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arXiv:1509.05653 · Physical Review A

Squeezed-light spin noise spectroscopy

Vito Giovanni Lucivero, Ricardo Jiménez-Martínez, Jia Kong, Morgan W. Mitchell

Published May 2, 2016• 74 citations
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Abstract

We report quantum enhancement of Faraday rotation spin noise spectroscopy by polarization squeezing of the probe beam. Using natural abundance Rb in 100 Torr of ${\mathrm{N}}_{2}$ buffer gas and squeezed light from a subthreshold optical parametric oscillator stabilized 20 GHz to the blue of the ${D}_{1}$ resonance, we observe that an input squeezing of 3.0 dB improves the signal-to-noise ratio by 1.5 to 2.6 dB over the combined (power)$\ensuremath{\bigotimes}$(number density) ranges (0.5--4.0 mW)$\ensuremath{\bigotimes}(1.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ to $1.3\ifmmode\times\else\texttimes\fi{}{10}^{13} {\mathrm{cm}}^{\ensuremath{-}3}$), covering the ranges used in optimized spin noise spectroscopy experiments. We also show that squeezing improves the tradeoff between statistical sensitivity and broadening effects, a previously unobserved quantum advantage.

DOI
10.1103/physreva.93.053802

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We report quantum enhancement of Faraday rotation spin noise spectroscopy by polarization squeezing of the probe beam. Using natural abundance Rb in 100 Torr of N2{\mathrm{N}}_{2}N2​ buffer gas and squeezed light from a subthreshold optical parametric oscillator stabilized 20 GHz to the blue of the D1{D}_{1}D1​ resonance, we observe that an input squeezing of 3.0 dB improves the signal-to-noise ratio by 1.5 to 2.6 dB over the combined (power)\ensuremath⨂\ensuremath{\bigotimes}\ensuremath⨂(number density) ranges (0.5--4.0 mW)\ensuremath⨂(1.5\ifmmode×\else\texttimes\fi1012cm\ensuremath−3\ensuremath{\bigotimes}(1.5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}\ensuremath⨂(1.5\ifmmode×\else\texttimes\fi1012cm\ensuremath−3 to 1.3\ifmmode×\else\texttimes\fi1013cm\ensuremath−31.3\ifmmode\times\else\texttimes\fi{}{10}^{13} {\mathrm{cm}}^{\ensuremath{-}3}1.3\ifmmode×\else\texttimes\fi1013cm\ensuremath−3), covering the ranges used in optimized spin noise spectroscopy experiments. We also show that squeezing improves the tradeoff between statistical sensitivity and broadening effects, a previously unobserved quantum advantage.
We measured the spin noise spectroscopy (SNS) of rubidium atomic ensemble with two different kinds of atomic vapor cells (filled with buffer gas or coated with paraffin film on the inner wall) and demonstrated the enhancement of the signal-to-noise ratio (SNR) by using polarization squeezed state (PSS) of 795-nm light field with Stokes operator S Λ 2 squeezed. The PSS is prepared by locking the relative phase between the squeezed vacuum state of light obtained with a sub-threshold optical parametric oscillator and the orthogonally polarized local oscillator beam by means of the quantum noise lock. Under the same conditions, the PSS can be employed not only to improve the SNR, but also to keep the full width at half maximum (FWHM) of SNS, compared with the case of using the polarization coherent state (PCS), enhancement of SNR is positively correlated with the squeezing level of the PSS. With increasing probe laser power and atomic number density, the SNR and FWHM of SNS will increase correspondingly. With the help of the PSS of the Stokes operator S Λ 2 , quantum improvements of both the SNR and FWHM of SNS signal has been demonstrated by controlling optical power of polarization squeezed light beam or atomic number density in our experiments.
Nowadays there is a considerable progress in optical magnetometry and spin noise spectroscopy, which use magnetically-sensitive atomic ensembles and optical read-out, approaching the limits set by quantum mechanics. In recent years optical magnetometers have become the most sensitive instruments for measuring low-frequency magnetic fields, achieving sub-femtotesla sensitivity and surpassing the competitive superconducting quantum interference devices (SQUIDs), and have found applications in biomedicine, geophysics, space science as well as in tests of fundamental physics. Another emerging technique is spin noise spectroscopy (SNS), which allows one to determine physical properties of an unperturbed spin system from its power noise spectrum. In the last decade technological advances like real-time spectrum analyzers and shot-noise-limited detectors have allowed improvements in the sensitivity of spin noise detection leading to a broad range of applications in both atomic and solid state physics. The main goal of this thesis is to address a major outstanding question: whether squeezed light can improve the sensitivity of atomic sensors under optimal sensitivity conditions, typically in a high-density regime due to the statistical advantage of using more atoms. Firstly, we describe the design, construction and characterization of a new versatile experimental apparatus for the study of squeezed-light atomic spectroscopy within a high-density regime (n=¿10¿^12 ¿cm¿^(-3)) and low-noise (¿pT/vHz) magnetic environment. The new experimental system is combined with an existing source of polarization squeezed light based on spontaneous parametric down conversion (SPDC) in a nonlinear crystal, which is the active medium of an optical parametric oscillator. Secondly, we report the first experimental demonstration of quantum-enhanced spin noise spectroscopy of natural abundance Rb via polarization squeezing of the probe beam. We found that input squeezing of 3.0 dB improves the signal-to-noise ratio by 1.5 dB to 2.6 dB over the combined (power¿number density) ranges (0.5 mW to 4.0 mW) ¿ (1.5 ׿10¿^12 ¿cm¿^(-3) to 1.3 ׿10¿^13 ¿cm¿^(-3)), covering the ranges used in optimized spin noise spectroscopy experiments. We also show that squeezing improves the trade-off between statistical sensitivity and broadening effects. Next, we introduce a novel theoretical model by defining a standard quantum limit (SQL) for optically-detected noise spectroscopy, identified as a bound to the covariance of the parameters estimated by fitting power noise spectra. We test the model for spin noise spectroscopy of natural abundance Rb and we demonstrate experimental performance of SNS at the SQL for a coherent probe and below the SQL for a polarization squeezed probe. Finally, we report an optical magnetometer based on amplitude modulated optical rotation (AMOR), using a 85Rb vapor cell, that achieves room temperature sensitivity of 70 fT/vHz at 7.6 µT and we demonstrate its photon shot-noise-limited (SNL) behaviour from 5 µT to 75 µT. While no quantum resources of light were used in this second experiment, the combination of best sensitivity, in the class of room-temperature scalar Hoy en día existe un considerable progreso en la magnetometría óptica y espectroscopía de ruido de espin, que utilizan conjuntos atómicos magnéticamente sensibles y lectura óptica, acercándose a los límites establecidos por la mecánica cuántica. En los últimos años los magnetómetros ópticos se han convertido en los instrumentos más sensibles para medir los campos magnéticos de baja frecuencia, logrando sensibilidad de sub-femtotesla y superando dispositivos como los superconductores de interferencia cuántica (SQUID), y han encontrado aplicaciones en biomedicina, geofísica, ciencia espacial, así como en varias pruebas de física fundamental. Otra técnica emergente es la espectroscopía de ruido de espin (SNS), que permite determinar las propiedades físicas de un sistema de espin sin perturbarlo por medio de su espectro de potencia de ruido. En la última década, los avances tecnológicos como analizadores de espectro en tiempo real y detectores limitados por el ruido de disparo de fotón han permitido mejoras en la sensibilidad de detección de ruido de spin que conduce a una amplia gama de aplicaciones tanto en la física del estado sólido como en la física atómica. El objetivo principal de esta tesis es responder a una cuestión pendiente e importante: si la "luz comprimida" puede mejorar la sensibilidad de los sensores atómicos en condiciones óptimas para la sensibilidad, típicamente en un régimen de alta densidad debido a la ventaja estadística de utilizar más átomos. En primer lugar, se describe el diseño, construcción y caracterización de un nuevo aparato experimental versátil para el estudio de la espectroscopia atómica con luz comprimida dentro de un régimen de alta densidad (n=¿10¿^12 ¿cm¿^(-3)) y bajo nivel de ruido magnético (¿pT/vHz). 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We study the fundamental limits of noise spectroscopy using estimation theory, Faraday rotation probing of an atomic spin system, and squeezed light. We find a simple and general expression for the Fisher information, which quantifies the sensitivity to spectral parameters such as resonance frequency and linewidth. For optically detected spin noise spectroscopy, we find that shot noise imposes ``local'' standard quantum limits for any given probe power and atom number, and also ``global'' standard quantum limits when the probe power and atom number are taken as free parameters. We confirm these estimation theory results using nondestructive Faraday rotation probing of hot Rb vapor, observing the predicted optima, and finding good quantitative agreement with a first-principles calculation of the spin noise spectra. Finally, we show sensitivity beyond the atom- and photon-number-optimized global standard quantum limit using squeezed light.
We study the effect of optical squeezing on the performance of a sensitive, quantum-noise-limited optically-pumped magnetometer. We use Bell-Bloom optical pumping to excite a 87^{87}87Rb vapor and Faraday rotation to detect spin precession. The sub-pT/Hz\mathrm{pT}/\sqrt{\mathrm{Hz}}pT/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 signal bandwidth. The accompanying polarization anti-squeezing perturbs only an unmeasured spin component, so there is no loss of sensitivity at any frequency. The method is compatible with high-density and multi-pass techniques that reach extreme sensitivity.
Abstract With the help of Stokes operator Ŝ 2 squeezed state (also called polarization squeezed state (PSS)) of 795 nm light, rubidium-87 ( 87 Rb) atomic magnetometer based on Faraday rotation (FR) has been implemented and characterized. The PSS of Stokes operator Ŝ 2 of 795 nm light has been prepared by means of coherently combining the polarization coherent state (PCS) of a linearly p-polarized bright 795 nm light beam and a linearly s-polarized squeezed vacuum state (SVS) generated by a 397.5 nm ultraviolet laser pumped sub-threshold optical parametric oscillator (OPO) with a PPKTP bulk crystal inside the OPO cavity. PSS with a squeezing level of −3.7 ± 0.3 dB has been achieved around the analysis frequency of 10 kHz. At different transitions of D 1 line, various frequency detuning, and reasonable atomic vapor cell’s temperature, FR has been measured and compared. To decrease absorption (scattering) losses and the back-action from atomic spin noise to the probe beam’s polarization noise for maintaining the quantum properties of PSS of Stokes operator Ŝ 2 of 795 nm light, we had to run our magnetometer with 87 Rb vapor cell’s temperature below 60 °C, at which the PSS was almost destroyed. The sensitivities of magnetic field measurement were characterized via measuring signal-to-noise ratio of the alternating current calibrated magnetic field signal with a balanced polarimeter. Under the conditions of the atomic number density of ∼5.8 × 10 10 cm −3 ( T ∼ 40 °C) and the probe beam with a detuning of ∼−400 MHz relative to the 5S 1/2 ( F g = 2) − 5P 1/2 ( F e = 1) transition of 87 Rb D 1 line, a typical sensitivity of ∼19.5 pT (Hz 1/2 ) −1 has been achieved employing PSS of Stokes operator Ŝ 2 as the probe, compared with a sensitivity of ∼28.3pT (Hz 1/2 ) −1 using PCS as the probe. We preliminarily demonstrated that the quantum-enhanced sensitivity in a Faraday-rotation-based 87 Rb atomic magnetometer with the help of PSS of 795 nm light.