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Beyond Maxwell-Boltzmann statistics using confined vapor cells

Gilad Orr, Eliran Talker

TL;DR

The work shows that coherence times for thermal photons in rubidium vapor cells depart from Maxwell–Boltzmann predictions when the cell is nanoscale, due to wall-induced quenching and transit-time broadening. The authors develop a Lindblad-based theory for $g^{(2)}(\uptau)$ with a refined treatment of $\Gamma_{eff}$ and $\Gamma_2$, and validate it experimentally across thicknesses from millimeters to 200 nm. A Monte Carlo calibration yields an effective transit-time factor $\alpha$ that explains the observed trends, including a doubling of coherence time as thickness drops below $8\,\mu$m and a coherence length reaching $\sim 280\,\text{nm}$ in the thinnest cell. These results highlight the breakdown of Maxwell–Boltzmann-based coherence descriptions in nanoscale confined gases and have implications for nanoscale photonics, precision sensing, and miniaturized quantum technologies.

Abstract

Coherence time of thermal photons in rubidium vapor cells with varying thicknesses, reveal that there is clear dependence of the photon correlation time on cell thickness. Standard theoretical models accurately predict the coherence time in centimeter-scale cells. In this study we demonstrated, that these models break down in micrometer and sub-micrometer regimes. Cell sizes ranging from mm-scale down to 200 nm did not adhere to prediction based on the standard models. In order to address this shortcoming, we develop an alternative approach better suited for estimating photonic coherence times in ultra-thin vapor cells. This work, highlights the need for a modified theoretical treatment of the coherence time in the nanoscale regime.

Beyond Maxwell-Boltzmann statistics using confined vapor cells

TL;DR

The work shows that coherence times for thermal photons in rubidium vapor cells depart from Maxwell–Boltzmann predictions when the cell is nanoscale, due to wall-induced quenching and transit-time broadening. The authors develop a Lindblad-based theory for with a refined treatment of and , and validate it experimentally across thicknesses from millimeters to 200 nm. A Monte Carlo calibration yields an effective transit-time factor that explains the observed trends, including a doubling of coherence time as thickness drops below m and a coherence length reaching in the thinnest cell. These results highlight the breakdown of Maxwell–Boltzmann-based coherence descriptions in nanoscale confined gases and have implications for nanoscale photonics, precision sensing, and miniaturized quantum technologies.

Abstract

Coherence time of thermal photons in rubidium vapor cells with varying thicknesses, reveal that there is clear dependence of the photon correlation time on cell thickness. Standard theoretical models accurately predict the coherence time in centimeter-scale cells. In this study we demonstrated, that these models break down in micrometer and sub-micrometer regimes. Cell sizes ranging from mm-scale down to 200 nm did not adhere to prediction based on the standard models. In order to address this shortcoming, we develop an alternative approach better suited for estimating photonic coherence times in ultra-thin vapor cells. This work, highlights the need for a modified theoretical treatment of the coherence time in the nanoscale regime.

Paper Structure

This paper contains 11 sections, 43 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. Experimental Methods
  4. Experimental results and discussion
  5. Conclusions
  6. Different relaxation effects as a function of cell thickness
  7. $g^{2}(\uptau)$derivation for submicron cells
  8. Calculation of the coherence time (Numerical approach)
  9. First case: $L\ll\bar{l}$, $\Gamma_{2}\gg\Gamma_{eff}$
  10. Second case: $\Gamma_{eff}\gg\Gamma_{dephase}$
  11. Detailed description of the experimental setup

Figures (7)

  • Figure 1: 3D illustration of the experimental setup. The cell is made from 3 channels varying from $8\mu m$ to $200\,nm$. The laser beam is stabilized to the close transition $F=3\rightarrow F'=4$ , laser beam power $50\mu W$ and the beam waist was set to $\sim7\mu m$. HWP - half wave plate; PBS - polarizing beam splitter; BS - non-polarizing beam splitter. A schematic layout of our whole setup is presented in the Supplemental Material supp.
  • Figure 2: Theoretical plot of the second-order intensity autocorrelation as a function of the cell length, the whole measurements done under low light intensity limit where the Rabi frequency was near zero $(\Omega\rightarrow0)$ and the frequency detuning is set to zero.
  • Figure 3: Measurements of the second-order intensity autocorrelation for different cell thickness (a) $200nm$ (b) $3\mu m$ (c) $8\mu m$ (d) 75 mm. The calculated result for the different cell thicknesses, based on equation \ref{['eq:Derived_correlation_fuction']} is shown to be in excellent agreement.
  • Figure 4: Measured coherence (a) time, as a function of cell length (b) length, as a function of the cell length.
  • Figure S1: A schematic showing the hyperfine structure and intervals of $^{85}Rb$ for the $D_{2}$ spectroscopic lines
  • ...and 2 more figures