Abstract Optical quantum sensors based on alkali-metal atoms enable highly sensitive magnetic-field measurements in warm vapor. Their performance can become limited by intrinsic spin noise once technical noise sources are sufficiently suppressed. Characterizing temporal spin correlations is therefore important both for optimizing sensor sensitivity and for investigating quantum-enhanced sensing protocols. Here we investigate correlated spin fluctuations in a radio-frequency optical quantum sensor based on a high-density potassium vapor cell using pulsed probe readout. Orthogonal pump and probe beams establish and detect the spin polarization, while a bias magnetic field defines the sensing frequency and the probe pulses are synchronized electronically with the driven spin response. The protocol combines periodic probing, phase cycling, and variable-delay window subtraction. Phase cycling suppresses reproducible probe-induced coherent transients between experimental cycles, whereas window subtraction probes correlations between two measurements within the same cycle. The measured difference noise increases toward an asymptotic value with delay, demonstrating temporal correlations in the processed signal. This behavior is compatible with correlations expected from a conditional quantum non-demolition mechanism, but the present experiment does not independently establish spin squeezing below the standard quantum limit or uniquely exclude residual technical correlations. The protocol provides a practical framework for studying correlated noise in warm-vapor radio-frequency optical quantum sensors.
Abstract Optical quantum sensors based on alkali-metal atoms enable highly sensitive magnetic-field measurements in warm vapor. Their performance can become limited by intrinsic spin noise once technical noise sources are sufficiently suppressed. Characterizing temporal spin correlations is therefore important both for optimizing sensor sensitivity and for investigating quantum-enhanced sensing protocols. Here we investigate correlated spin fluctuations in a radio-frequency optical quantum sensor based on a high-density potassium vapor cell using pulsed probe readout. Orthogonal pump and probe beams establish and detect the spin polarization, while a bias magnetic field defines the sensing frequency and the probe pulses are synchronized electronically with the driven spin response. The protocol combines periodic probing, phase cycling, and variable-delay window subtraction. Phase cycling suppresses reproducible probe-induced coherent transients between experimental cycles, whereas window subtraction probes correlations between two measurements within the same cycle. The measured difference noise increases toward an asymptotic value with delay, demonstrating temporal correlations in the processed signal. This behavior is compatible with correlations expected from a conditional quantum non-demolition mechanism, but the present experiment does not independently establish spin squeezing below the standard quantum limit or uniquely exclude residual technical correlations. The protocol provides a practical framework for studying correlated noise in warm-vapor radio-frequency optical quantum sensors.
For spin-polarized ensembles of alkali-metal atoms with hyperfine structure and spin greater than 1/2, the interplay between spin dynamics and quantum noise mechanisms remains largely unexplored, especially in the spin-exchange-relaxation-free (SERF) regime. In particular, the theoretical understanding of the dynamics for the mean values of the spin operators was established shortly after the advent of optical pumping. In contrast, a corresponding theory for spin fluctuations has not yet been developed, and is addressed in this work. Here, we develop such a first-principles theory of spin fluctuations in alkalimetal vapors. The nonlinearity bottleneck of spin-exchange collisions, which dominate the physics of such vapors, is overcome by linearizing the dynamics around the equilibrium density matrix. The result is a precise calculation of the absolute magnetic sensing limit of optically pumped atomic magnetometers, which can precisely benchmark quantum limited and quantum enhanced protocols, in contrast to the traditional approach shown to be adequate only within a factor of 2. Further, we elucidate how signal and noise in atomic magnetometers are distributed among the spin eigenmodes defined under continuous optical pumping and probing via the paramagnetic Faraday rotation. Notably, in the SERF regime, alongside the magnetic resonance narrowing, we find a reduction of spin noise at the spin-precession frequency as a consequence of strong hyperfine correlations redistributing spin noise, when both hyperfine manifolds are simultaneously probed. These insights can lead to improved quantum devices utilizing alkali-metal atoms or similar spin-based sensing platforms.
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.
Quantum non-demolition measurement with an off-resonance polarized probe is a widely utilized technique for atomic sensors. Typically, QND instruments read out spin states through optical polarimetry using a linearly off-resonance probe in atomic media. This optical read-out process offers high accuracy, with potential applications in biomagnetism, inertial navigation and new physics exploration beyond the standard model. It was observed that previously unexplored spin-alignment polarization induced by the far-detuned off-resonance linear probe in an ultrasensitive optical polarimetry. The evolution of probe-generated multipole moments exacerbates probe noise due to strong magnetic couplings. A method was demonstrated to decouple spin-alignment from magnetic fields by manipulating the multipole moments in zero fields. A suppression of the probe noise by 8.2 dB at 1 Hz and 10.4 dB at 10 Hz with the proposed method, reaching the standard quantum limit, was achieved. The realized shot-noise-limited optical polarimetry shows significant potential for advancing the performance of atomic sensors, particularly in applications requiring ultra-high sensitivity, such as precision measurements and quantum metrology. These findings provide a pathway toward enhanced sensor precision in diverse scientific and technological applications.
We experimentally demonstrate a non-linear dependence of the spin noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin noise spectroscopy (SNS) near the D2 transition of rubidium, a quadratic spin noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in non-interacting ensembles. This non-linear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross-correlations due to resonant dipole-dipole interaction (DDI) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.
Spin squeezing can suppress quantum projection noise via interparticle entanglement, therefore enabling measurement sensitivities beyond the standard quantum limit. In practice, however, the Gaussian and finite intensity profiles of the optical probe beam induce spatially inhomogeneous atom-light interactions. As polarized atoms move within a vapor cell, they experience position-dependent optical intensities, generating transit noise that limits spin squeezing performance. Here, we investigate the transit noise in a coated rubidium vapor cell through combined theoretical analysis and experimental measurements. By varying the probe beam diameter, we quantify the dependence of transit noise on beam size and atomic Larmor frequency. Our results show that, for a vapor cell with fixed dimensions, the transit noise increases as the probe beam spot area decreases. Moreover, when the Larmor frequency is below the characteristic linewidth of the transit noise, the noise contribution becomes larger. We further calculated and measured spin squeezing for different beam sizes and found an experimental difference of 2.7±0.2 dB between 2~mm and 0.6~mm, similar to the theoretical prediction of 3.0±0.3 dB. Theoretical analysis under conditions of stronger squeezing shows that transit noise becomes an even more critical limiting factor. These results provide practical guidance for optimizing probe beam parameters and suppressing transit noise in spin squeezing experiments.
In atomic spin sensors based on optical pumping, pump beam instabilities can drive atomic spin polarization fluctuations, referred to here as pump-induced spin polarization noise, which may limit sensitivity and long-term stability. Because the local pump field inside the cell can differ from that inferred from external optical diagnostics, it remains difficult to directly quantify the actual in situ spin polarization noise and to evaluate and suppress its contribution to the sensor noise floor. Here, we propose an in situ decoupling method based on spin dynamics, in which a large longitudinal detuning field suppresses magnetic field and rotation responses, while a transverse projection field converts pump-induced fluctuations in longitudinal spin polarization into a measurable transverse spin signal. Demonstrated in a K-Rb-21Ne spin exchange relaxation free (SERF) comagnetometer, the proposed method suppresses the magnetic-field response by approximately 180-fold and enhances the pump-power-noise response by approximately 380-fold, thereby enabling effective separation and evaluation of pump-induced spin polarization noise. The method employs the atomic ensemble as an in situ probe of the spin dynamic response to the local pump optical field. It enables quantitative identification of pump fluctuation associated noise and direct evaluation of optical field stability under actual operating conditions, thereby providing an experimental basis for optical field stabilization and noise suppression assessment in SERF comagnetometers and related alkali atomic spin sensors.