Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the effects of the conventional superradiance in the pulse delay time. The identified features depend on the intensity of an external coherent field as well as make it possible to assess whether the Stark interaction of an ensemble with a photon-free vacuum electromagnetic field is significant or not.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms
N and a temporal width reduced by
N compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength
λ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than
λ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
In order to study the cooperative emission of radiation from an extended system of
N two-level atoms, we use the master-equation approach within the Born and Markov approximations. All the properties of the emission of radiation can be deduced from the diagonalization of the coupling matrix $\ensuremath{\Gamma}$, where an element ${\ensuremath{\Gamma}}_{\mathrm{jk}}$ gives the coupling between the atoms labeled
j and
k via the electromagnetic field. We choose a pencil-shaped volume and study analytically the coupling matrix in the limit for small and large Fresnel numbers. For Fresnel numbers of order unity numerical methods are used. Thus we prove that, for the pencil-shaped geometry, any elaborated model must take into account the interaction of the atoms with the infinity of electromagnetic field modes lying inside two small solid angles about the axis of the largest linear dimension, which we label the
z axis. In other words, the intensity of radiation emitted by any atom of the system depends on its position with respect to the others and this "propagation effect" cannot be neglected when interpreting superradiance experiments. For small Fresnel numbers the
z dependence predominates, in the opposite case the (
x,y) dependence does, while for Fresnel numbers of order unity the dependence of all three components must be taken into account. Preliminary calculations are given for which only the
z dependence is considered; for Fresnel numbers of magnitude of order unity or smaller, the effect of propagation along the
z axis displays large delays for the appearance of superradiance with respect to the time at which the superradiant pulse is maximum when the "propagation effects" are neglected (one-mode model).
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states
∣j,m⟩ with distinct numbers of excitations
n=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-
N, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.