arXiv:1707.09832 · Physical Review A

Correlation function of spin noise due to atomic diffusion

Vito Giovanni Lucivero, Nathaniel David McDonough, Nezih Dural, Michael V. Romalis

Published Dec 4, 2017• 31 citations

Abstract

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of ${\mathrm{N}}_{2}$ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral line shape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and the measured spin noise spectra for ${\mathrm{N}}_{2}$ gas pressures ranging from 56 to 820 Torr.

DOI: 10.1103/physreva.96.062702

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arXiv:1707.09832 · Physical Review A

Correlation function of spin noise due to atomic diffusion

Vito Giovanni Lucivero, Nathaniel David McDonough, Nezih Dural, Michael V. Romalis

Published Dec 4, 2017• 31 citations

arXiv HTML PDF

Abstract

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of

{\mathrm{N}}_{2}

buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral line shape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and the measured spin noise spectra for

{\mathrm{N}}_{2}

gas pressures ranging from 56 to 820 Torr.

DOI: 10.1103/physreva.96.062702

Related papers

Spin-noise spectrum of hot vapor atoms in an anti-relaxation-coated cell

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We study the spin-noise spectrum (SNS) of unpolarized Rb vapor in an evacuated anti-relaxation-coated cell using parametric Faraday rotation of a flat-top probe beam with variable diameter. We identify a distinct structure in the spectrum, called the Ramsey peak. We find that the power of the Ramsey peak is inversely proportional to the total number of atoms in the cell, and the power of the total spin noise is inversely proportional to the number of atoms within the probe beam. We further present a full theoretical analysis of the SNS by comparing three models of spin diffusion: Fickian diffusion, the ballistic flight, and Langevin's diffusion. We find that Fickian diffusion fails, while the ballistic flight is acceptable. However, Langevin's diffusion yields a remarkable agreement with the experimental spectrum.We study the spin-noise spectrum (SNS) of unpolarized Rb vapor in an evacuated anti-relaxation-coated cell using parametric Faraday rotation of a flat-top probe beam with variable diameter. We identify a distinct structure in the spectrum, called the Ramsey peak. We find that the power of the Ramsey peak is inversely proportional to the total number of atoms in the cell, and the power of the total spin noise is inversely proportional to the number of atoms within the probe beam. We further present a full theoretical analysis of the SNS by comparing three models of spin diffusion: Fickian diffusion, the ballistic flight, and Langevin's diffusion. We find that Fickian diffusion fails, while the ballistic flight is acceptable. However, Langevin's diffusion yields a remarkable agreement with the experimental spectrum.

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Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has $1/{f}^{2}$ ( $f$ is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has $1/{f}^{2}$ ($f$ is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.

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M. Yu. Petrov, I. I. Ryzhov, Dmitry S. Smirnov +7 more

The spin-noise spectroscopy, being a nonperturbative linear optics tool, is still reputed to reveal a number of capabilities specific to nonlinear optics techniques. The effect of the Doppler broadening homogenization discovered in this work essentially widens these unique properties of spin-noise spectroscopy. We investigate spin noise of a classical system---cesium atoms vapor with admixture of buffer gas---by measuring the spin-induced Faraday rotation fluctuations in the region of $D{}_{2}$ line. The line, under our experimental conditions, is strongly inhomogeneously broadened due to the Doppler effect. Despite that, optical spectrum of the spin-noise power has the shape typical for the homogeneously broadened line with a dip at the line center. This fact is in stark contrast with the results of previous studies of inhomogeneous quantum dot ensembles and Doppler broadened atomic systems. In addition, the two-color spin-noise measurements have shown, in a highly spectacular way, that fluctuations of the Faraday rotation within the line are either correlated or anticorrelated depending on whether the two wavelengths lie on the same side or on different sides of the resonance. The experimental data are interpreted in the frame of the developed theoretical model which takes into account both kinetics and spin dynamics of Cs atoms. It is shown that the unexpected behavior of the Faraday rotation noise spectra and effective homogenization of the optical transition in the spin-noise measurements are related to smallness of the momentum relaxation time of the atoms as compared with their spin-relaxation time. Our findings demonstrate abilities of spin-noise spectroscopy for studying dynamic properties of inhomogeneously broadened ensembles of randomly moving spins.The spin-noise spectroscopy, being a nonperturbative linear optics tool, is still reputed to reveal a number of capabilities specific to nonlinear optics techniques. The effect of the Doppler broadening homogenization discovered in this work essentially widens these unique properties of spin-noise spectroscopy. We investigate spin noise of a classical system---cesium atoms vapor with admixture of buffer gas---by measuring the spin-induced Faraday rotation fluctuations in the region of $D{}_{2}$ line. The line, under our experimental conditions, is strongly inhomogeneously broadened due to the Doppler effect. Despite that, optical spectrum of the spin-noise power has the shape typical for the homogeneously broadened line with a dip at the line center. This fact is in stark contrast with the results of previous studies of inhomogeneous quantum dot ensembles and Doppler broadened atomic systems. In addition, the two-color spin-noise measurements have shown, in a highly spectacular way, that fluctuations of the Faraday rotation within the line are either correlated or anticorrelated depending on whether the two wavelengths lie on the same side or on different sides of the resonance. The experimental data are interpreted in the frame of the developed theoretical model which takes into account both kinetics and spin dynamics of Cs atoms. It is shown that the unexpected behavior of the Faraday rotation noise spectra and effective homogenization of the optical transition in the spin-noise measurements are related to smallness of the momentum relaxation time of the atoms as compared with their spin-relaxation time. Our findings demonstrate abilities of spin-noise spectroscopy for studying dynamic properties of inhomogeneously broadened ensembles of randomly moving spins.

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Alexander Pouliot, Gehrig Carlse, Thomas Vacheresse +1 more

We demonstrate a technique for the accurate measurement of diffusion coefficients for alkali vapor in an inert buffer gas. The measurement was performed by establishing a spatially periodic density grating in isotopically pure 87Rb vapor and observing the decaying coherent emission from the grating due to the diffusive motion of the vapor through N2 buffer gas. We obtain a diffusion coefficient of 0.245 ± 0.002 cm2 /s at 50°C and 564 Torr. Scaling to atmospheric pressure, we obtain D0 = 0.1819 ± 0.0024 cm2 /s. To the best of our knowledge, this represents the most accurate determination of the Rb-N2 diffusion coefficient. Our measurements can be extended to different buffer gases and alkali vapors used for magnetometry and can be used to constrain theoretical diffusion models for these systemsWe demonstrate a technique for the accurate measurement of diffusion coefficients for alkali vapor in an inert buffer gas. The measurement was performed by establishing a spatially periodic density grating in isotopically pure 87Rb vapor and observing the decaying coherent emission from the grating due to the diffusive motion of the vapor through N2 buffer gas. We obtain a diffusion coefficient of 0.245 ± 0.002 cm2 /s at 50°C and 564 Torr. Scaling to atmospheric pressure, we obtain D0 = 0.1819 ± 0.0024 cm2 /s. To the best of our knowledge, this represents the most accurate determination of the Rb-N2 diffusion coefficient. Our measurements can be extended to different buffer gases and alkali vapors used for magnetometry and can be used to constrain theoretical diffusion models for these systems

Optical and Quantum Sensing and Precision Metrology IIMar 3, 20220 citations

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of

{\mathrm{N}}_{2}

{\mathrm{N}}_{2}

gas pressures ranging from 56 to 820 Torr.

^{41}\mathrm{K}

atoms are in good agreement with the predicted values. Experimental and theoretical spin noise spectra are directly and quantitatively compared in both longitudinal and transverse magnetic fields up to the high magnetic-field regime (where Zeeman energies exceed the intrinsic hyperfine energy splitting of the

^{41}\mathrm{K}

ground state).

1/{f}^{2}

(

f

is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.

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.

D{}_{2}

line. The line, under our experimental conditions, is strongly inhomogeneously broadened due to the Doppler effect. Despite that, optical spectrum of the spin-noise power has the shape typical for the homogeneously broadened line with a dip at the line center. This fact is in stark contrast with the results of previous studies of inhomogeneous quantum dot ensembles and Doppler broadened atomic systems. In addition, the two-color spin-noise measurements have shown, in a highly spectacular way, that fluctuations of the Faraday rotation within the line are either correlated or anticorrelated depending on whether the two wavelengths lie on the same side or on different sides of the resonance. The experimental data are interpreted in the frame of the developed theoretical model which takes into account both kinetics and spin dynamics of Cs atoms. It is shown that the unexpected behavior of the Faraday rotation noise spectra and effective homogenization of the optical transition in the spin-noise measurements are related to smallness of the momentum relaxation time of the atoms as compared with their spin-relaxation time. Our findings demonstrate abilities of spin-noise spectroscopy for studying dynamic properties of inhomogeneously broadened ensembles of randomly moving spins.