6 research outputs found
Generalization of short coherent control pulses: extension to arbitrary rotations
We generalize the problem of the coherent control of small quantum systems to
the case where the quantum bit (qubit) is subject to a fully general rotation.
Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315),
the systematic expansion in the shortness of the pulse is extended to the case
where the pulse acts on the qubit as a general rotation around an axis of
rotation varying in time. The leading and the next-leading corrections are
computed. For certain pulses we prove that the general rotation does not
improve on the simpler rotation with fixed axis.Comment: 6 pages, no figures; published versio
Optimization of Short Coherent Control Pulses
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 and pulses.Comment: 9 pages, 6 figures; published versio
High Order Coherent Control Sequences of Finite-Width Pulses
The performance of sequences of designed pulses of finite length is
analyzed for a bath of spins and it is compared with that of sequences of
ideal, instantaneous pulses. The degree of the design of the pulse strongly
affects the performance of the sequences. Non-equidistant, adapted sequences of
pulses, which equal instantaneous ones up to , outperform
equidistant or concatenated sequences. Moreover, they do so at low energy cost
which grows only logarithmically with the number of pulses, in contrast to
standard pulses with linear growth.Comment: 6 pages, 5 figures, new figures, published versio
Optimized pulses for the perturbative decoupling of spin and decoherence bath
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 . We show explicity
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 . 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
vanish by an appropriate design of the pulse. For and 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.Comment: 9 pages, 7 figures. Published versio