58,473 research outputs found
Quantum control with spectral constraints
Various constraints concerning control fields can be imposed in the realistic
implementations of quantum control systems. One of the most important is the
restriction on the frequency spectrum of acceptable control parameters. It is
important to consider the limitations of experimental equipment when trying to
find appropriate control parameters. Therefore, in this paper we present a
general method of obtaining a piecewise-constant controls, which are robust
with respect to spectral constraints. We consider here a Heisenberg spin chain,
however the method can be applied to a system with more general interactions.
To model experimental restrictions we apply an ideal low-pass filter to
numerically obtained control pulses. The usage of the proposed method has
negligible impact on the control quality as opposed to the standard approach,
which does not take into account spectral limitations.Comment: 6 pages, 4 figure
Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field
We propose a new monotonically convergent algorithm which can enforce
spectral constraints on the control field (and extends to arbitrary filters).
The procedure differs from standard algorithms in that at each iteration the
control field is taken as a linear combination of the control field (computed
by the standard algorithm) and the filtered field. The parameter of the linear
combination is chosen to respect the monotonic behavior of the algorithm and to
be as close to the filtered field as possible. We test the efficiency of this
method on molecular alignment. Using band-pass filters, we show how to select
particular rotational transitions to reach high alignment efficiency. We also
consider spectral constraints corresponding to experimental conditions using
pulse shaping techniques. We determine an optimal solution that could be
implemented experimentally with this technique.Comment: 16 pages, 4 figures. To appear in Physical Review
Exploring constrained quantum control landscapes
The broad success of optimally controlling quantum systems with external
fields has been attributed to the favorable topology of the underlying control
landscape, where the landscape is the physical observable as a function of the
controls. The control landscape can be shown to contain no suboptimal trapping
extrema upon satisfaction of reasonable physical assumptions, but this
topological analysis does not hold when significant constraints are placed on
the control resources. This work employs simulations to explore the topology
and features of the control landscape for pure-state population transfer with a
constrained class of control fields. The fields are parameterized in terms of a
set of uniformly spaced spectral frequencies, with the associated phases acting
as the controls. Optimization results reveal that the minimum number of phase
controls necessary to assure a high yield in the target state has a special
dependence on the number of accessible energy levels in the quantum system,
revealed from an analysis of the first- and second-order variation of the yield
with respect to the controls. When an insufficient number of controls and/or a
weak control fluence are employed, trapping extrema and saddle points are
observed on the landscape. When the control resources are sufficiently
flexible, solutions producing the globally maximal yield are found to form
connected `level sets' of continuously variable control fields that preserve
the yield. These optimal yield level sets are found to shrink to isolated
points on the top of the landscape as the control field fluence is decreased,
and further reduction of the fluence turns these points into suboptimal
trapping extrema on the landscape. Although constrained control fields can come
in many forms beyond the cases explored here, the behavior found in this paper
is illustrative of the impacts that constraints can introduce.Comment: 10 figure
Generating Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum
We present a scheme for generating polarization-entangled photons pairs with
arbitrary joint spectrum. Specifically, we describe a technique for spontaneous
parametric down-conversion in which both the center frequencies and the
bandwidths of the down-converted photons may be controlled by appropriate
manipulation of the pump pulse. The spectral control offered by this technique
permits one to choose the operating wavelengths for each photon of a pair based
on optimizations of other system parameters (loss in optical fiber, photon
counter performance, etc.). The combination of spectral control, polarization
control, and lack of group-velocity matching conditions makes this technique
particularly well-suited for a distributed quantum information processing
architecture in which integrated optical circuits are connected by spans of
optical fiber.Comment: 6 pages, 3 figure
Tailoring laser pulses with spectral and fluence constraints using optimal control theory
Within the framework of optimal control theory we develop a simple iterative
scheme to determine optimal laser pulses with spectral and fluence constraints.
The algorithm is applied to a one-dimensional asymmetric double well where the
control target is to transfer a particle from the ground state, located in the
left well, to the first excited state, located in the right well. Extremely
high occupations of the first excited state are obtained for a variety of
spectral and/or energetic constraints. Even for the extreme case where no
resonance frequency is allowed in the pulse the algorithm achieves an
occupation of almost 100%
Optimal Dynamical Decoherence Control of a Qubit
A theory of dynamical control by modulation for optimal decoherence reduction
is developed. It is based on the non-Markovian Euler-Lagrange equation for the
energy-constrained field that minimizes the average dephasing rate of a qubit
for any given dephasing spectrum.Comment: 6 pages, including 2 figures and an appendi
Realistic and verifiable coherent control of excitonic states in a light harvesting complex
We explore the feasibility of coherent control of excitonic dynamics in light
harvesting complexes, analyzing the limits imposed by the open nature of these
quantum systems. We establish feasible targets for phase and phase/amplitude
control of the electronically excited state populations in the
Fenna-Mathews-Olson (FMO) complex and analyze the robustness of this control
with respect to orientational and energetic disorder, as well as decoherence
arising from coupling to the protein environment. We further present two
possible routes to verification of the control target, with simulations for the
FMO complex showing that steering of the excited state is experimentally
verifiable either by extending excitonic coherence or by producing novel states
in a pump-probe setup. Our results provide a first step toward coherent control
of these complex biological quantum systems in an ultrafast spectroscopy setup.Comment: 12 pages, 8 figure
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