Correlation function of spin noise due to atomic diffusion

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 N2 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 lineshape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and measured spin noise spectra for N2 gas pressures ranging from 56 to 820 torr.Measurements of the quantum spin noise provide an ideal way of studying diffusion because they allow one to follow motion of identical atoms in thermal equilibrium that are distinguishable only by their intrinsic quantum fluctuations. All other techniques for studying diffusion rely on non-equilibrium spin populations or other methods of labeling atoms, for example through isotopic composition. From a practical point of view, atomic diffusion can limit the efficiency of light-atom interaction processes, such as electromagnetically induced transparency (EIT) [1,2], coherent population trapping (CPT) [3], and four-wave-mixing [4]. It can also affect applications, such as quantum memories and repeaters [5][6][7] and the sensitivity of atomic sensors [8] and optical magnetometers [9][10][11][12].In general the intrinsic atomic spin fluctuations, i.e. spin noise, becomes more relevant when the light-atom interaction area is reduced [13], i.e. when the probe light is strongly focused, entering into a diffusion-limited scenario. While spin projection noise is a fundamental noise source in atomic measurements [14][15][16][17], it is the main source of information in spin noise spectroscopy (SNS), a powerful technique for measuring physical properties of unperturbed spin systems [18] A first quantitative approach for analyzing the effect of diffusion on quantum spin noise was introduced for SNS of quantum wells [29], in multipass-cell magnetometry [32] and in two-beam SNS [33]. However, to the best of our knowledge, neither a general analytical expression of the diffusion time-correlation function and the resonance lineshape, nor a conclusive comparison between theory and experiment has been reported. In contrast, here we derive a full analytical model for the diffusion component of the spin noise time-correlation function, based on Green's function for a general spin evolution with known relaxation rate and diffusion coefficient, which is valid over a practical range of beam waists. The theory predicts that the decay time of the diffusion correlation function follows a power law in the strong focusing case and it is not modified by an increase in buffer gas pressure. We experimentally study the effect of diffusion on the spin noise spectra of warm Rb vapor to test the model predictions under different con...

Utilising NV based quantum sensing for velocimetry at the nanoscale

“…This behavior derives from the fact that the correlation function at long times decays as t −3∕2 due to diffusion dynamics which transforms to ω dependence in the power spectrum. This non-Lorentzian behavior has been observed experimentally for diffusing Rb vapor in N 2 gas 51,52 . In the following we show that this non-analytic behavior has important implications for parameter estimation.…”

Homogenization of Doppler broadening in spin-noise spectroscopy

“…The power spectrum of the spin noise in this case can be formally obtained from Eqs. (12) and (14) by considering the limit of τ p τ s as…”

“…At present, however, it became clear that specific merits of the SNS extend far beyond its nonperturbativity [5]. In the framework of linear optics, this technique allows one, along with getting the data traditionally provided by the ESR spectroscopy, such as Landé factors and spin relaxation rates [6], to obtain information about spatial characteristics of the spin system [7], mechanisms of broadening of optical transitions [8], kinetic parameters of motion of the spin carriers [10][11][12], dynamics of local magnetic fields in the sample [9], etc.…”

Spin noise correlations in multispecies hot atomic vapors

“…Deeper understanding of spin noise and its relation to the collisional relaxation processes [85][86][87] paves the way towards improving quantum enhanced metrology in hot vapor systems [88][89][90][91]. Some of the modern applications of spin noise spectroscopy in hot vapors are: measurement of zero-field spin noise using magnetic pulses [92], measurement of higher order spin noise like alignment noise [93,94], spin noise measurements with time-dependent magnetic fields [95,96], demonstration of quantum random number generator using spin noise [97], effects of atomic diffusion on the spin noise spectrum [98,99] and dual-species spin noise measurements [100][101][102][103][104]. Of particular interest in this thesis is the study of the noise properties in multispecies atomic systems.…”

“…The DL-780 pro is tuned to λ 0 =780. To perform fiber-coupling with high coupling efficiency and in order to have a precise knowledge of the beam waist at various positions along the beam propagation axis, we perform beam-waist measurements using the scanning knife-edge technique [98,210,211]. With this technique the beam intensity is modulated using an optical chopper at a frequency f c where the light is collected with a photodetector and is presented with an oscilloscope referenced to the chopping frequency.…”