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.

We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spinboson model for baths with power law spectra. The sequence of ideal π pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder.

In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration p . We show explicitly that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in p . The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coupling between the spin and the environment. The resulting corrections can be made to vanish by an appropriate design of the pulse. For and / 2 pulses, we demonstrate explicitly that pulses exist which annihilate the first-and the second-order corrections even if the bath is fully quantum mechanical, i.e., it displays internal dynamics. Such pulses will also be useful for quantum information processing.

Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment by non-instantaneous pulses, we introduce an optimized sequence of N control π pulses which are realistic in the sense that they have a finite duration and a finite amplitude. We show that optimized dynamical decoupling is still applicable and that higher-order decoupling can be reached if shaped pulses are implemented. The sequence suppresses decoherence up to the order O(T N+1 ) + O(τ M mx ), with T the total duration of the sequence and τmx the maximum length of the pulses. The exponent M ∈ N depends on the shape of the pulse. Based on existing experiments, a concrete setup for the verification of the properties of the advocated sequence is proposed.

Vesicle shape and bilayer parameters are studied by small-angle X-ray (SAXS) and small-angle neutron (SANS) scattering in the presence of the saponin aescin. We confirm successful incorporation of aescin molecules by analysis of the radii of gyration RG and study furthermore the impact of aescin incorporation on bilayer thickness parameters from the neutron and X-ray perspective. Additionally, the bending elasticity (κ) of these 1,2-dimyristoyl-sn-glycero-3-phosphocholine vesicle bilayers is studied in the presence of aescin. Neutron spin-echo spectroscopy (NSE) allows to detect subtle changes in the dynamics and κ of lipid membranes. Changes of κ are detectable at temperatures below and above the main phase transition temperature Tm of the lipid. The impact of aescin is much more significant below Tm. It has been found that below Tm the addition of aescin to the vesicles decreases the value of κ and softens the bilayer. Above Tm the value of κ increases with increasing aescin content and the bilayer becomes more rigid. Altogether, we demonstrate by analysis of the structure and dynamics of the vesicles that the impact of aescin strongly depends on the lipid state. Below Tm the membrane becomes fluidized and softer, above Tm solidified and stiffer compared to a DMPC membrane without additive at similar conditions.