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The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for π and π 2 pulses.

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder, which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.PACS numbers: 75.10. Kt, 02.30.Mv, 75.50.Ee § To correspond with our approach in second quantization we use the vacuum state |0 as the starting vector for the minimization. In principle, one can use an arbitrary starting vector.

Abstract. -Sufficiently dimerized quantum antiferromagnets display elementary S = 1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1 ≈ −2.3 meV, J2 ≈ 1.2 meV, J3 ≈ 2.9 meV and J4 ≈ −0.3 meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S = 1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Low-dimensional antiferromagnetic quantum spin systems display various fascinating properties, e.g., spinPeierls transition [1, 2], appearance of a Haldane gap for integer spins [3,4], high-temperature superconductivity upon doping [5], and the Bose-Einstein condensation (BEC) in spin-dimer systems [6][7][8][9], where the latter one is characterized by a phase transition from a non-magnetic phase to a long-range antiferromagnetically ordered gapless phase at a critical magnetic field H c1 .Another fascinating phenomenon recently observed in low-dimensional antiferromagnets is the decay of their elementary S = 1 excitations, triplons [10], at higher energies so that the triplons exist only in a restricted part of the Brillouin zone [11,12]. Theoretically as well, there is rising interest in the understanding and quantitative description of this phenomenon for gapped triplons [13][14][15][16] as well as for gapless magnons [17][18][19].The description of quasiparticle decay faces an intrinsic difficulty. The merging of the long-lived, infinitely sharp elementary triplon with a multitriplon continuum requires to describe the resulting resonance and its edges precisely. This is still a challenge for numerical approaches such as exact diagonalization or dynamic density-matrix (a) fischer@fkt.physik.tu-dortmund.de (b) goetz.uhrig@tu-dortmund.de renormalization [20]. Diagrammatic approaches are able to capture the qualitative features but may encounter difficulties in the quantitative description in the regime of strong merging where the sharp mode dissolves completely in the continuum because this is a strong coupling phenomenon [13,14]. Unitary transformations also face difficulties when modes of finite life-time occur [16].A crucial step in the understanding of both phenomena is to identify a suitable experimental system. The best studied candidate for the BEC in coupled spin-dimer systems is TlCuCl 3 . Unfortunately, recent research suggests that the high field spectrum remains gapped [21,22] in contrast to what is expected from a phase where a continuous s...

The space-resolved Gouy phase shift for focused surface plasmon polaritons (SPPs) in the optical regime is experimentally demonstrated for the first time. SPPs are excited by CW laser radiation focused onto a dielectric ridge placed on a cover glass surface coated by a silver film. The Gouy phase measurements are performed using interference between a reference plane wave and leakage radiation. The measured Gouy shift has a value of π/2 corresponding to the two-dimensional nature of surface plasmon polaritons.