Dimensional Control of the Coherence Time of Scattered Light in Cold Atom Clouds

Abstract

Cold atomic clouds are promising platforms for generating correlated photons, but multiple scattering and associated Doppler broadening limit their temporal coherence. Here we demonstrate that cloud geometry provides a powerful means to extend the coherence time of scattered light. In the experiment, intensity-correlation measurements show that an elongated (quasi-1D) cloud exhibits systematically longer coherence times than a spherical (3D) cloud of the same on-axis optical thickness, as a direct consequence of the suppression of multiple scattering in the elongated geometry. Random-walk simulations reproduce this trend and further show that elongation drives the coherence time toward the single-scattering limit. The combined results establish cloud geometry as a robust control parameter for temporal coherence in cold-atom ensembles, with potential applications in quantum optics and communication.

Figures (4)

• Figure 1: Coherence time of light scattered by a cold atomic cloud, normalized to the single-scattering coherence time, as a function of cloud aspect ratio for different optical thicknesses $b(\delta)$, obtained from random-walk simulations. Illustrations show typical photon paths in spherical (center) and elongated (top-right) clouds, where lighter atoms are in a dark state and do not scatter. Inset plots show the corresponding $g^{(2)}(\tau)$: a narrow peak (short coherence) for multiple- and a broader Gaussian (long coherence) for single-scattering.
• Figure 2: (a) Experimental setup. A probe laser beam is circularly polarized using a polarizing beam splitter (PBS) and a quarter wave plate (QWP), then sent onto the cold atomic cloud (CA). The transmitted light is detected by a photodetector (PD), and used to determine the on-resonant optical thickness of the cloud. Light from the whole cloud scattered at $\theta=6.3^\circ$ is collected using a single-mode fiber after passing through a QWP, a half-wave plate (HWP), and a PBS to select the relevant polarization (see text). The collected light is then split by a 50:50 fiber beam splitter (1:2 PMF), with the outputs directed to two avalanche photodiodes (APDs). Single-photon counts from each APD are time-tagged using a time-to-digital converter (TDC) and analyzed on a computer (PC). A constant magnetic field $\vec{B}$ along the probe axis sets the quantization axis. (b) Relevant atomic levels of the D2 hyperfine transition of $^{85}$Rb. (c) Typical measured intensity correlation function. The gray curve represents experimental data obtained from the 3D cloud with $b(\delta) = 1.56$, while the black curve shows a fit of the data using Eq. \ref{['eq:fitg2']}. The central narrow peak corresponds to multiple scattering, whereas the broader Gaussian feature arises from single-scattered photons.
• Figure 3: (a) Coherence time $\tau_\textrm{c}$, normalized by the single-scattering coherence time $\tau_\textrm{s}$, as a function of the optical thickness $b(\delta)$. Symbols: experimental data for 3D (red circles) and quasi-1D (black triangles) cold atomic cloud. Solid (dashed) curves: random-walk simulations including polarization at all events (only at the first event, with subsequent scatterings treated as depolarized), with polarization filtering at detection; see main text. Inset: Probability distribution of the number of scattering events $N_\mathrm{sc}$ for $b(\delta) = 1.6$. (b) Coherence time as a function of the relative weight of multiple scattering, $I_\mathrm{m}/I_\mathrm{tot}$. Symbols correspond to the same datasets as in (a), with marker size scaling with $b(\delta)$ (see legend for examples). The dashed line corresponds to Eq. \ref{['eq:ratiotsm']} with $\tau_\mathrm{s}/\tau_\mathrm{m} = 40$.
• Figure S1: Angular distribution of singly (a,d) and multiply (b,e) scattered photons for optical thicknesses $b(\delta)=1$ (a--c) and $b(\delta)=3.5$ (d--f) in quasi-1D and 3D cold atom configuration, obtained from RW simulations. Panels (c,f) show the multiple-scattering ratio $I_\mathrm{m}/I_\mathrm{tot}$, where $I_\mathrm{tot}=I_\mathrm{s}+I_\mathrm{m}$. The solid curves correspond to the model where polarization is considered at each scattering event (polarization-tracking model), while dashed lines represent the case where polarization is taken into account only for the first scattering event (depolarized model). For these angular distribution plots, the polarization filtering has not been included.