Superradiance in a Large and Dilute Cloud of Cold Atoms in the Linear-Optics Regime

Michelle O. Araújo, Ivor Krešić, Robin Kaiser, and William Guerin

Phys. Rev. Lett. 117, 073002 – Published 10 August 2016

Abstract

Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluorescence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or “single-photon superradiance,” has been investigated much more recently, and superradiant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute cloud of cold rubidium atoms after the sudden switch off of a low-intensity laser driving the atomic transition. We show that, at large detuning, the decay rate increases with the on-resonance optical depth. In contrast to forward scattering, the superradiant decay of off-axis fluorescence is suppressed near resonance due to attenuation and multiple-scattering effects.

Received 22 March 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.073002

Physics Subject Headings (PhySH)

Atomic spectra Lifetimes & widths Superradiance & subradiance

Fluorescence spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

Michelle O. Araújo^1,2, Ivor Krešić³, Robin Kaiser¹, and William Guerin^1,*

¹Université Côte d’Azur, CNRS, INLN, 06560 Valbonne, France
²CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020, Brazil
³SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom

^*william.guerin@inln.cnrs.fr

Observation of Single-Photon Superradiance and the Cooperative Lamb Shift in an Extended Sample of Cold Atoms

S. J. Roof, K. J. Kemp, M. D. Havey, and I. M. Sokolov

Phys. Rev. Lett. 117, 073003 (2016)

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Vol. 117, Iss. 7 — 12 August 2016

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Figure 1
Numerical study of the initial collective decay rate $Γ_{N}$ . (a) Temporal evolution of the fluorescence after the switch off of the driving laser at $t = 0$ , with $b_{0} = 11.3$ , $ρ_{0} λ^{3} = 4.6$ , $Δ = 10 Γ$ , averaged over 50 configurations, for two different angles, in the forward direction $θ = 0 °$ and at 90° ( $θ = π / 2$ ). The amplitude is normalized to the steady-state amplitude, which is much larger for $θ = 0 °$ as shown in the emission diagram (inset, in log scale). The time axis is normalized to the lifetime of the excited state $τ_{at} = Γ^{- 1} \approx 26 ns$ . An exponential fit in the range $0 < t / τ_{at} \leq 0.2$ allows us to extract the initial decay rate $Γ_{N}$ . At late time, the decay becomes subradiant [34, 35]. The dashed line shows the decay expected for a single atom (rate $Γ$ ). (b) Decay rate as a function of the resonant optical thickness $b_{0} = 3 N / (k R)^{2}$ for different densities ( $ρ_{0}$ is the density at the center of the cloud). Filled symbols are for $θ = 0 °$ and open symbols for $θ = π / 2$ . The increase is mainly linear in $b_{0}$ . The slope of the linear increase slightly depends on the angle. The dotted line shows the expectation for the decay of the timed-Dicke state [Eq. (4)]. (c) Decay rate as a function of the detuning, for $b_{0} = 17$ , $ρ_{0} λ^{3} = 4.6$ , and detection angles $θ = 0$ , $π / 2$ . Off-axis superradiance is suppressed near resonance. The error bars shown in panel (c) and omitted in panel (b) for clarity correspond to the 95% confidence interval for the exponential fit of the decay rate.
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Figure 2
(a) Decay of the measured fluorescence power $P$ after switching off the probe laser for two different $b_{0}$ (red and blue solid lines) at a given detuning $Δ = - 6 Γ$ . The vertical axis is normalized to the steady-state fluorescence level. The dashed line shows the expected decay for a single atom, $e^{- t / τ_{at}}$ , and the black solid line is the switch off of the laser (the fast part with a poor extinction ratio is due to the EOM and the slower part is due to the AOM). (b) Same data at shorter time scales, with the exponential fit of the initial decay that allows us to measure $Γ_{N}$ .
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Figure 3
Experimental study of the initial collective decay rate $Γ_{N}$ . (a) Systematic analysis of $Γ_{N}$ as a function of the resonance optical thickness $b_{0}$ and the detuning $Δ$ . (b) Same data shown as a function of $b (Δ)$ . When $b (Δ) ≳ 1$ , it becomes the scaling parameter. (c) $Γ_{N}$ as a function of the saturation parameter $s (Δ)$ , for $b_{0} = 21 \pm 1$ and $Δ = - 4 Γ$ . In all panels, the error bars represent the 95% confidence interval of the fit.
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