Spin-noise spectroscopy of a noise-squeezed atomic state

Letter
Open Access

Spin-noise spectroscopy of a noise-squeezed atomic state

V. Guarrera, R. Gartman, G. Bevilacqua, and W. Chalupczak

Phys. Rev. Research 3, L032015 – Published 12 July 2021

Abstract

Spin-noise spectroscopy is emerging as a powerful technique for studying the dynamics of various spin systems also beyond their thermal equilibrium and linear response. In this context, we demonstrate a nonstandard mode of the spin-noise analysis applied to an out-of-equilibrium nonlinear atomic system realized by a Bell-Bloom atomic magnetometer. Driven by an external pump and undergoing a parametric excitation, this system is known to produce noise squeezing. Our measurements not only reveal a strong asymmetry in the noise distribution of the atomic signal quadratures at the magnetic resonance, but also provide insight into the mechanism behind its generation and evolution. In particular, a structure in the spectrum is identified which allows to investigate the main dependencies and the characteristic timescales of the noise process. The results obtained are compatible with parametrically induced noise squeezing. Notably, the noise spectrum provides information on the spin dynamics even in regimes where the macroscopic atomic coherence is lost, effectively enhancing the sensitivity of the measurements. Our Letter promotes spin-noise spectroscopy as a versatile technique for the study of noise squeezing in a wide range of spin-based magnetic sensors.

Received 10 December 2020
Accepted 16 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.L032015

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields Atomic spectra Light-matter interaction

Atomic, Molecular & Optical

Authors & Affiliations

V. Guarrera ^1,*, R. Gartman ², G. Bevilacqua ³, and W. Chalupczak ²

¹Midlands Ultracold Atom Research Centre, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
²National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom
³DIISM, Università di Siena, via Roma 56, 53100 Siena, Italy

^*v.guarrera@bham.ac.uk

Article Text

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Issue

Vol. 3, Iss. 3 — July - September 2021

Subject Areas

Atomic and Molecular Physics

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Images

Figure 1
Variance of the in-phase $[{(Δ F_{X})}^{2}$ , red diamonds] and out-of-phase $[{(Δ F_{Y})}^{2}$ , black dots] amplitudes of the magneto-optical rotation signal oscillating at $ω$ as a function of the Larmor frequency and recorded for different pump beam powers of (a) $1.4 μ W$ , (b) $21.5 μ W$ , and (c) $94 μ W$ . (d) Dependence of the ratio of the two noise components ${(Δ F_{Y})}^{2} / {(Δ F_{X})}^{2}$ on the Larmor frequency recorded with pump beam powers of $1.4 μ W$ (red triangles), $21.5 μ W$ (blue squares), and $94 μ W$ (black dots). Gray/light blue solid lines in (d) are Lorentzian fits to the tails. The insets: (e) full width at half maximum (FWHM) of the broad feature and (f) FWHM of the narrow near-resonance feature as a function of pump power. The signal is acquired with lock-in reference fixed to $ω = 370 Hz \approx ω_{L}$ and time constant of $τ = 100 ms$ (e) and $τ = 3 ms$ (f), the latter corresponding to the best time resolution of our lock-in amplifier. The optical excitation modulation frequency is equal to $2 ω$ . All the measurements have been performed with probe beam power of $146 μ W$ . At this power, the probe beam does not have any significant effect on the observed noise spectra.
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Figure 2
(a) Parametric model for the in-phase $[{(Δ F_{X})}^{2}$ , red dotted line] and out-of-phase $[{(Δ F_{Y})}^{2}$ , black solid line] signal variances as a function of the Larmor frequency and calculated for different amplitudes of the parametric term $Γ = 0, 0.2 γ, 0.3 γ$ with $γ$ as the spin coherence relaxation rate due to spin-exchange collisions. (b) Dependence of the ratio of the two noise components ${(Δ F_{Y})}^{2} / {(Δ F_{X})}^{2}$ on the Larmor frequency calculated for different values of $Γ$ . The inset: FWHM of the narrow near-resonance feature as a function of parametric gain. The error bars are obtained from Lorenztian fits of the signals calculated for different $M$ parameters [28].
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Figure 3
(a) Variances ratio measured on resonance, i.e., for $ω_{L} = ω = ω_{M} / 2$ as a function of the pump power. The solid line is a fit with the function in Eq. (1), and the dashed line is a fit of the initial plateau. Indication of parametric-induced noise squeezing is observed for pump power below $ω = 370 Hz$ , in agreement with Ref. [19]. (b) Integrated noise signal as a function of the pump beam power. The solid line is a fit with a linear function, and the dashed line is a fit of the initial plateau.
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Figure 4
Dependence of the signal variance on Larmor frequency recorded with the lock-in time constants (a) 3, (b) 30, and (c) 300 ms (lock in referenced to $ω = 370 Hz$ ). (d) Dependence of the ratio of the two noise quadratures ${(Δ F_{Y})}^{2} / {(Δ F_{X})}^{2}$ on the lock-in time constant with $τ = 3 ms$ (blue dots), 30 ms (black squares), and 300 ms (red triangles). The measurements were made with pump power of $79 μ W$ and probe power of $146 − μ W$ beam power.
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Figure 5
(a) Dependence of the noise spectra on the total acquisition time, recorded with lock-in time constant of 3 ms (lock in referenced to $ω = 370 Hz$ ) and pump power of $79 μ W$ . Note that the color scales are different for the two quadratures. (b) Spectra of the two noise components' ratio ${(Δ F_{Y})}^{2} / {(Δ F_{X})}^{2}$ for different acquisition times, starting from the beginning of the pumping process: 1 ms (gray stars), 5 ms (red squares), 10 ms (blue triangles), 15 ms (green diamonds), and 100 ms (black upside-down triangle).
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