Steady-state, cavityless, multimode superradiance in a cold vapor

Joel A. Greenberg and Daniel J. Gauthier

Phys. Rev. A 86, 013823 – Published 17 July 2012

Abstract

We demonstrate steady-state, mirrorless superradiance in a cold vapor pumped by weak optical fields. Beyond a critical pump intensity of 1 mW/cm $^{2}$ , the vapor spontaneously transforms into a spatially self-organized state: a density grating forms. Scattering of the pump beams off this grating generates a pair of new, intense optical fields that act back on the vapor to enhance the atomic organization. We map out experimentally the superradiant phase transition boundary and show that it is well described by our theoretical model. The resulting superradiant emission is nearly coherent, persists for several seconds, displays strong temporal correlations between the various modes, and has a coherence time of several hundred $μ$ s. This system therefore has applications in fundamental studies of many-body physics with long-range interactions as well as all-optical and quantum information processing.

Received 14 March 2012

DOI:https://doi.org/10.1103/PhysRevA.86.013823

Authors & Affiliations

Joel A. Greenberg^* and Daniel J. Gauthier

Department of Physics and the Fitzpatrick Institute for Photonics, Duke University, Durham, North Carolina 27708, USA

^*jag27@phy.duke.edu

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Vol. 86, Iss. 1 — July 2012

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Images

Figure 1
(a) When we shine a pair of weak, counterpropagating pump beams on a pencil-shaped cloud of cold atoms, scattering via the spontaneously formed density grating produces signal and idler fields propagating along the trap's long axis. We use a pair of matched photomultiplier tubes (PMTs) and a charge-coupled device (CCD) camera to image the temporal and spatial profile of the generated light, respectively. Measured (points) and predicted (line) boundary between the uniform (normal) and superradiant phases as a function of (b) detuning (for $D_{opt} = 20 \pm 1$ ) and (c) optical depth (for $Δ / Γ = - 7$ ). We find that $I_{thresh} \sim Δ^{2} / D_{opt}$ [23]. The error bars represent typical measurement uncertainties of one standard deviation.Reuse & Permissions
Figure 2
Dependence of $I_{peak}$ on (a) $I_{p}$ for $D_{opt} = 20 \pm 1$ and (b) $D_{opt}$ for $I_{p} = 5 \pm 0.1$ mW/cm $^{2}$ . The dashed lines in (a) and (b) are given by the equation $I_{peak} = 331 (I_{p} - 1.2)$ and $I_{peak} = 104 {(D_{opt} - 5.2)}^{2}$ , respectively, where $I_{p}$ is in mW/cm $^{2}$ and $I_{peak}$ is in $μ$ W/cm $^{2}$ . The data in (a) and (b) correspond to $Δ / Γ = - 5 \pm 0.5$ . (c) Spatial dependence of $I_{s}$ in the far field for two MOT realizations with identical system parameters, where the center of the image (indicated by a $+$ ) corresponds to light propagating along the $\hat{z}$ direction. The angular width of each mode is $θ_{D} = 0.18 \pm {0.02}^{\circ}$ , corresponding to a diffraction-limited beam waist ( $1 / e$ field radius) of $158 \pm 20$ $μ$ m at the exit of the trap. The vertical black line is an imaging artifact. (d) Temporal dependence of $I_{s, i}$ after we turn the pump beams on at $t = 0$ . After a dwell time, the fields grow exponentially, reach a maximum value of $I_{peak}$ , and display ringing. The fields are highly correlated [ $r_{s, i} (0) = 0.987$ ] and terminate after $\sim 250$ $μ$ s. For the data in (c) and (d), we use $I_{p} = 4 \pm 0.1$ mW/cm $^{2}$ , $Δ = - 5 \pm 0.5$ $Γ$ and $D_{opt} = 30 \pm 1$ .Reuse & Permissions
Figure 3
(a) Typical steady-state temporal waveform of the signal intensity when we leave the MOT beams on at a reduced intensity during the application of the pump beams. (b) The degree of second-order coherence $g_{s}^{(2)} (τ)$ for the signal beam time series shown in (a). We find that $g_{s}^{(2)} (0) = 1.18$ , where $g^{(2)} (τ) = 1$ for a coherent field. (c) Normalized power spectral density (PSD) of the pump-reference (upper, shifted vertically by 0.25) and signal-reference (lower) beat notes as a function of detuning from the pump frequency ( $δ$ ). The solid (dashed) lines correspond to experimental data (Lorentzian fit with a FWHM of 20 kHz). For the data shown, $I_{p} = 4 \pm 0.1$ mW/cm $^{2}$ , $Δ = - 6 \pm 0.5$ $Γ$ , and $D_{opt} = 20 \pm 1$ .Reuse & Permissions

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