Quantum noise in a squeezed-light-enhanced multiparameter quantum sensor

We study quantum enhancement of sensitivity using squeezed light in a multi-parameter quantum sensor, the hybrid dc-rf optically pumped magnetometer (hOPM) [Phys. Rev. Applied 21, 034054, (2024)]. Using a single spin ensemble, the hOPM acquires both the dc field strength (scalar magnetometry), and resonantly detects one quadrature of the ac magnetic field at a chosen frequency (rf magnetometry). In contrast to the Bell-Bloom scalar magnetometer [Phys. Rev. Lett. 127, 193601 (2021)], the back-action evasion in the hOPM is incomplete, leading to a nontrivial interplay of the three quantum noise sources in this system: photon shot noise, spin projection noise, and measurement back-action noise. We observe these interactions using squeezed light as a tool to control the distribution of optical quantum noise between $S_2$ and $S_3$ polarization Stokes components, and the resulting effect on readout quantum noise and measurement back-action. These results demonstrate quantum-enhanced sensitivity in a continuously operating multi-parameter sensor and reveal fundamental trade-offs between sensitivity, back-action, and bandwidth.

💡 Research Summary

This paper investigates quantum‑enhanced sensitivity in a continuously operating, multi‑parameter sensor: the hybrid dc‑rf optically pumped magnetometer (hOPM). The hOPM uses a single ensemble of ^87Rb atoms to simultaneously measure a static magnetic field (dc) via the Larmor precession frequency and an oscillating magnetic field (rf) at a chosen frequency via the amplitude of the spin precession. Unlike the Bell‑Blo​om scalar magnetometer, the hOPM does not fully evade measurement back‑action (MBA), so three fundamental quantum noise sources—photon shot noise (PSN), spin projection noise (SPN), and MBA—interact in a non‑trivial way.

The authors introduce polarization‑squeezed probe light to control the distribution of quantum fluctuations between the Stokes components S₂ and S₃. Squeezing reduces fluctuations in S₂ (the component that carries the signal) while anti‑squeezing necessarily increases fluctuations in S₃ (the orthogonal component). The S₂ reduction directly lowers PSN, whereas the increased S₃ noise manifests as a fluctuating optical Zeeman shift (OZS) that adds a stochastic term GS₃ ẑ to the Bloch equation for the collective spin. This term is the source of MBA in the hOPM.

Experimentally, the authors generate squeezed vacuum with an optical parametric oscillator and inject it into the probe beam. They record the demodulated in‑phase (I) and quadrature (Q) signals at the pump repetition frequency ωₚ, which is synchronized to the Larmor frequency ω_L. Power spectral densities S_I(ω) and S_Q(ω) are modeled as a sum of PSN, SPN, and MBA contributions, each multiplied by the appropriate squeezing (ξ²) or anti‑squeezing ( ξ̄²) factor. By fitting the spectra for three probe states—coherent, squeezed, and anti‑squeezed—the authors extract the noise amplitudes and verify that:

• Squeezed probing reduces PSN by ≈ 1.59 dB, while anti‑squeezed probing raises it by ≈ 2.91 dB.
• SPN remains unchanged across probe states, as expected for a fixed atom number and relaxation rate.
• MBA increases under squeezed probing (consistent with larger S₃ fluctuations) and shows no systematic reduction under anti‑squeezed probing.

Sensitivity is quantified by calibrating the transfer functions R_I(ω) = dI/dB_rf and R_Q(ω) = dQ/dB_dc, then converting the measured noise spectra into equivalent magnetic‑field noise S_B_rf(ω) and S_B_dc(ω). In the PSN‑dominated high‑frequency region, squeezed light improves dc sensitivity by 1.42 dB and rf sensitivity by 1.61 dB; anti‑squeezed light degrades them by 2.88 dB and 2.69 dB respectively. Bandwidth analysis shows a modest (~10 %) increase in the 3 dB bandwidth for the squeezed case, indicating that squeezing primarily reduces noise amplitudes rather than altering the dynamical response.

Figure 3 provides a conceptual illustration of why the hOPM suffers MBA while the Bell‑Blo​om scalar magnetometer does not. In the scalar device, OZS only perturbs the Fₓ component, leaving the precession plane (F_y‑F_z) untouched; thus the measurement is back‑action evading. In the hOPM, the same OZS term couples to all three spin components, modifying both amplitude and phase of the precession and generating MBA. Consequently, squeezing S₂ inevitably introduces extra S₃ noise, which manifests as increased low‑frequency MBA.

The authors conclude that multi‑parameter operation fundamentally changes the quantum noise landscape: improving one part of the sensitivity spectrum (e.g., high‑frequency rf detection) by squeezing inevitably trades off against another (low‑frequency dc detection) through increased MBA. The optimal squeezing level therefore depends on the specific frequency band of interest and the relative importance of bandwidth versus ultimate sensitivity. The observed trade‑offs are captured by a simple analytical model that incorporates the three noise sources and their dependence on ξ² and ξ̄².

Beyond the specific hOPM platform, the work suggests that any continuously monitored quantum sensor—atomic, optomechanical, or superconducting—will exhibit similar interplays between PSN, SPN, and MBA when quantum resources such as squeezed light are employed. The demonstrated compatibility with integrated OPMs and on‑chip squeezed‑light sources points toward compact, quantum‑enhanced multi‑parameter sensing devices for real‑world applications ranging from biomagnetic imaging to navigation and quantum communication.