Optical Transmission of an Atomic Vapor in the Mesoscopic Regime

By measuring the transmission of near-resonant light through an atomic vapor confined in a nanocell we demonstrate a mesoscopic optical response arising from the nonlocality induced by the motion of atoms with a phase coherence length larger than the cell thickness. Whereas conventional dispersion theory—where the local atomic response is simply convolved by the Maxwell-Boltzmann velocity distribution—is unable to reproduce the measured spectra, a model including a nonlocal, size-dependent susceptibility is found to be in excellent agreement with the measurements. This result improves our understanding of light-matter interaction in the mesoscopic regime and has implications for applications where mesoscopic effects may degrade or enhance the performance of miniaturized atomic sensors.

Figure 1

(a) Illustration of the nonlocal response in the presence of an interface in a slab of thickness $L$. Orange filled: nonlocal response $\chi$ for $\xi \sim L$. Blue filled: local response $\chi$ for $\xi \ll L$. (b) Blue line: experimental transmission spectrum for $L=420\mathrm{nm}$ and $\mathrm{\Theta }\approx 170°\mathrm{C}$ as a function of the laser detuning $\mathrm{\Delta }$ with respect to the transition $F=4$ to $F^{\prime }=3$. The data are binned 10 times by steps of 2 MHz. The lines correspond, respectively, to the Cs $D1$ hyperfine transitions $F=4$ to $F^{\prime }=3$ (left), and $F=4$ to $F^{\prime }=4$ (right). Dashed green line: fit by the first local model.

Figure 2

Top panel. Blue dots: experimental transmission spectrum for $\mathrm{\Theta }=170°\mathrm{C}$ and $L=360\mathrm{nm}$ binned as in Fig. 1. Black dot-dashed line: fit by the second model. Red dashed line: fit by the third model (see text). Inset: zoom near resonance. Low panel: absolute value of the residuals for both fits.

Figure 3

(a) Minimum of transmission $T_{\min }$ for the transition from $F=4$ to $F^{\prime }=3$ against the cell thickness $L$. Blue squares: experimental data. Black and red lines: values deduced from the fit of the spectra using the second and third models, respectively. Error bars are smaller than markers. (b) Absolute value of the residuals for the second (black) and third (red) models. (c) (respectively, $d$): broadening parameter ${\mathrm{\Gamma }}_p$ (respectively, shift parameter ${\mathrm{\Delta }}_p$) obtained from the fit of the spectra using the second model (black squares) and third model (red circles). Error bars are the quadratic sum of statistic and fit errors. Blue dotted line: collisional broadening prediction [33].