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arXiv:1912.00216 · Physical Review A

Quadrupole effects on nuclear-magnetic-resonance gyroscopes

Yue Chang, Shuangai Wan, Jie Qin

Published Jul 9, 2020• 5 citations
arXivHTMLPDF

Abstract

Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant ${C}_{q}$ is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant ${C}_{q}$ is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including ${C}_{q}$. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-${C}_{q}$ regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.

DOI
10.1103/physreva.102.013507

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Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant Cq{C}_{q}Cq​ is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant Cq{C}_{q}Cq​ is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including Cq{C}_{q}Cq​. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-Cq{C}_{q}Cq​ regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.
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We develop a quantum model for the rotational dynamics of a freely floating levitated ferromagnetic gyroscope (LFG), emphasizing the interplay between intrinsic spin S\boldsymbol{S}S, mechanical angular momentum L\boldsymbol{L}L, and magnetic torque. The conserved total angular momentum projection along the zzz-directed magnetic field B\boldsymbol{B}B, Jz=Sz+LzJ_z=S_z+L_zJz​=Sz​+Lz​, is quantized, leading in the small-libration-amplitude limit to discrete precessional states ∣m⟩|m\rangle∣m⟩ (eigenstates of JzJ_zJz​ with eigenvalues Jz=mℏJ_z = m\hbarJz​=mℏ) and librational harmonic oscillator states ∣n⟩|n\rangle∣n⟩ (n=0,1,2,…n=0,1,2,\ldotsn=0,1,2,…). The discreteness of the energies and dynamical variables is governed by the quantum precession scale ΩQ=ℏ/IΩ_Q=\hbar/IΩQ​=ℏ/I, where III is the moment of inertia of the LFG. We find that the phenomenon of LFG precession persists into high-field regimes where the magnitude of the rotational angular momentum associated with precession exceeds the total intrinsic spin. We analyze the complementary quantum limits of localized semiclassical LFG orientation wave packets and exact JzJ_zJz​-eigenstates ∣m⟩|m\rangle∣m⟩, clarifying the relation between classical precession signals and the underlying quantized spin-rotor dynamics. We further show that radio-frequency fields can drive Δm=±1Δm = \pm 1Δm=±1 and Δn=±1Δn = \pm 1Δn=±1 transitions, enabling ladder spectroscopy, tilt-angle control, and sideband-like coupling between precession and libration. The coupled dynamics also exhibit branch-point magnetic resonances where precession and librational motion become strongly coupled. These results establish a framework for using LFGs not only as ultrasensitive torque and magnetic-field sensors, but also as controllable mesoscopic quantum systems. The techniques developed here may be applied to searches for exotic, beyond-the-standard model spin-dependent interactions, ultralight dark matter, and spin-gravity couplings.
Control over nuclear-spin fluctuations is essential for processes that rely on preserving the quantum state of an embedded system. For this purpose, squeezing is a viable alternative, so far that has not been properly exploited for the nuclear spins. Of particular relevance in solids is the electric quadrupole interaction (QI), which operates on nuclei having spin higher than 1/2. In its general form, QI involves an electric-field gradient (EFG) biaxiality term. Here, we show that as this EFG biaxiality increases, it enables continuous tuning of single-particle squeezing from the one-axis twisting to the two-axis countertwisting limits. A detailed analysis of QI squeezing is provided, exhibiting the intricate consequences of EFG biaxiality. The initial states over the Bloch sphere are mapped out to identify those favorable for fast initial squeezing, or for prolonged squeezings. Furthermore, the evolution of squeezing in the presence of a phase-damping channel and an external magnetic field are investigated. We observe that dephasing drives toward an antisqueezed terminal state, the degree of which increases with the spin angular momentum. Finally, QI squeezing in the limiting case of a two-dimensional EFG with a perpendicular magnetic field is discussed, which is of importance for two-dimensional materials, and the associated beat patterns in squeezing are revealed.
Abstract— Designing a compact balanced quantum rotation sensor (gyroscope) based on nuclear magnetic resonance in xenon is one of the most urgent and promising tasks in modern metrology. The ultimate accuracy of the sensor is mostly constrained by the isotope shift conditioned by the difference in relaxation rates of two xenon isotopes under spatially nonuniform spin-exchange pumping of nuclear magnetic moments. The proposed method for suppressing the isotope shift and its partial derivatives is based on creating the external magnetic field with nonlinear spatial gradient. The simulation results based on experimental data demonstrate that the method can be applied to small gas cells with higher spatial nonlinearity of pumping parameters.
We describe a nuclear spin gyroscope based on an alkali-metal--noble-gas comagnetometer. Optically pumped alkali-metal vapor is used to polarize the noble-gas atoms and detect their gyroscopic precession. Spin precession due to magnetic fields as well as their gradients and transients can be cancelled in this arrangement. The sensitivity is enhanced by using a high-density alkali-metal vapor in a spin-exchange relaxation free regime. With a $\mathrm{K}\mathrm{\text{\ensuremath{-}}}^{3}\mathrm{He}$ comagnetometer we demonstrate rotation sensitivity of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{rad}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Hz}}^{\ensuremath{-}1/2}$, equivalent to a magnetic field sensitivity of 2.5  fT/Hz1/22.5\text{ }\text{ }\mathrm{fT}/{\mathrm{Hz}}^{1/2}2.5  fT/Hz1/2. The rotation signal can be increased by a factor of 10 using 21Ne^{21}\mathrm{Ne}21Ne with a smaller magnetic moment. The comagnetometer is also a promising tool in searches for anomalous spin couplings beyond the standard model.
An alkali-metal--noble-gas NMR gyroscope is widely used for precision rotation measurement in fundamental and applied physics. By numerically simulating the alkali-metal--nuclear--nuclear trispin dynamics, we investigate the dependence of gyroscope response on alkali-metal spin relaxation time and nuclear spin magnetization. We found additional resonance peaks appear due to a new source of instability, namely, the inherent multistability of trispin dynamics. The numerical simulation results agree well with the recent experiment, enabling a better understanding and exploitation of the gyroscope signal.