Spin Precession Frequency Research Articles

Analytical estimations of the chromaticity and corrections to the spin precession frequency in weak focusing magnetic storage rings

Understanding beam and spin dynamics are fundamental in accelerator-based experiments concerning polarized beams. And there has been growing interest in having more precise estimations of the beam and spin dynamics variables, as more high precision particle physics experiments in the intensity frontier appear. This paper provides analytical estimations of some of the important variables such as beam transverse chromaticities and corrections to the spin precession frequency in the simplest type of particle accelerator: a circular magnetic storage ring with weak vertical focusing. We attempt to precisely obtain the next order approximations from the small betatron oscillations or the momentum dispersion, verified by high precision spin tracking simulation. We also discuss a potential way to suppress the corrections to the spin precession frequency, which relevant experiments may find beneficial.

Nuclear-induced frequency focusing and Overhauser field distributions in periodically pumped gallium arsenide

Periodic optical pumping of semiconductor systems like gallium arsenide grants insight into the spin dynamics and coupling of electrons and nuclei. Nuclear-induced frequency focusing occurs when spin-polarized nuclei alter the Larmor spin precession frequency of the electrons to approach discrete values. These discrete values are integer or half-integer multiples of a quantity that is proportional to the repetition rate of the optical pulses. In earlier work, we presented a numerical model based on the optical Stark effect that captures the interplay of electron and nuclear spins in bulk gallium arsenide. In this paper, we report the observation of nuclear-induced frequency focusing in our material and show that this behavior can help to explain the peak deformations that we observe to persist in subsequent peaks in a magnetic-field scan measurement of Kerr rotation when the field scan is paused for an extended time interval. We demonstrate that extending our model to account for a distribution of electron spins with different Overhauser fields allows us to reproduce these observations as well as additional phenomena, including changes in Kerr rotation amplitude, from our previous work.

Room-temperature spin–orbit magnetic fields in slightly misoriented (110) InGaAs/InAlAs multiple quantum wells

Spin–orbit (SO) magnetic fields caused by the Dresselhaus SO interaction in slightly misoriented (110) InGaAs/InAlAs quantum wells (QWs) are investigated using the time-resolved and spatially resolved optical Kerr rotation technique. The Dresselhaus SO magnetic field is directed along the in-plane in the (001) QWs and along the out-of-plane in the (110) QWs. On the contrary, in QWs grown on a slightly misoriented (110) substrate, the out-of-plane and in-plane components of the Dresselhaus SO magnetic field coexist. In this study, the strong out-of-plane and the in-plane SO magnetic fields peculiar to the misoriented (110) InGaAs QWs are revealed at room temperature by analyzing spatially resolved diffusion-driven spin precession dynamics with a diagonally applied external magnetic field. Based on the scan position dependence of the spin precession frequency induced by the SO magnetic field, the simultaneous observations of the out-of-plane and the in-plane SO magnetic fields are achieved and Dresselhaus SO parameter is extracted to be 1.9×10−12 eV m. This value accounts for the scan position dependencies with various magnetic fields and reveals the reliability of the extracted SO parameter.

Revisiting 129Xe electric dipole moment measurements applying a new global phase fitting approach

By measuring the spin precession frequencies of polarized 129Xe and 3He, a new upper limit on the 129Xe atomic electric dipole moment (EDM) was reported in Sachdev et al (2019 Phys. Rev. Lett. 123, 143003). Here, we propose a new evaluation method based on global phase fitting (GPF) for analyzing the continuous phase development of the 3He–129Xe comagnetometer signal. The Cramer–Rao lower bound on the 129Xe EDM for the GPF method is theoretically derived and shows the potential benefit of our new approach. The robustness of the GPF method is verified with Monte-Carlo studies. By optimizing the analysis parameters and adding data that could not be analyzed with the former method, we obtain a result of in an unblinded analysis. For the systematic uncertainty analyses, we adopted all methods from the aforementioned PRL publication except the comagnetometer phase drift, which can be omitted using the GPF method. The updated null result can be interpreted as a new upper limit of at the 95% C.L.

Magnetic anisotropy manipulation and interfacial coupling in Sm3Fe5O12 films and CoFe/Sm3Fe5O12 heterostructures* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0303603 and 2016YFA0401803), the National Natural Science Foundation of China (Grant Nos. U2032218, 11574316, 11874120, 61805256, and 11904367), the Plan for Major Provincial Science & Technology Project (Grant No. 202003a05020018), and the Key Research

The magnetic anisotropy manipulation in the Sm3Fe5O12 (SmIG) films and its effect on the interfacial spin coupling in the CoFe/SmIG heterostructures were studied carefully. By switching the orientation of the Gd3Ga5O12 substrates from (111) to (001), the magnetic anisotropy of obtained SmIG films shifts from in-plane to out-of-plane. Similar results can also be obtained in the films on Gd3Sc2Ga3O12 substrates, which identifies the universality of such orientation-induced magnetic anisotropy switching. Additionally, the interfacial spin coupling and magnetic anisotropy switching effect on the spin wave in CoFe/SmIG magnetic heterojunctions have also been explored by utilizing the time-resolved magneto–optical Kerr effect technique. It is intriguing to find that both the frequency and effective damping factor of spin precession in CoFe/SmIG heterojunctions can be manipulated by the magnetic anisotropy switching of SmIG films. These findings not only provide a route for the perpendicular magnetic anisotropy acquisition but also give a further path for spin manipulation in magnetic films and heterojunctions.

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46ppm.

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35ppm) increases the tension between experiment and theory to 4.2 standard deviations.

Magnetic-field measurement and analysis for the Muon g−2 Experiment at Fermilab

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb.

Tilting Uranus: Collisions versus Spin–Orbit Resonance

Abstract In this paper, we investigate whether Uranus’s 98° obliquity was a by-product of a secular spin–orbit resonance assuming that the planet originated closer to the Sun. In this position, Uranus’s spin precession frequency is fast enough to resonate with another planet located beyond Saturn. Using numerical integration, we show that resonance capture is possible in a variety of past solar system configurations but that the timescale required to tilt the planet to 90° is of the order ∼108 yr—a time span that is uncomfortably long. A resonance kick could tilt the planet to a significant 40° in ∼107 yr only if conditions were ideal. We also revisit the collisional hypothesis for the origin of Uranus’s large obliquity. We consider multiple impacts with a new collisional code that builds up a planet by summing the angular momentum imparted from impactors. Because gas accretion imparts an unknown but likely large part of the planet’s spin angular momentum, we compare different collisional models for tilted, untilted, spinning, and nonspinning planets. We find that a 1 M ⊕ strike is sufficient to explain the planet’s current spin state, but that two 0.5 M ⊕ collisions produce better likelihoods. Finally, we investigate hybrid models and show that resonances must produce a tilt of at least ∼40° for any noticeable improvements to the collision model. Because it is difficult for spin–orbit resonances to drive Uranus’s obliquity to 98° even under these ideal conditions, giant impacts seem inescapable.

Search for topological defect of axionlike model with cesium atomic comagnetometer* *Project supported by the National Natural Science Foundation of China (Grant No. 62071012), the National Science Fund for Distinguished Young Scholars of China (Grant No. 61225003), and National Hi-Tech Research and Development Program of China.

Many terrestrial experiments have been designed to detect domain walls composed of axions or axionlike particles (ALPs), which are promising candidates of dark matter. When the domain wall crosses over the Earth, the pseudoscalar field of ALPs could couple to the atomic spins. Such exotic spin-dependent couplings can be searched for by monitoring the transient-in-time change of the atomic spin precession frequency in the presence of a magnetic field. We propose here a single-species cesium atomic comagnetometer, which measures the spin precession frequencies of atoms in different ground-state hyperfine levels, to eliminate the common-mode magnetic-field variations and search for the exotic non-magnetic couplings solely between protons and ALPs. With the single-species atomic comagnetometer, we experimentally rule out the possibility that the decay constant of the linear pseudoscalar couplings of ALPs to protons is f p ≲ 3.71 × 107 GeV. The advanced system has the potential to constrain the constant to be f p ≲ 10.7 × 109 GeV, promising to improve astrophysical constraint level by at least one order of magnitude. Our system could provide a sensitive detection method for the global network of optical magnetometers to search for exotic physics.

All-optical single-species cesium atomic comagnetometer with optical free induction decay detection

Atomic comagnetometers, which measure the spin precession frequencies of overlapped species simultaneously, are widely applied to search for exotic spin-dependent interactions. Here we propose and implement an all-optical single-species Cs atomic comagnetometer based on the optical free induction decay (FID) signal of Cs atoms in hyperfine levels $F_g=3~\&~4$ within the same atomic ensemble. We experimentally show that systematic errors induced by magnetic field gradients and laser fields are highly suppressed in the comagnetometer, but those induced by asynchronous optical pumping and drift of residual magnetic field in the shield dominate the uncertainty of the comagnetometer. With this comagnetometer system, we set the constraint on the strength of spin-gravity coupling of the proton at a level of $10^{-18}$ eV, comparable to the most stringent one. With further optimization in magnetic field stabilization and spin polarization, the systematic errors can be effectively suppressed, and signal-to-noise ratio (SNR) can be improved, promising to set more stringent constraints on spin-gravity interactions.

Control of spin relaxation anisotropy by spin-orbit-coupled diffusive spin motion

Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between spin-orbit field and external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity.This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion.

Quantum Zeno effect and quantum nondemolition spin measurement in a quantum dot–micropillar cavity in the strong coupling regime

We theoretically describe the quantum Zeno effect in a spin-photon interface represented by a charged quantum dot in a micropillar cavity in the strong coupling regime. This simplest model allows for various generalizations for the different systems. We derive a simple expression for the spin measurement rate, which allows one to tune the electron spin precession frequency in an external magnetic field and spin relaxation time. We calculate the spin noise bispectrum, which reveals the qualitative change of the spin dynamics with an increase of the measurement strength and proves the quantum nature of the spin noise. We also calculate the quantum information gain rate and find the conditions when it equals the spin dephasing rate, i.e., reaches the quantum limit.

New approach to search for parity-even and parity-odd time-reversal violation beyond the Standard Model in a storage ring

Time-reversal breaking and parity-conserving millistrong interactions, suggested in 1965, still remain a viable mechanism of CP-violation beyond the Standard Model. One of its possible manifestations is the T-odd asymmetry in the transmission of tensor-polarized deuterons through a vector-polarized hydrogen gas target. Upon the rotation of the deuteron polarization from the vertical direction into the ring plane, the T-odd asymmetries, odd against the reversal of the proton polarization in the target, will continuously oscillate with first or second harmonics of the spin precession frequency. The Fourier analysis of the oscillating T-odd asymmetries allows for an easy separation from background persistent in conventional experiments employing static vector and tensor polarizations.

Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment

The Muon g−2 experiment at Fermilab (E989) aims to measure the anomalous magnetic moment, aμ, of the muon with a precision of 140 parts-per-billion. This requires a precise measurement of both the anomalous spin precession frequency, ωa, of muons stored in a magnetic field of 1.45 T, and a precise measurement of that magnetic field in terms of the shielded proton Larmor frequency, ω′p. The measurement of ω′p with a total systematic uncertainty of 70 parts-per-billion involves a combination of various nuclear magnetic resonance (NMR) probes. There are 378 probes mounted in fixed locations that constantly monitor field drifts. A water-based, cylindrical calibration probe provides the calibration in terms of the shielded proton Larmor frequency. A crucial element for the multi-step measurement of ω′p is the regular mapping of the magnetic field over the muon storage region. The former experiment at Brookhaven National Laboratory (BNL) employed an in-vacuum field mapping system equipped with 17 NMR probes, which was developed by the University of Heidelberg. We have refurbished and upgraded this system with new probes and electronics. The upgrades include the addition of 16-bit, 1 MSPS digitization of the NMR signals, which replaced the hardware-implemented zero-crossing counting of the system at Brookhaven. The digitized signals offer new capabilities in the NMR frequency analysis and its related systematic uncertainties. To sustain the higher data rates, a new communication scheme with time-division multiplexing was implemented to separate the important NMR reference clock from the data communication in order to reach the specifications for the accuracy and stability of the reference clock. A new barcode reader provides more precise azimuthal position determination during the measurement and calibration. While the mechanical systems that move the field mapper inside the storage ring have been mostly refurbished from BNL, the motion control system was completely replaced with a custom-built electronics centered around a commercial Galil motion controller. Both the field mapping NMR system and its motion control were successfully commissioned at Fermilab and have been in reliable operation during the first three data taking periods of the experiment at Fermilab. This article will provide the details of the upgrades of the field mapper and its performance.

Dynamics of Colombo’s Top: Generating Exoplanet Obliquities from Planet–Disk Interactions

Abstract Large planetary spin–orbit misalignments (obliquities) may strongly influence atmospheric circulation and tidal heating in a planet. A promising avenue to generate obliquities is via spin–orbit resonances, where the spin and orbital precession frequencies of a planet cross each other as the system evolves in time. One such mechanism involves a dissipating (mass-losing) protoplanetary disk that drives orbital precession of an interior planet. We study this scenario analytically in this paper, and obtain the mapping between the general initial spin orientation and the final obliquity. We show that (i) under adiabatic evolution (i.e., the disk dissipates at a sufficiently slow rate), the final planetary obliquity as a function of the initial spin orientation bifurcates into distinct tracks governed by interactions with the resonance; and (ii) under nonadiabatic evolution, a broad range of obliquities can be excited. We obtain analytical expressions for the final obliquities for various regimes of parameter space. The dynamical system studied in this paper is an example of “Colombo’s top,” and our analysis and results can be adapted to other applications.

Electrical control of spin relaxation anisotropy during drift transport in a two-dimensional electron gas

Spin relaxation was studied in a two-dimensional electron gas confined in a wide GaAs quantum well. Recently, the control of the spin relaxation anisotropy by diffusive motion was first shown in D. Iizasa et al., arXiv:2006.08253 (2020). Here, we demonstrate electrical control by drift transport in a system with two-subbands occupied. The combined effect of in-plane and gate voltages was investigated using time-resolved Kerr rotation. The measured relaxation time present strong anisotropy with respect to the transport direction. For an in-plane accelerating electric field along $\left[110\right]$, the lifetime was strongly suppressed irrespective of the applied gate voltage. Remarkably, for transport along $\left[1\bar{1}0\right]$, the data shows spin lifetime that was gate-dependent and longer than in the $\left[110\right]$ direction regardless of the in-plane voltage. In agreement, independent results of anisotropic spin precession frequencies are also presented. Nevertheless, the long spin lifetime, strong anisotropy and drift response seen in the data are beyond the existing models for spin drift and diffusion.

Dual-frequency cesium spin maser

Co-magnetometers have been validated as valuable components of the atomic physics toolbox in fundamental and applied physics. So far, the explorations have been focused on systems involving nuclear spins. Presented here is a demonstration of an active alkali-metal (electronic) system, i.e. a dual frequency spin maser operating with the collective caesium F=3 and F=4 spins. The experiments have been conducted in both magnetically shielded and unshielded environments. In addition to the discussion of the system's positive feedback mechanism, the implementation of the dual frequency spin maser for industrial non-destructive testing is shown. The stability of the F=3 and F=4 spin precession frequency ratio measurement is limited at the $3 \times 10^{-8}$ level, by the laser frequency drift, corresponding to a frequency stability of 1.2 mHz for $10^4$ sec integration time. We discuss measurement strategies that could improve this stability to nHz, enabling measurements with sensitivities to the axion-nucleon and axion-electron interactions at the levels of $f_a/C_N \sim 10^9$ GeV and $f_a/C_e \sim 10^8$ GeV, respectively.

In-plane anisotropy of the hole g factor in CdTe/(Cd,Mg)Te quantum wells studied by spin-dependent photon echoes

We use the two-pulse spin-dependent photon echo technique to study the in-plane hole spin anisotropy in a 20~nm-thick CdTe/Cd$_{0.76}$Mg$_{0.24}$Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter $q=0.095$, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions manifest as different harmonics of the spin precession frequencies in the photon echo experiment, when strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole $g$ factor is found to vary in the range $|\tilde{g_h}|$=0.125--0.160 in the well plane.

Spin–orbit parameters derivation using single-frequency analysis of InGaAs multiple quantum wells in transient spin dynamics regime

The deriving method of spin–orbit (SO) parameters using a single-frequency analysis was examined in a transient regime of diffusive spin dynamics in InGaAs/InAlAs multiple quantum wells. Transient regime of diffusive spin dynamics is the time regime when the spin precession frequency induced by SO magnetic fields decreases and changes with time. Recently, we have established a method of deriving SO parameters by scanning time-resolved Kerr rotation microscopy in this transient regime [Kawaguchi et al., Appl. Phys. Lett. 115, 172406 (2019)] using the time-dependent spin precession frequency analysis. Although reliable SO parameters were derived, time-independent single-frequency analysis is still attractive because of its simplicity. In this paper, SO parameters’ derivation was performed by the single-frequency analysis comparing the experiment and the Monte Carlo (MC) simulation. The best fit of the simulation to the measurement for the SO-induced frequency yields the derivation of SO parameters; however, the derived values were different from the reliable SO parameters derived by the time-dependent analysis. This discrepancy arises from a spin relaxation time difference between the experiment and MC simulation. After intentionally adjusting the spin relaxation time of the MC simulation to the experiment, the SO-induced frequency obtained by the MC simulation with reliable SO parameters reproduced the experiment well. We found that the spin relaxation time adjustment of the MC simulation to the experiment is necessary to obtain accurate SO parameters from the single-frequency analysis comparing the experiment with the MC simulation.

Gyroscope precession frequency analysis of a five-dimensional charged rotating Kaluza-Klein black hole

We study the spin precession frequency of a test gyroscope attached to a stationary observer in the five-dimensional rotating Kaluza-Klein black hole (RKKBH). We derive the conditions under which the test gyroscope moves along a timelike trajectory in this geometry, and the regions where the spin precession frequency diverges. The magnitude of the gyroscope precession frequency around the KK black hole diverges at two spatial locations outside the event horizon. However, in the static case, the behavior of the Lense-Thirring frequency of a gyroscope around the KK black hole is similar to the ordinary Schwarzschild black hole. Since a rotating Kaluza-Klein black hole is a generalization of the Kerr-Newman black hole, we present two mass-independent schemes to distinguish these two spacetimes.