arXiv subjects

M. Lapert

Publications and source records attributed to M. Lapert.

13 recordsLinked to original sources

arXiv2017

Optimal control theory for applications in magnetic resonance imaging

We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical limits of the corresponding spin dynamics in the presence of typical experimental imperfections and limitations. We study in this paper two important goals, namely the optimization of image contrast and the maximization of the signal to noise per unit time. We anticipate that the proposed techniques will find practical applications in medical imaging in a near future to help the medical diagnosis.

quant-ph↗

arXiv2015

A discrete-pulse optimal control algorithm with an application to spin systems

This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose a generalization of the standard GRAPE algorithm suited to this constraint. We test the validity and the efficiency of this approach for the inversion of an inhomogeneous ensemble of spin systems with different offset frequencies. It is shown that a remarkable efficiency can be achieved even for a very limited number of discrete values. Some applications in Nuclear Magnetic Resonance are discussed.

math.OC↗

arXiv2014

Optimal control of the signal to noise ratio per unit time for a spin 1/2 particle

We investigate the maximum signal to noise ratio per unit time that can be achieved for a spin 1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal to noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing use of shaped pulses.

quant-ph↗

arXiv2013

Comparative study of monotonically convergent optimization algorithms for the control of molecular rotation

We apply two different monotonically convergent optimization algorithms to the control of molecular rotational dynamics by laser pulses. This example represents a quantum control problem where the interaction of the system with the external field is non-linear. We test the validity and accuracy of the two methods on the key control targets of producing molecular orientation and planar delocalization at zero temperature, and maximizing permanent alignment at non-zero temperature.

quant-ph↗

arXiv2012

Exploring the physical limits of saturation contrast in Magnetic Resonance Imagign

Magnetic Resonance Imaging has become nowadays an indispensable tool with applications ranging from medicine to material science. However, so far the physical limits of the maximum achievable experimental contrast were unknown. We introduce an approach based on principles of optimal control theory to explore these physical limits, providing a benchmark for numerically optimized robust pulse sequences which can take into account experimental imperfections. This approach is demonstrated experimentally using a model system of two spatially separated liquids corresponding to blood in its oxygenated and deoxygenated forms.

physics.med-ph↗

arXiv2012

Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.

quant-ph↗

arXiv2012

Field-free molecular orientation by THz laser pulses at high temperature

We investigate to which extend a THz laser pulse can be used to produce field-free molecular orientation at high temperature. We consider laser pulses that can be implemented with the state of the art technology and we show that the efficiency of the control scheme crucially depends on the parameters of the molecule. We analyze the temperature effects on molecular dynamics and we demonstrate that, for some molecules, a noticeable orientation can be achieved at high temperature.

quant-ph↗

arXiv2012

Time-optimal monotonic convergent algorithms for the control of quantum systems

We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the field fluence. A standard algorithm designs a control field of fixed duration which both brings the system close to the target state and minimizes its fluence, whereas here we include in addition the optimization of the duration in the cost functional. We apply this new algorithm to the control of spin systems in Nuclear Magnetic Resonance. We show how to implement CNOT gates in systems of two and four coupled spins.

quant-ph↗

arXiv2011

Saturation of a spin 1/2 particle by generalized Local control

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.

quant-ph↗

arXiv2010

Simultaneous time-optimal control of the inversion of two spin 1/2 particles

We analyze the simultaneous time-optimal control of two-spin systems. The two non coupled spins which differ in the value of their chemical offsets are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a non-resonant control field in the laboratory frame. An example is implemented experimentally using techniques of Nuclear Magnetic Resonance.

quant-ph↗

arXiv2010

Singular extremals for the time-optimal control of dissipative spin 1/2 particles

We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.

quant-ph↗

arXiv2009

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.

quant-ph↗

arXiv2009

Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field

We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.

quant-ph↗