Determining the absolute number density of a thermal vapor via photon correlations

We propose a technique to determine the absolute number density <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mstyle scriptlevel="0" displaystyle="true"><a:mi>N</a:mi></a:mstyle></a:math> of an alkali-metal vapor confined within a nanocell. This method is based on near-resonant driving of the vapor's constituent atoms and determining the mean interparticle distance (or equivalently the temperature) from the power spectrum associated with the offset photon intensity-intensity correlation function <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mstyle scriptlevel="0" displaystyle="true"><d:mrow><d:msup><d:mi>g</d:mi><d:mrow><d:mo>(</d:mo><d:mn>2</d:mn><d:mo>)</d:mo></d:mrow></d:msup><d:mrow><d:mo>(</d:mo><d:mi>τ</d:mi><d:mo>)</d:mo></d:mrow><d:mo>−</d:mo><d:mn>1</d:mn></d:mrow></d:mstyle></d:math>. In our investigation, we treat the atoms as an average of interacting and radiating dipole pairs randomly positioned within the nanocell. We observe that the power spectrum of the emitted light has a central dip for interparticle distances corresponding to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mo>∼</g:mo><g:mi>λ</g:mi><g:mo>/</g:mo><g:mn>5</g:mn></g:mrow></g:math> and that this result is robust to variations in the driving Rabi frequency and the average detuning. With our proposed method, we can overcome the limitations in defining the absolute number density <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mstyle scriptlevel="0" displaystyle="true"><h:mi>N</h:mi></h:mstyle></h:math>, which is currently typically deduced from the temperature of heating elements applied externally to the cell. Published by the American Physical Society 2024