le}31$. The excitation signal amplitude begins to decrease for $ng50$, consistent with the onset of motional electric field ionization in the 3.5-mT magnetic field at the Ps formation target.

Heating rates and ion-motion control in aY-junction surface-electrode trap

We measure ion heating following transport throughout a Y-junction surface-electrode ion trap. By carefully selecting the trap voltage update rate during adiabatic transport along a trap arm, we observe minimal heating relative to the anomalous heating background. Transport through the junction results in an induced heating between 37 and 150 quanta in the axial direction per traverse. To reliably measure heating in this range, we compare the experimental sideband envelope, including up to fourth-order sidebands, to a theoretical model. The sideband envelope method allows us to cover the intermediate heating range inaccessible to the first-order sideband and Doppler recooling methods. We conclude that quantum information processing in this ion trap will likely require sympathetic cooling in order to support high fidelity gates after junction transport.