Squeezed-Light Enhancement and Backaction Evasion in a High Sensitivity Optically Pumped Magnetometer

C. Troullinou, R. Jiménez-Martínez, J. Kong, V. G. Lucivero, and M. W. Mitchell

Phys. Rev. Lett. 127, 193601 – Published 2 November 2021

Abstract

We study the effect of optical polarization squeezing on the performance of a sensitive, quantum-noise-limited optically pumped magnetometer. We use Bell-Bloom (BB) optical pumping to excite a ${}^{87}{Rb}$ vapor containing $8.2 \times 10^{12} atoms / {cm}^{3}$ and Faraday rotation to detect spin precession. The sub- $pT / \sqrt{Hz}$ sensitivity is limited by spin projection noise (photon shot noise) at low (high) frequencies. Probe polarization squeezing both improves high-frequency sensitivity and increases measurement bandwidth, with no loss of sensitivity at any frequency, a direct demonstration of the evasion of measurement backaction noise. We provide a model for the quantum noise dynamics of the BB magnetometer, including spin projection noise, probe polarization noise, and measurement backaction effects. The theory shows how polarization squeezing reduces optical noise, while measurement backaction due to the accompanying ellipticity antisqueezing is shunted into the unmeasured spin component. The method is compatible with high-density and multipass techniques that reach extreme sensitivity.

Received 4 August 2021
Revised 31 August 2021
Accepted 16 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.193601

Physics Subject Headings (PhySH)

Light-matter interaction Optical pumping Quantum fluctuations & noise Quantum states of light Squeezing of quantum noise

Atoms

Atomic, Molecular & Optical

Authors & Affiliations

C. Troullinou ^1,*, R. Jiménez-Martínez ¹, J. Kong ^2,†, V. G. Lucivero ¹, and M. W. Mitchell ^1,3

¹ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²Department of Physics, Hangzhou Dianzi University, 310018 Hangzhou, China
³ICREA - Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain

^*Corresponding author. charikleia.troullinou@icfo.es
^†Corresponding author. jia.kong@hdu.edu.cn

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Issue

Vol. 127, Iss. 19 — 5 November 2021

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Images

Figure 1
Squeezed-light Bell-Bloom OPM. (a) Experimental setup. Tapered amplified second harmonic generator (TA-SHG); optical parametric oscillator (OPO); PPKTP, Nonlinear crystal; local oscillator (LO); polarizing beam splitter (PBS); quarter wave-plate (QWP); vapor cell (VC); beam stopper (BSt); half wave plate (HWP); photodiode (PD); differential transimpedance amplifier (DTIA); data acquisition (DAQ); function generator (FG); noise lock electronics (NLE). Bell-Bloom inset: Because of the magnetic field $B_{x}$ atomic spins precess at the Larmor frequency $ω_{L}$ in the transverse plane. Synchronously modulated optical pumping maintains the atomic spin polarization. A linearly polarized cw probe undergoes paramagnetic Faraday rotation. Squeezer inset: Vertically polarized squeezed vacuum is combined with horizontally polarized LO on a polarizing beam splitter to generate a polarization squeezed probe. (b) Power spectral density (PSD). Power spectrum of the BB signal for coherent and squeezed light around the Larmor frequency. The spectra are averages of 100 measurements, each one with duration of 0.5 sec. (c) Polarimeter signal (Top): Signal $S_{2}$ [Eq. (2)] for fixed pumping modulation frequency while scanning the magnetic field around resonance. OPM signal (bottom):—lock-in quadrature output ( $v$ ) whose slope, calculated from the linear fit of the dispersive curve around the resonant field value, is used for the calibration of the magnetic sensitivity.
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Figure 2
Polarization rotation noise after demodulation. (a) Spin noise for unpolarized atoms. We fit the spectrum (black) with a model function of Eq. (S45) to estimate the response bandwidth, the photon shot noise (dashed green line) and the low frequency spin projection noise. Subtracting the constant shot noise contribution from the fitted combined noise (yellow) we infer the spin projection noise curve in the unpolarized state probed (dashed cyan). These noise levels define the spin projection noise (cyan) and photon shot noise (green) limited areas and the intermediate transition region (white). Purple dots and curve show, on the right axis, the measured normalized frequency response $| \hat{R} (ω) |^{2}$ to an applied $B_{x}$ modulation, and its fit with Eq. (3) with best fit parameter $Δ ω = 170 Hz$ . (b) Magnetometer noise for polarized atoms. With $500 μ W$ of pump power, the noise spectrum of the magnetometer shows a very similar behaviour to the unpolarized spectrum and apart from the technical noise peaks at the power-line frequency and harmonics, quantum noise is dominant. At high frequencies, the noise level is reduced by 1.9 dB for squeezed-light (green), with respect to the coherent (blue) probing. The dashed lines and the red dots depict estimates of photon shot noise level and cross-over frequencies when the squeezer is on and off, respectively.
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Figure 3
Magnetic sensitivity. Sensitivity spectra for BB magnetometer probed with coherent (blue) and squeezed light (green). All data acquired with $P_{probe} = 400 μ W$ , $P_{pump} = 500 μ W$ , $T = 105 ° C$ , $n = 8.2 \times 12 atoms / {cm}^{3}$ , $B_{0} = 4.3 μ T$ , $f_{mod} = 30.164 kHz$ . Polarization squeezing was 2.4 dB before the atomic cell and 1.9 dB at the detectors.
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