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Analysis and Suppression of the Residual Optical Rotation Angle in NMR Sensor

Junjie Zhang, Hao Tian, Hanyu Wang, Jianli Li, Zhanchao Liu

Published Nov 21, 2025• 0 citations
Publisher

Abstract

As a type of atomic sensor, the residual optical rotation angle during the detection process of the nuclear magnetic resonance (NMR) sensor limits its performance improvement. By establishing the optical rotation detection signal theoretical model of the NMR sensor, the influence of the residual optical rotation angle on the signal output is analyzed. Further, the theoretical analysis indicates that adjusting the detection laser frequency based on the D1 line resonance frequency and resonance linewidth can effectively increase the scale factor and achieve suppression of residual optical rotation angle. The temperature change rate of D1 line resonance frequency and linewidth in the NMR sensor is -15.5 MHz/°C, and the linewidth coefficients are 19.9 MHz/°C, respectively. The experimental results indicate that, following the optimization of probe laser frequency, the sensitivity of the NMR sensor has significantly improved. Furthermore, the residual optical rotation angle suppression method proposed in this study demonstrates potential applicability to other atomic sensors utilizing optical rotation detection.

DOI
10.1109/mcai66356.2025.11381978

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•Aug 18, 2011•1 citation
As a type of atomic sensor, the residual optical rotation angle during the detection process of the nuclear magnetic resonance (NMR) sensor limits its performance improvement. By establishing the optical rotation detection signal theoretical model of the NMR sensor, the influence of the residual optical rotation angle on the signal output is analyzed. Further, the theoretical analysis indicates that adjusting the detection laser frequency based on the D1 line resonance frequency and resonance linewidth can effectively increase the scale factor and achieve suppression of residual optical rotation angle. The temperature change rate of D1 line resonance frequency and linewidth in the NMR sensor is -15.5 MHz/°C, and the linewidth coefficients are 19.9 MHz/°C, respectively. The experimental results indicate that, following the optimization of probe laser frequency, the sensitivity of the NMR sensor has significantly improved. Furthermore, the residual optical rotation angle suppression method proposed in this study demonstrates potential applicability to other atomic sensors utilizing optical rotation detection.
Optical rotation detection systems are widely used in various kinds of atomic sensors, such as atomic magnetometers, co-magnetometers, and nuclear magnetic resonance (NMR) gyroscopes; and appear in many applications such as fundamental physics, biomagnetism, magnetism test, etc. The study analyses the frequency responses to three-axis dynamic magnetic fields in optical rotation detection systems (ORDS) of Spin-Exchange Relaxation-Free (SERF) magnetometers. Because of the imperfections of the optical elements, the probe light is actually elliptically polarised in ORDS, which can polarise the atom ensemble and cause the responses to the three-axis magnetic field. Theoretically it analyse the frequency responses to the sinusoidal magnetic field, and prove that the responses are closely associated with the DC magnetic field. The values of the DC magnetic fields are calculated with special frequency points, called ‘break points’, in the transverse responses. The relationships between the DC magnetic field and the sensitivities of ORDS, and effectively suppress the magnetic noise responses with the residual magnetic field compensation. The paper demonstrated the influence of elliptically polarised light on the sensitivity of ORDS in SERF magnetometers. The elliptically polarised probe light polarises the alkali atom ensemble, which leads to the responses of the magnetic noise in the shield. Finally, the sensitivity of ORDS is improved by approximately two times at 10-20 Hz. This method is beneficial for improving probe sensitivity in SERF magnetometers, co-magnetometers, and NMR gyroscopes.
Nuclear magnetic resonance gyroscope (NMRG) is the smallest atomic sensor in navigation level. Spin precession can be detected by measuring the optical rotation of the plane of an off-resonant linearly polarized probe beam. The optimal frequency and power of the probe beam counts for the performance of NMRG, which has been verified by our former experiments. The NMRG system would have higher sensitivity and lower consumption comparing to the circularly polarized probe beam. In this paper, we demonstrate the optimal frequency and power of an off-resonant linearly polarized probe beam by theoretical analysis and experimental verification. In theory, the off-resonant linearly polarized probe beam can be decomposed into two circularly polarized components of opposite helicity. Its plane of polarization will be rotated by an angle, due to the positive and negative helicity light experience different induces of refraction as it propagates through a birefringent medium. The off-resonant linearly polarized probe beam becomes partially absorbed by the alkali vapor as it propagates through the NMRG cell. The overall signal is determined by both optical signal and beam absorption. After optimizing the frequency and power of the probe, the magnetic field sensitivity was 2pT/Hz1/2.
We evaluated the alignment-to-orientation conversion (AOC) at the cesium D1 line to improve a nonlinear magneto–optical rotation (NMOR) optical atomic magnetometer’s signal amplitude and bandwidth. For the 6 2S1/2 F = 3 → 6 2P1/2 F′ = 4 transition, the AOC-related NMOR achieves a 1.7-fold enhancement in signal amplitude compared to the conventional NMOR, benefiting from narrow linewidth and ultraweak power broadening. Therefore, an effective amplitude-to-linewidth ratio is maintained in the high-laser-power region. This method is beneficial for detecting high-frequency magnetic signals in nuclear magnetic resonance and biomagnetism, as the NMOR magnetometer bandwidth increases with laser power.
The paper considers a common operation principle of a quantum rotation sensor based on nuclear magnetic resonance, giving a semi-classical description of processes in the sensor circuit, that is useful for obtaining the analytical representation of a signal at the optical circuit output. The principles of numerical calculation are briefly presented for an optical signal of the rotation sensor based on a one-dimensional quantum model. Comparison of calculations according to classical model and more stringent quantum model has shown that the sensor signal has a more complicated structure than that following from the classical description which shows only some properties of dynamic processes in the circuit. The results are important for the development of methods for demodulating the quantum rotation sensor optical signal and for estimation of expected characteristics of practical devices.
We analyze and suppress the magnetic noise response in optical rotation detection system (ORDS) in atomic magnetometers in this study. Because of the imperfections of the optical elements, the probe light is actually elliptically polarized in ORDS, which can polarize the atom ensemble and cause the responses to the three-axis magnetic noise. We theoretically analyze the frequency responses to the magnetic noise, and prove that the responses are closely associated with the DC magnetic field. The values of the DC magnetic fields are calculated with special frequency points, called 'break points', in the transverse responses. We reveal the relationships between the DC magnetic field and the sensitivities of ORDS, and effectively suppress the magnetic noise responses with the residual magnetic field compensation. Finally, the sensitivity of ORDS is improved by approximately two times at 10-20 Hz.
Optically pumped radio frequency (RF) atomic magnetometers have been shown to have an improved sensitivity over standard tuned coils for frequencies less than 50 MHz, making these RF magnetometers attractive for the detection of nuclear quadrupole resonance (NQR) and low-field nuclear magnetic resonance (NMR) signals. In an atomic magnetometer a linearly polarized probe beam measures, through Faraday rotation, the transverse atomic magnetization induced by the resonant RF signal. The resonance, or Larmor, frequency of the magnetometer is easily tuned with a small magnetic field. We construct an atomic magnetometer based on a potassium vapor cell with a measured sensitivity of 0.22 ± 0.02 fT/ √ Hz and a detection bandwidth of 334 ± 11 Hz when tuned to 423 kHz, giving a Q of over 1200. While high Q magnetometers are sensitive to weak magnetic fields, they are also sensitive to magnetic transients, such as those associated with the excitation pulses needed for magnetic resonance. The ringing created by such transients can obscure the signal of interest. This is particularly detrimental for magnetic resonance signals that decay faster than the transverse relaxation rate. We demonstrate that by feeding back part of the optical signal to orthogonal electromagnetic coils, this unwanted ringing can be quickly damped out leaving the magnetometer ready for the detection of the signal. This negative feedback as applied to the K spins is called spin-damping and can be used to relax the K atoms faster by more than two orders of magnitude. Using spin-damping we reduce the dead-time before data acquisition from 0.8 to 0.2 ms in the detection of NQR signals from ammonium nitrate, one of the so-called fertilizer bomb explosives with an NQR frequency of 423 kHz. Furthermore, we discover that spin-damping can not only be used to suppress signals, it can also be used to suppress noise. We show that it can be used to suppress both environmental noise and more fundamental quantum noise, such as photon shot and spin projection noise. The latter suppression opens the door for its use in quantum control to initialize spin systems before measurements. For phase-sensitive detection, as is often used in magnetic resonance, spin-damping suppresses signal and noise in such a way as to increase the sensitivity bandwidth of the magnetometer. We prove, both theoretically and experimentally, that it is possible to increase the magnetometer detection bandwidth by a factor of 3 or more without significant loss in sensitivity. Such gains in bandwidth for a high Q magnetometer translate into savings in detection time, particularly for substance detection where the frequency of the signal of interest may not be completely known.