We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general N-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely, the diversity degree and the degeneracy configuration of a symmetric state. Those parameters give rise to a simple method of identifying operational families of SLOCC entanglement classes of all symmetric N-qubit states, where the number of families grows as the partition function of the number of qubits.

We study the interconversion of multipartite symmetric N -qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or Greenberger-Horne-Zeilinger (GHZ) entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric N -qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.

We report measurements of the isotope shifts of the 3d 6 4s 2 a 5 D 4 −3d 6 4s4p z 5 F 5 o Fe I resonance line at 372 nm between all four stable isotopes 54 Fe, 56 Fe, 57 Fe, and 58 Fe, as well as the complete hyperfine structure of that line for 57 Fe, the only stable isotope having a nonzero nuclear spin. The field and specific mass shift coefficients of the transition have been derived from the data, as well as the experimental value for the hyperfine structure magnetic dipole coupling constant A of the excited state of the transition in 57 Fe:The measurements were carried out by means of high-resolution Dopplerfree laser saturated absorption spectroscopy in a Fe-Ar hollow cathode discharge cell using both natural and enriched iron samples. The measured isotope shifts and hyperfine constants are reported with uncertainties at the percent level.

We present experimental schemes that allow us to study the entanglement classes of all symmetric states in multiqubit photonic systems. We compare the efficiency of the proposed schemes and highlight the relation between the entanglement properties of symmetric Dicke states and a recently proposed entanglement scheme for atoms. In analogy to the latter, we obtain a one-to-one correspondence between well-defined sets of experimental parameters and multiqubit entanglement classes inside the symmetric subspace of the photonic system.

We report on the hyperfine-structure splitting of the 716 nm R903-10 molecular iodine transition. We show that this particular iodine line provides a very useful frequency reference in the context of a laser cooling experiment of iron atoms, an atomic species that has so far never been laser cooled and trapped to our knowledge. We provide experimental values for the hyperfine constants ΔeQq and ΔC of the investigated iodine transition. Dispersive signals of this transition are also presented and used to lock the frequency of a Ti:sapphire laser. The reported stabilization performance is fully compatible with the requirements of a laser cooling experiment of iron atoms.