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

Abstract

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.

Figures (3)

• Figure 1: Experimental setup of a quantum-enhanced hybrid dc/rf optically pumped magnetometer (QE-hOPM). WP – Wollaston prism, BD – balanced detector, OPO – optical parametric oscillator, LO – local oscillator, SqV – squeezed vacuum, PM – polarization maintaining fiber, PBS – polarizing beam splitter, DAQ – data acquisition card, Bdrv – low noise current driver, ECDL – extended cavity diode laser, TA-SHG – tapered amplified second harmonic generator, PPKTP – periodically poled potassium titanyl phosphate nonlinear crystal, Bdu – beam dump, GEN – function generator, PZT – piezoelectric element. Description in the text.
• Figure 2: Observed quantum noise in the dc (a,c,e) and rf (b,d,f) magnetometer signals for squeezed (black) coherent-state (red) and anti-squeezed (blue) probing. (a, b) Polarization noise after demodulation. Light traces show data, dark traces show maximum likelihood fits with \ref{['eq:NoiseSpectra']}. Probe power 560µW throughout. Pump power 110µW ( solid curves), 0µW (spin-noise spectroscopy, dashed curves). Shaded regions show $\pm 1 \sigma$ uncertainty from bootstrapping. (c, d) best-fit parameters $\mathcal{S}^{\mathrm{PSN}}$, $\mathcal{S}^{\mathrm{SPN}}$, $\mathcal{S}^{\mathrm{MBA}}$. Error bars show the statistical uncertainties of the extracted PSN, SPN, and MBA amplitudes, obtained from the bootstrap-estimated standard deviations of the fitted parameters. (e,f) Sensitivity of the hOPM for the dc and rf detection. Shaded regions show $\pm 1 \sigma$ uncertainty from bootstrapping.
• Figure 3: Visualization of the effect of $S_3$ noise on spin precession. Left: BBOPM, as in Troullinou2021TroullinouPRL2023. Right: hOPM, as in lipka2024multiparameter. The probing direction is along $z$. The thick blue arrow shows the magnetic-field direction. Red double-headed arrows represent perturbations to spin precession (direction and relative magnitude) due to the optical Zeeman shift (OZS), which produces a random rotation about the $z$ axis proportional to the ellipticity, i.e., the Stokes component $S_3$.