We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique.

We study dS 5 vacua within matter-coupled N = 4 gauged supergravity in five dimensions using the embedding tensor formalism. With a simple ansatz for solving the extremization and positivity of the scalar potential, we derive a set of conditions for the gauged supergravity to admit dS 5 as maximally symmetric background solutions. The results provide a new approach for finding dS 5 vacua in five-dimensional N = 4 gauged supergravity and explain a number of notable features pointed out in previous works. These conditions also determine the form of the gauge groups to be SO(1, 1) × G nc with G nc being a non-abelian non-compact group. In general, G nc can be a product of SO(1, 2) and a smaller non-compact group G ′ nc together with (possibly) a compact group. The SO(1, 1) factor is gauged by one of the six graviphotons, that is singlet under SO(5) ∼ U Sp(4) Rsymmetry. The compact parts of SO(1, 2) and G ′ nc are gauged by vector fields from the gravity and vector multiplets, respectively. In addition, we explicitly study dS 5 vacua for a number of gauge groups and compute scalar masses at the vacua. As in the four-dimensional N = 4 gauged supergravity, all the dS 5 vacua identified here are unstable.

We propose a three dimensional optical instrument with an isotropic gradient index in which all ray trajectories form Lissajous curves. The lens represents the first absolute optical instrument discovered to exist without spherical symmetry (other than trivial cases such as the plane mirror or conformal maps of spherically-symmetric lenses). An important property of this lens is that a three-dimensional region of space can be imaged stigmatically with no aberrations, with a point and its image not necessarily lying on a straight line with the lens center as in all other absolute optical instruments. In addition, rays in the Lissajous lens are not confined to planes. The lens can optionally be designed such that no rays except those along coordinate axes form closed trajectories, and conformal maps of the Lissajous lens form a rich new class of optical instruments.

We study dS 4 vacua within matter-coupled N = 4 gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of dS 4 solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to dS 4 vacua. One of them consists of gauge groups of the form G e × G m × H with H being a compact group and G e × G m a non-compact group with SO(3) × SO(3) subgroup and dynonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric AdS 4 vacua. The dS 4 and AdS 4 vacua arise from different coupling ratios between G e and G m factors. Another class of gauge groups is given by SO(2, 1) e × SO(2, 1) m × G nc × G ′ nc × H with SO(2, 1), G nc and G ′ nc dyonically gauged. We explicitly check that all known dS 4 vacua in N = 4 gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on dS 4 vacua in a simple framework. Accordingly, the results provide a new approach for finding dS 4 vacua. In addition, relations between the embedding tensors for gauge groups admitting dS 4 and dS 5 vacua are studied, and a new gauge group, SO(2, 1) × SO(4, 1), with a dS 4 vacuum is found by applying these relations to SO(1, 1) × SO(4, 1) gauge group in five dimensions. Conclusions 32A Useful formulae 33

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