Control of light trapping in a large atomic system by a static magnetic field

We propose to control light trapping in a large ensemble of cold atoms by an external, static magnetic field. For an appropriate choice of frequency and polarization of the exciting pulse, the field is expected to speed up the fluorescence of a dilute atomic system. In a dense ensemble, the field does not affect the early-time superradiant signal but amplifies intensity oscillations at intermediate times and induces a very slow, nonexponential long-time decay. The slowing down of fluorescence is due to the excitation of spatially localized collective atomic states that appear only under a strong magnetic field and have exponentially long lifetimes. Our results therefore pave a way towards experimental observation of the disorder-induced localization of light in cold atomic systems.

Figure 1

Time-dependent fluorescence of dilute $[\rho /k_0^3=1.6\times {10}^{-3}$ (a)] and dense $[\rho /k_0^3=0.2$ (b)] clouds of two-level atoms, with ($\mathrm{\Delta }={10}^3)$ and without $(\mathrm{\Delta }=0)$ magnetic filed. The calculations were performed for the fluorescence in the direction $\theta =\pi /6$ for the left-handed circular polarized rectangular exciting pulse of duration ${\tau }_{\mathrm{L}}=5{\mathrm{\Gamma }}_0^{-1}$ detuned by ${\delta }_{\mathrm{L}}$ from the fundamental atomic resonance, and for the total number of atoms $N=1448$ (a) or 838 (b). $t=0$ corresponds to the end of the exciting pulse. The inset of panel (a) shows a sketch of the considered experimental situation.

Figure 2

Inverse fluorescence decay rate $\mathrm{\Gamma }$ in a dense atomic cloud in a strong magnetic field ($\mathrm{\Delta }={10}^3$) and in the absence of the field ($\mathrm{\Delta }=0$), for different detunings ${\delta }_{\mathrm{L}}$ of the exciting pulse. Calculations have been performed for the same parameters as in Fig. 1 but for a much longer exciting pulse (${\tau }_{\mathrm{L}}={10}^3{\mathrm{\Gamma }}_0^{-1}$) to restrict the excitation to a narrow spectral region.

Figure 3

Time-dependent fluorescence of a dense cloud of two-level atoms ($\rho /k_0^3=0.2$) in a strong magnetic field under the same conditions as in Fig. 1 but for excitations of transitions with different magnetic quantum numbers $m$ of the excited state: $m=-1$ [red solid line and circles, the same data as in Fig. 1] and $m=0$ (orange dashed line and triangles). The inset shows a sketch of experimental situation for the excitation of $m=0$ transition.

Figure 4

Short-time dynamics of fluorescence under the same conditions as in Fig. 1. The dashed straight line shows the fast initial decay due to the superradiance phenomenon, with the decay rate ${\mathrm{\Gamma }}_{\max }\simeq 12{\mathrm{\Gamma }}_0$ following from Eq. (5).

Figure 5

Spectral distributions of eigenstates with different decay rates $\mathrm{\Gamma }$ for a dense ($\rho /k_0^3=0.2$) spherical cloud of $N=4\times {10}^3$ atoms in a strong magnetic field ($\mathrm{\Delta }={10}^3$). Only a part of frequency range around $\delta =-\mathrm{\Delta }$ is shown; a similar picture is obtained around $\delta =\mathrm{\Delta }$.

Figure 6

Energy-level diagrams of Sr (a) and Yb (b) where we show the two relevant levels (solid red lines) and the levels that are the closest to the excited ones (dashed lines). The large thicknesses of the excited levels symbolize their natural widths ${\mathrm{\Gamma }}_0$, whereas the shaded gray areas show the energy ranges explored by the excited levels in a magnetic field for Zeeman shifts up to $\delta ={10}^3{\mathrm{\Gamma }}_0/2\pi$ (distances between levels are not to scale).