The superradiant level shift of a system of $N$ two-level molecules, interacting with the radiation field, is calculated for pencil-like geometry. Introducing the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ of the molecular systems due to its radiative interaction, we first discuss the trivial ( $N=1$ ) and familiar ( $N=2$ ) cases in more detail. The analytic properties of the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ are used to derive dispersion relations for its real and imaginary parts ${\ensuremath{\Delta}}^{(N)}(E)$, ${\ensuremath{\Gamma}}^{(N)}(E)$. We then generalize to the case of $N\ensuremath{\gg}1$, employing a self-consistency argument advanced by Arecchi and Courtens. The modified Dicke expression for the cooperative spontaneous decay rate is then used in the dispersion relation for the shift ${\ensuremath{\Delta}}^{(N)}$ and a value of \ensuremath{\sim}6 MHz calculated corresponding to typical molecular-gas parameters. The physical measurability of the shift is discussed and a Brewer-Shoemaker experiment in a molecular gas is proposed for the observation of the shift.The superradiant level shift of a system of $N$ two-level molecules, interacting with the radiation field, is calculated for pencil-like geometry. Introducing the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ of the molecular systems due to its radiative interaction, we first discuss the trivial ($N=1$) and familiar ($N=2$) cases in more detail. The analytic properties of the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ are used to derive dispersion relations for its real and imaginary parts ${\ensuremath{\Delta}}^{(N)}(E)$, ${\ensuremath{\Gamma}}^{(N)}(E)$. We then generalize to the case of $N\ensuremath{\gg}1$, employing a self-consistency argument advanced by Arecchi and Courtens. The modified Dicke expression for the cooperative spontaneous decay rate is then used in the dispersion relation for the shift ${\ensuremath{\Delta}}^{(N)}$ and a value of \ensuremath{\sim}6 MHz calculated corresponding to typical molecular-gas parameters. The physical measurability of the shift is discussed and a Brewer-Shoemaker experiment in a molecular gas is proposed for the observation of the shift.

Physical Review AMar 1, 197333 citations

Collective Mode Interferences in Light--Matter Interactions

Robert J. Bettles, Teodora Ilieva, Hannes Busche +4 more

We present a theoretical and experimental analysis of transient optical properties of a dense cold atomic gas. After the rapid extinction of a weak coherent driving field (mean photon number $\sim 1.5$ ), a transient `flash' is observed. Surprisingly the decay of the `flash' is faster than the decay of the fastest superradiant mode of the system. We show that this `faster than superradiance decay' is expected due to the interference between collective eigenmodes that exhibit a range of frequency shifts away from the bare atomic transition. Experimental results confirm that the initial decay rate of the superradiant flash increases with optical depth, in agreement with the numerical simulations for the experimental conditions.We present a theoretical and experimental analysis of transient optical properties of a dense cold atomic gas. After the rapid extinction of a weak coherent driving field (mean photon number $\sim 1.5$), a transient `flash' is observed. Surprisingly the decay of the `flash' is faster than the decay of the fastest superradiant mode of the system. We show that this `faster than superradiance decay' is expected due to the interference between collective eigenmodes that exhibit a range of frequency shifts away from the bare atomic transition. Experimental results confirm that the initial decay rate of the superradiant flash increases with optical depth, in agreement with the numerical simulations for the experimental conditions.

arXiv:1808.08415Aug 25, 20188 citations

Intensity of superradiant generation in two-level systems

N. N. Bogolyubov, Kien Le Fam, A. S. Shumovskiǐ

Theoretical and Mathematical PhysicsAug 1, 19840 citations

Deviation from the sech2 superradiant emission law in a two-level atomic system

Antonio Edson Gonçalves, Salomon Sylvain Mizrahi, B. M. Pimentel

The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the ${\mathrm{sech}}^{2}$ law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the ${\mathrm{sech}}^{2}$ law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.

Physical Review ASep 1, 19900 citations

Superradiant enhancement of resonance energy transfer

Jan 1, 20190 citations

The superradiant level shift of a system of

N

two-level molecules, interacting with the radiation field, is calculated for pencil-like geometry. Introducing the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ of the molecular systems due to its radiative interaction, we first discuss the trivial (

N=1

) and familiar (

N=2

) cases in more detail. The analytic properties of the self-energy ${\ensuremath{\Sigma}}^{(N)}(E)$ are used to derive dispersion relations for its real and imaginary parts ${\ensuremath{\Delta}}^{(N)}(E)$, ${\ensuremath{\Gamma}}^{(N)}(E)$. We then generalize to the case of $N\ensuremath{\gg}1$, employing a self-consistency argument advanced by Arecchi and Courtens. The modified Dicke expression for the cooperative spontaneous decay rate is then used in the dispersion relation for the shift ${\ensuremath{\Delta}}^{(N)}$ and a value of \ensuremath{\sim}6 MHz calculated corresponding to typical molecular-gas parameters. The physical measurability of the shift is discussed and a Brewer-Shoemaker experiment in a molecular gas is proposed for the observation of the shift.

We present a theoretical and experimental analysis of transient optical properties of a dense cold atomic gas. After the rapid extinction of a weak coherent driving field (mean photon number

\sim 1.5

), a transient `flash' is observed. Surprisingly the decay of the `flash' is faster than the decay of the fastest superradiant mode of the system. We show that this `faster than superradiance decay' is expected due to the interference between collective eigenmodes that exhibit a range of frequency shifts away from the bare atomic transition. Experimental results confirm that the initial decay rate of the superradiant flash increases with optical depth, in agreement with the numerical simulations for the experimental conditions.

{\mathrm{sech}}^{2}

law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.