We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\ensuremath{\gamma}$ and ${\ensuremath{\gamma}}_{0}$ and a single parameter ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically for up to 30 atoms, and obtain the large- $N$ limit by a mean-field approach. We find that there is a critical difference ${\ensuremath{\gamma}}_{0}\ensuremath{-}\ensuremath{\gamma}$ that depends on $N$ beyond which superradiance is lost. We show that exact nontrivial dark states (i.e., states other than the ground state with vanishing spontaneous emission) only exist for $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$ and that those states (dark when $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$) are subradiant when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{0}$.We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\ensuremath{\gamma}$ and ${\ensuremath{\gamma}}_{0}$ and a single parameter ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically for up to 30 atoms, and obtain the large-$N$ limit by a mean-field approach. We find that there is a critical difference ${\ensuremath{\gamma}}_{0}\ensuremath{-}\ensuremath{\gamma}$ that depends on $N$ beyond which superradiance is lost. We show that exact nontrivial dark states (i.e., states other than the ground state with vanishing spontaneous emission) only exist for $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$ and that those states (dark when $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$) are subradiant when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{0}$.

arXiv:1606.05102Physical Review ASep 21, 201629 citations

Superradiance and Subradiance in Dense Atomic Gases: An Integrated Method

H. Ma, Oriol Rubies-Bigordà, Susanne F. Yelin

When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.

arXiv:2205.15255May 30, 20224 citations

Superradiant phases of an atomic beam traversing an optical cavity

Simon B. Jäger, Haonan Liu, Athreya Shankar +2 more

Bulletin of the American Physical SocietyJun 4, 20210 citations

Possibility of superradiant phase transitions in coupled two-level atoms

Tao Liu, Yuyu Zhang, Qing‐Hu Chen +1 more

arXiv:2108.08973Physics Letters AMay 1, 20125 citations

Decay dynamics in the coupled-dipole model

M. Araujo, William Guerin, Robin Kaiser

Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.

arXiv:1705.02190Journal of Modern OpticsOct 5, 201729 citations

N=2

atoms, numerically for up to 30 atoms, and obtain the large-

N

limit by a mean-field approach. We find that there is a critical difference ${\ensuremath{\gamma}}_{0}\ensuremath{-}\ensuremath{\gamma}$ that depends on

N

beyond which superradiance is lost. We show that exact nontrivial dark states (i.e., states other than the ground state with vanishing spontaneous emission) only exist for $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$ and that those states (dark when $\ensuremath{\gamma}={\ensuremath{\gamma}}_{0}$) are subradiant when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{0}$.