Complete nonlinear polarization control in an optical fiber system.

International audience; We consider the counterpropagating interaction of a signal and a pump beam in an isotropic optical fiber. On the basis of recently developed mathematical techniques, we show that an arbitrary state of polarization of the signal beam can be converted into any other desired state of polarization. On the other hand, an unpolarized signal beam may be repolarized into two specific states of polarization, without loss of energy. Both processes of repolarization and polarization conversion may be controlled by adjusting the polarization state of the backward pump.

Monotonically convergent algorithm for the control of molecular dynamics under non-linear interaction with the control field

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 con…

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.

On the application of canonical perturbation theory to molecular dynamics

Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings

We solve a time-optimal control problem in a linear chain of three coupled spins 1/2 with unequal couplings. We apply the Pontryagin maximum principle and show that the associated Hamiltonian system is the one of a three-dimensional rigid body. We express the optimal control fields in terms of the components of the classical angular momentum of the rigid body. The optimal trajectories and the minimum control time are given in terms of elliptic functions and elliptic integrals.

Manifestation of Hamiltonian Monodromy in Nonlinear Wave Systems

International audience; We show that the concept of dynamical monodromy plays a natural fundamental role in the spatiotemporal dynamics of counterpropagating nonlinear wave systems. By means of an adiabatic change of the boundary conditions imposed to the wave system, we show that Hamiltonian monodromy manifests itself through the spontaneous formation of a topological phase singularity (2 - or -phase defect) in the nonlinear waves. This manifestation of dynamical Hamiltonian monodromy is illustrated by generic nonlinear wave models. In particular, we predict that its measurement can be realized in a direct way in the framework of a nonlinear optics experiment.

Time-dependent unitary perturbation theory for intense laser-driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.

Time optimization and state-dependent constraints in the quantum optimal control of molecular orientation

We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.

Impulsions d'excitation basse énergie robustes aux inhomogénéités B1

International audience

Field-free molecular alignment for probing collisional relaxation dynamics

International audience; We report the experimental study of field-free molecular alignment in CO2 gas mixtures induced by intense femtosecond laser pulses in the presence of collisional processes. We demonstrate that the alignment signals exhibit specific features due to nontrivial collisional propensity rules that tend to preserve the orientation of the rotational angular momentum of the molecules. The analysis is performed with a quantum approach based on the modeling of rotational J- and M-dependent state-to-state transfer rates. The present work paves the way for strong-field spectroscopy of collisional dynamics.

A universal all-fiber omnipolarizer

The all-optical control of light polarization is nowadays a fundamental issue which finds important applications in optical networks. In this field, the research has moved on the development of nonlinear methods of re-polarization of a partially coherent and initially depolarized light [1]. The main drawback of most of these devices is that they suffer from a large amount of output Relative-Intensity-Noise (RIN). However, a class of polarizers have been recently proposed which is based on the nonlinear interaction between two optical beams counter-propagating in a fiber [2]: in these devices the arbitrary state of polarization (SOP) of one of the two beams (signal) is attracted towards a sp…

Optimal control of a three-level quantum system by laser fields plus von Neumann measurements

International audience; We investigate the control of a three-level quantum system by laser fields assisted by von Neumann measurements. We consider a system which is not completely controllable by unitary evolution but which becomes controllable if particular measurements are used. The optimal control is defined from a cost functional which takes into account the measurements. The cost corresponds either to the minimization of the duration of the control or to the minimization of the energy of the laser field. Using the Pontryagin maximum principle, we determine the optimal control which steers the system from a given initial state toward a desired target state. This allows one to determin…

Rovibrational controlled-NOT gates using optimized stimulated Raman adiabatic passage techniques and optimal control theory

International audience; Implementation of quantum controlled-NOT (CNOT) gates in realistic molecular systems is studied using stimulated Raman adiabatic passage (STIRAP) techniques optimized in the time domain by genetic algorithms or coupled with optimal control theory. In the first case, with an adiabatic solution (a series of STIRAP processes) as starting point, we optimize in the time domain different parameters of the pulses to obtain a high fidelity in two realistic cases under consideration. A two-qubit CNOT gate constructed from different assignments in rovibrational states is considered in diatomic (NaCs) or polyatomic (SCCl2) molecules. The difficulty of encoding logical states in…

Molecular alignment in CO2 mixtures induced by a short nonresonant intense pulse : effect of collisional relaxation

TIME-MINIMAL CONTROL OF DISSIPATIVE TWO-LEVEL QUANTUM SYSTEMS: THE INTEGRABLE CASE

The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus our analysis on the case where the extremal Hamiltonian is integrable.

Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecommunication optical fiber

We report the experimental observation of bistability and hysteresis phenomena of the polarization signal in a telecommunication optical fiber. This process occurs in a counterpropagating configuration in which the optical beam nonlinearly interacts with its own Bragg-reflected replica at the fiber output. The proof of principle of optical flip–flop memory and 10  Gbit/s routing operation is also reported based on this polarization bistability. Finally, we also provide a general physical understanding of this behavior on the basis of a geometrical analysis of an effective model of the dynamics. Good quantitative agreement between theory and experiment is obtained.

Rotation Forms and Local Hamiltonian Monodromy

International audience; The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach …

Laser control for the optimal evolution of pure quantum states

Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, post-pulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.

Monodromie Hamiltonienne: de la spectroscopie à l'optique non-linéaire

International audience

MRI phase control with Optimal Control Theory

International audience

Geometric optimal control and two-level dissipative quantum systems

International audience; The objective of this article is to present techniques of geometric time-optimal control developed to analyze the control of two-level dissipative quantum systems. Combined with numerical simulations they allow to compute the time-minimal control using a shooting method. The robustness with respect to initial conditions and dissipative parameters is also analyzed using a continuation method.

Contrôle Optimal appliqué au contrôle de la phase en IRM : simulations et expériences sur fantômes

National audience; IntroductionLes techniques IRM utilisant la phase du signal IRM, à la place ou en complément de l’amplitude, sont de plus en plus nombreuses. Dans ces techniques, la phase est gérée par l’application de gradients. Nous proposons ici de contrôler la phase du signal directement avec des impulsions RF. Pour cela, nous avons utilisé la théorie du contrôle optimal1 et calculé des impulsions RF optimisées pour atteindre des états cibles (dans notre cas, des motifs de phase) préalablement définis. Dans cette étude, une preuve de faisabilité de contrôle de la phase IRM par impulsions RF est présentée au travers de simulations (avec le logiciel ODIN2) ainsi que d’expériences IRM s…

Relaxation of counter-propagating waves and singular Hamiltonian tori

International audience

Time-optimal control of spin-1/2 particles with dissipative and generalized radiation-damping effects

We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.

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 ex…

Quantum vibrational chaos : how subtle a concept is it ?

International audience

Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control

Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin …

Robust digital optimal control on IBM quantum computers

The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We experimentally implement the protocols on IBM quantum computers for a single qubit, obtaining an optimal robust transfer in a time T = 382 ns.

Understanding the global structure of two-level quantum systems with relaxation: Vector fields organized through the magic plane and the steady-state ellipsoid

Hamiltonian tools for the analysis of optical polarization control

Import JabRef; International audience; The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrate…

Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation

The constraint of time-integrated zero-area on the laser field is a fundamental, both theoretical and experimental requirement in the control of molecular dynamics. By using techniques of local and optimal control theory, we show how to enforce this constraint on two benchmark control problems, namely molecular orientation and photofragmentation. The origin and the physical implications on the dynamics of this zero-area control field are discussed.

Rovibrational controlled-NOT gates using optimized stimulated Raman adiabatic passage techniques and optimal control theory

Implementation of quantum controlled-NOT (CNOT) gates in realistic molecular systems is studied using stimulated Raman adiabatic passage (STIRAP) techniques optimized in the time domain by genetic algorithms or coupled with optimal control theory. In the first case, with an adiabatic solution (a series of STIRAP processes) as starting point, we optimize in the time domain different parameters of the pulses to obtain a high fidelity in two realistic cases under consideration. A two-qubit CNOT gate constructed from different assignments in rovibrational states is considered in diatomic (NaCs) or polyatomic $({\text{SCCl}}_{2})$ molecules. The difficulty of encoding logical states in pure rota…

Reaching optimally oriented molecular states by laser kicks

We present a strategy for post-pulse orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.

On the application of canonical perturbation theory to floppy molecules

International audience; Canonical perturbation theory (CPT) is a powerful tool in the field of molecular physics. It consists of a series of coordinate transformations aimed at rewriting the Hamiltonian in a simpler form without modifying the geometry of the phase space. The major achievement of CPT is the straightforward derivation of relations between the physically meaningful parameters of potential energy surfaces and the coefficients of the so-called effective Hamiltonians. While most of the studies performed up to date deal with surfaces expanded in polynomial series around a single minimum, CPT has also been applied to mixed polynomial/trigonometric expansions in the treatment of tor…

Nuclear magnetic resonance: The contrast imaging problem

Starting as a tool for characterization of organic molecules, the use of NMR has spread to areas as diverse as pharmacology, medical diagnostics (medical resonance imaging) and structural biology. Recent advancements on the study of spin dynamics strongly suggest the efficiency of geometric control theory to analyze the optimal synthesis. This paper focuses on a new approach to the contrast imaging problem using tools from geometric optimal control. It concerns the study of an uncoupled two-spin system and the problem is to bring one spin to the origin of the Bloch ball while maximizing the modulus of the magnetization vector of the second spin. It can be stated as a Mayer-type optimal prob…

Geometric Origin of the Tennis Racket Effect

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the Monster flip, an almost impossibl…

Optical flip-flop memory and routing operation based on polarization bistability in optical fiber

A polarization bistability and hysteresis cycle phenomenon is demonstrated in optical fibers thanks to a counter-propagating four-wave mixing interaction. Based on this process, we successfully report the proof-of-principle of an optical flip-flop memory and a 10-Gbit/s routing operation.

A NOT gate in a cis-trans photoisomerization model

We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by non adiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photo-switch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in t…

Optimal control of the signal-to-noise ratio per unit time of a spin 1/2 particle: The crusher gradient and the radiation damping cases

We show to which extent the signal to noise ratio per unit time of a spin 1/2 particle can be maximized. We consider a cyclic repetition of experiments made of a measurement followed by a radio-frequency magnetic field excitation of the system, in the case of unbounded amplitude. In the periodic regime, the objective of the control problem is to design the initial state of the system and the pulse sequence which leads to the best signal to noise performance. We focus on two specific issues relevant in nuclear magnetic resonance, the crusher gradient and the radiation damping cases. Optimal control techniques are used to solve this non-standard control problem. We discuss the optimality of t…

Geometric optimal control of the contrast problem in Magnetic Resonance Imaging

Abstract The control of the dynamics of spin systems by magnetic fields has opened intriguing possibilities in quantum computing and in Nuclear Magnetic Resonance spectroscopy. In this framework, optimal control theory has been used to design control fields able to realize a given task while minimizing a prescribed cost such as the energy of the field or the duration of the process. However, some of the powerful tools of optimal control had not been used yet for NMR applications in medical imagery. Here, we show that the geometric control theory approach can be advantageously combined with NMR methods to crucially optimize the imaging contrast. This approach is applied to a benchmark proble…

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Geometric versus numerical optimal control of a dissipative spin-12particle

We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.

Optimizing MRI contrast with B1 pulses using optimal control theory

The variety of achievable contrasts by MRI makes it a highly flexible and valuable diagnostic tool. Contrast results from relaxation time differences, which are intrinsic properties of each tissue. Using optimal control theory, one can control the obtained contrast by applying excitation pulses that bring the magnetization in a user-defined target state. Simulation results are presented to illustrate the feasibility and the flexibility of using optimal contrast pulses. The robustness to experimental variable parameters such as field inhomogeneities is also studied. Finally, an in-vitro contrast experiment is performed on a small-animal MRI showing a reasonable match with the simulation resu…

Simultaneous time-optimal control of the inversion of two spin-12particles

We analyze the simultaneous time-optimal control of two-spin systems. The two noncoupled 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 nonresonant control field in the laboratory frame. An example is implemented experimentally using nuclear magnetic resonance techniques.

Constant gradient magnetic resonance elastography experiments on phantom and bovine liver

International audience; SynopsisMagnetic Resonance Elastography (MRE) is performed by the application of motion-sensitive gradients. In this study, RF pulses are designed with an optimal control algorithm to obtain a desired magnetization phase distribution. Such pulse, in presence of a constant gradient, allows tosimultaneously perform spatially selective excitation and motion encoding. This offers some advantages when compared to standard MRE encoding strategy. Simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved. These results demonstrate that optimal control-based pulses can be used to encode motion in the MRE excitation phase with relevant advantage…

Towards the time-optimal control of dissipative spin-1/2 particles in nuclear magnetic resonance

International audience; We consider the time-optimal control of a spin 1/2 particle whose dynamics is governed by the Bloch equations with both longitudinal and transverse relaxation terms. We solve this control problem by using geometric optimal control techniques. We show the crucial role of singular extremals in the time-optimal synthesis. This role can mainly be attributed to the presence of dissipation. We also analyze the robustness of the optimal control sequence when both the maximum amplitude of the control field and the dissipative parameters are varied. Finally, we present an experimental implementation of the different solutions using techniques of Nuclear Magnetic Resonance.

Training Schrödinger’s cat: quantum optimal control

It is control that turns scientific knowledge into useful technology: in physics and engineering itprovides a systematic way for driving a dynamical system from a given initial state into a desired targetstate with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantumtechnologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhancedsensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry,magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantumsimulation. In this communication, state-of-the-art quantum control techniques are r…

Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case

International audience; The objective of this article is to complete preliminary results from [5], [17] concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. The extremal system is described by a 3-D-Hamiltonian depending upon three parameters. We combine geometric techniques with numerical simulations to deduce the optimal solutions.

External constraints on optimal control strategies in molecular orientation and photofragmentation: Role of zero-area fields

We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation.

Highly excited vibrational dynamics

International audience

Target states and control of molecular alignment in a dissipative medium

Received 17 August 2006; published 14 November 2006We investigate how and to what extent molecular alignment can be controlled in a dissipative medium by asuitable train of laser pulses. We focus primarily on the extension of a scheme of control originally constructedfor unitary evolution. The procedure is applied to control the alignment of CO molecules in an Ar gas. Theparameters of the train of kicks—i.e., the intensity of each kick and the delay between them—are eitherobtained by a systematic procedure maximum strategy or by optimization by evolutionary algorithms.DOI: 10.1103/PhysRevA.74.053411 PACS number s : 32.80.Lg, 33.80. b, 42.50.Hz

Magnetic resonance elastography without oscillating gradients

International audience

Fundamental bounds on qubit reset

Qubit reset is a basic prerequisite for operating quantum devices, requiring the export of entropy. The fastest and most accurate way to reset a qubit is obtained by coupling the qubit to an ancilla on demand. Here, we derive fundamental bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. Using the Cartan decomposition of the Lie algebra of qubit plus two-level ancilla, we identify the types of interaction and controls for which the qubit can be purified. For these configurations, we show that a time-optimal protocol consists of purity exchange between qubit and ancilla brought into resonance, where the maximu…

Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse

We show that a combination of a half-cycle pulse and a short nonresonant laser pulse produces a strongly enhanced postpulse orientation. Robust transients that display both efficient and long-lived orientation are obtained. The mechanism is analyzed in terms of optimal oriented target states in finite Hilbert subspaces and shows that hybrid pulses can prove useful for other control issues.

Field-free permanent molecular planar alignment

We show the existence of a permanent molecular planar alignment in field-free conditions. We present different control strategies using shaped laser pulses to reach this state. The strategies are robust with respect to the temperature and can be implemented with the state of the art technology. They can be applied not only to linear molecules but also to symmetric or asymmetric top molecules along the most polarizable molecular axis. We propose potential applications of this planar alignment such as the increase of the adsorption on a surface.

Laser control in open molecular systems: STIRAP and Optimal Control

We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic oscillators (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channe…

Newton algorithm for Hamiltonian characterization in quantum control

We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown paramete…

Geometric optimal control of dissipative quantum systems

International audience

BEEEP: B1-robust Energy Efficient Excitation Pulses

International audience; SynopsisThis study introduces a new family of broadband B1-robust excitation (90°) pulses for MRI with large enough bandwidth (+/- 1 kHz) to account forstatic field inhomogeneities, and minimal energy deposition. RF pulses are designed with a regularized optimal control algorithm, which is able toadapt the pulse B1-robustness range to fit the coil limits in terms of peak amplitude and energy. In vitro acquisitions using an endoluminal-shapedRF transmit coil show comparable excitation profiles than BIR4 pulses, although BEEEP pulses deposit 5.2 times less energy.https://index.mirasmart.com/ISMRM2019/PDFfiles/4623.html

Time-optimal control of two-level dissipative quantum systems

International audience

Field-free molecular alignment of CO2 mixtures in presence of collisional relaxation

The present work explores the extension of the concept of short-pulse-induced alignment to dissipative environments within quantum mechanical density matrix formalism (Liouville equation) from the weak to the strong field regime. This is illustrated within the example of the CO2 molecule in mixture with Ar and He, at room temperature, for which a steep decrease of the alignment is observed at moderate pressure because of the collisional relaxation. The field-free alignment is measured by a polarization technique where the degree of alignment is monitored in the time domain by measuring the resulting transient birefringence with a probe pulse Raman induced polarization spectroscopy (RIPS) Co…

A Simplified Framework for Contrast Optimization in MRI

International audience

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.

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.

Contrôle optimal appliqué à l’Elastographie par Résonance Magnétique avec un gradient constant: expériences ex vivo et in vitro

International audience

All-optical regeneration of polarization of a 40 Gbit/s return-to-zero telecommunication signal

International audience; We report all-optical regeneration of the state of polarization of a 40 Gbit/s return-to-zero telecommunication signal. The device discussed here consists of a 6.2-km-long nonzero dispersion-shifted fiber, with low polarization mode dispersion, pumped from the output end by a backward propagating wave coming from either an external continuous source or a reflection of the signal. An initially scrambled signal acquires a degree of polarization close to 100% toward the polarization generator output. All-optical regeneration is confirmed by means of polarization and bit-error-rate measurements as well as real-time observation of the eye diagrams. We show that the physic…

Optimal Control Pulse Design for Contrast in MRI: in vivo applications

International audience; Optimal control RF pulse design has recently been proposed to address the optimization of image contrast in MRI - in order to explore the theoretical contrast bound of a given imaged system. Their use has recently been validated on a real MRI scanner to contrast various in vitro samples. This abstract extends these results to in vivo applications, and shows that contrasts obtained with standard weighting strategies on rat and mouse brains can be improved or inverted. This demonstrates both the interest and flexibility that one can get when using optimal contrast pulses for in vitro and in vivo applications.

Observation of laser-induced field-free permanent planar alignment of molecules

International audience; Permanent planar alignment of gas-phase linear molecules is achieved by a pair of delayed perpendicularly polarized short laser pulses. The experiment is performed in a supersonic jet, ensuring a relatively high number density of molecules with moderately low rotational temperature. The effect is optically probed on a femtosecond time scale by the use of a third short pulse, enabling a time-resolved birefringence detection performed successively in two perpendicular planes of the laboratory frame. The technique allows for an unambiguous estimation of the molecular planar delocalization produced within the polarization plane of the pulse pair after the turn-off of the…

Optimal control of the inversion of two spins in Nuclear Magnetic Resonance

International audience; We investigate the optimal control of the inversion of two spin 1/2 particles in Nuclear Magnetic Resonance. The two spins, which differ by their resonance offset, are controlled by the same radio frequency magnetic field. Using the Pontryagin Maximum Principle, we compute the optimal control sequence which allows to reach the target state in a given time, while minimizing the energy of the magnetic field. A comparison with the time-optimal solution for bounded control amplitude realizing the same control in the same time is made. An experimental illustration is done using techniques of Nuclear Magnetic Resonance.

Application of the small-tip-angle approximation in the toggling frame for the design of analytic robust pulses in quantum control

We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

Integrable Hamiltonian systems with swallowtails

International audience; We consider two-degree-of-freedom integrable Hamiltonian systems with bifurcation diagrams containing swallowtail structures. The global properties of the action coordinates in such systems together with the parallel transport of the period lattice and corresponding quantum cells in the joint spectrum are described in detail. The relation to the concept of bidromy which was introduced in Sadovski´ı and Zhilinski´ı (2007 Ann. Phys. 322 164–200) is discussed.

Investigation of the vibrational dynamics of the HCN/CNH isomers through high order canonical perturbation theory

International audience; Molecular vibrations of the molecule HCN/CNH are examined using a combination of a minimum energy path Hamiltonian and high order canonical perturbation theory , as suggested in a recent work [D. Sugny and M. Joyeux, J. Chem. Phys. 112, 31 (2000)]. In addition, the quantum analog of the classical CPT is presented and results obtained therefrom are compared to the classical ones. The MEP Hamiltonian is shown to provide an accurate representation of the original potential energy surface and a convenient starting point for the CPT. The CPT results are subsequently used to elucidate the molecular dynamics: It appears that the isomerization dynamics of HCN/CNH is very tri…

Field-free molecular alignment in presence of collisional relaxations

Time-optimal control of the purification of a qubit in contact with a structured environment

We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strategy corresponds to a qubit in resonance with the reservoir mode. We investigate under which conditions qubit coherence and correlation between the qubit and the environment can speed up the control process.

Field-free molecular orientation of1Σand2Πmolecules at high temperature

We analyze the control of field-free molecular orientation at high temperature by use of a two-color laser bipulse strategy proposed in Zhang et al. [Phys. Rev. A 83, 043410 (2011)]. A general study shows that there exist two types of linear molecules for which a different mechanism has to be used. For molecules with a large hyperpolarizability, a monochromatic laser pre-pulse is applied before the two-color laser pulse at a time close to the rotational period ${T}_{r}$, while for molecules with a small hyperpolarizability, the optimal delay is found close to ${T}_{r}/4$ or $3{T}_{r}/4$. We extend this analysis to the case of a ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Pi}$ molecule …

Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension

International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.

Exploring the Physical Limits of Saturation Contrast in Magnetic Resonance Imaging

International audience; 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.

Optimal control of quantum superpositions in a bosonic Josephson junction

We show how to optimally control the creation of quantum superpositions in a bosonic Josephson junction within the two-site Bose-Hubbard model framework. Both geometric and purely numerical optimal control approaches are used, the former providing a generalization of the proposal of Micheli et al [Phys. Rev. A 67, 013607 (2003)]. While this method is shown not to lead to significant improvements in terms of time of formation and fidelity of the superposition, a numerical optimal control approach appears more promising, as it allows to create an almost perfect superposition, within a time short compared to other existing protocols. We analyze the robustness of the optimal solution against at…

Geometric optimal control of spin systems

International audience

Self-polarization effect in the middle point of an optical fiber

In this paper, we report both numerically and experimentally an unexpected phenomenon of self-polarization occurring in the middle point of an isotropic optical fiber when two uncorrelated partially polarized waves are simultaneously injected at the ends of the fiber. More precisely, we demonstrate that two counterpropagating waves of equal intensity exhibit a spontaneous organization of their polarization states around two pools of attraction just in the middle point of propagation, and then both recover a partially polarized state at their respective fiber outputs. The self-polarization effect then remains hidden within the optical fiber in the sense that no apparent sign of this process …

Optimal control design of preparation pulses for contrast optimization in MRI

Abstract This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system. Simulation experiments carried out…

The tennis racket effect in a three-dimensional rigid body

We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\pi$- rotation) of the head of the racket when a full ($2\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Differen…

Line of polarization attraction in highly birefringent optical fibers

We investigate the phenomenon of polarization attraction in a highly birefringent fiber. This polarization process originates from the nonlinear interaction of two counter-propagating beams. We show that all polarization states of the forward (signal) beam are attracted toward a specific line of polarization states on the surface of the Poincare sphere, whose characteristics are determined by the polarization state of the injected backward (pump) beam. This phenomenon of polarization attraction takes place without any loss of energy for the signal beam. The stability of different stationary solutions is also discussed through intensive numerical simulations. On the basis of mathematical tec…

Hamiltonian monodromy from a Gauss-Manin monodromy

International audience

The energy minimization problem for two-level dissipative quantum systems

In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.

Optimizing MRI contrast with optimal control theory

International audience; Magnetic Resonance Imaging (MRI) uses the difference in tissue relaxation times to create contrast. Various image weightings can be obtained by tuning acquisition parameters which are usually empirically defined. In this article, optimal control theory is used to design excitation pulses that produce the optimal contrast between given tissues. The designed pulses are tested on numerical phantoms with and without magnetic field inhomogeneities and for the first time in vitro on a small-animal MRI. The reasonable match between simulation and real experiments is promising for the development of such pulses in further in vivo applications.

A universal optical all-fiber omnipolarizer

International audience; Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarizatio…

All-Optical Polarization Control for Telecom Applications

We describe a phenomenon of self-organization of the light state-of-polarization in optical fibers based on a nonlinear cross-polarization interaction between an incident signal and its backward replica. Several proof-of-principles for telecom applications are reported.

Resonances in classical and quantum hamiltonian systems

International audience

Polarization control in spun and telecommunication optical fibers

International audience; We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are d…

Fast polarization scrambler based on chaotic dynamics in optical fibers

Robust optimal control of two-level quantum systems

We investigate the time and the energy minimum optimal solutions for the robust control of two-level quantum systems against offset or control field uncertainties. Using the Pontryagin Maximum Principle, we derive the global optimal pulses for the first robustness orders. We show that the dimension of the control landscape is lower or equal to 2N for a field robust to the N th order, which leads to an estimate of its complexity.

All-fiber based chaotic polarization scrambler

We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.

Laser control in a bifurcating region

We present a complete analysis of the laser control of a model molecular system using both optimal control theory and adiabatic techniques. This molecule has a particular potential energy surface with a bifurcating region connecting three potential wells which allows a variety of processes such as isomerization, tunnelling or implementation of quantum gates on one or two qubits. The parameters of the model have been chosen so as to reproduce the main features of H3CO which is a molecule-benchmark for such dynamics. We show the feasibility of different processes and we investigate their robustness against variations of laser field. We discuss the conditions under which each method of control…

Optimal control of an inhomogeneous spin ensemble coupled to a cavity

We apply optimal control techniques to an inhomogeneous spin ensemble coupled to a cavity. A general procedure is proposed for designing the control strategies. We numerically show the extent to which optimal control fields robust against system uncertainties help enhancing the sensitivity of the detection process. The parameters of the numerical simulations are taken from recent Electron Spin Resonance experiments. The low and high cooperativity regimes are explored.

Time-optimal selective pulses of two uncoupled spin-1/2 particles

We investigate the time-optimal solution of the selective control of two uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive the global time-optimal pulses for two spins with different offsets. We show that the Pontryagin Hamiltonian can be written as a one-dimensional effective Hamiltonian. The optimal fields can be expressed analytically in terms of elliptic integrals. The time-optimal control problem is solved for the selective inversion and excitation processes. A bifurcation in the structure of the control fields occurs for a specific offset threshold. In particular, we show that for small offsets, the optimal solution is the concatenation of regular and sin…

Training Schr\"odinger's cat: quantum optimal control

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. --- Here state-of-the-art qu…

Robust quantum control by a single-shot shaped pulse

Considering the problem of the control of a two-state quantum system by an external field, we establish a general and versatile method allowing the derivation of smooth pulses which feature the properties of high fidelity, robustness, and low area. Such shaped pulses can be interpreted as a single-shot generalization of the composite pulse-sequence technique with a time-dependent phase.

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.

Contrast Preparation Pulses Robust to B1 and B0 inhomogeneities: an Optimal Control Approach

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A universal all-fiber Omnipolarizer

We report the experimental observation of self-polarization of light in optical fibers through a counter-propagating four-wave mixing between an incident signal and its backward replica. An efficient self-polarization of a 40-Gbit/s signal is demonstrated.

Time-optimal control of SU(2) quantum operations

We propose an analysis of the time-optimal control of SU(2) quantum operations. By using the Pontryagin Maximum Principle, we show how to determine the optimal trajectory reaching a given target state. Explicit analytical solutions are given for two specific examples. We discuss the role of the detuning in the construction of the optimal synthesis.

Singular tori as attractors of four-wave-interaction systems

We study the spatiotemporal dynamics of the Hamiltonian four-wave interaction in its counterpropagating configuration. The numerical simulations reveal that, under rather general conditions, the four-wave system exhibits a relaxation process toward a stationary state. Considering the Hamiltonian system associated to the stationary state, we provide a global geometrical view of all the stationary solutions of the system. The analysis reveals that the stationary state converges exponentially toward a pinched torus of the Hamiltonian system in the limit of an infinite nonlinear medium. The singular torus thus plays the role of an attractor for the spatiotemporal wave system. The topological pr…

Application de la théorie des perturbations canoniques à la dynamique moléculaire

Optimal control of two-level dissipative quantum systems

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A simplified framework to optimize MRI contrast preparation

PURPOSE This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences. METHODS Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution. RESULTS The proposed approach reduces the computation time of B 0 -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. …

Polarization shaping for unidirectional rotational motion of molecules.

Control of the orientation of the angular momentum of linear molecules is demonstrated by means of laser polarization shaping. For this purpose, we combine two orthogonally polarized and partially time-overlapped femtosecond laser pulses so as to produce a spinning linear polarization which in turn induces unidirectional rotation of N2 molecules. The evolution of the rotational response is probed by a third laser beam that can be either linearly or circularly polarized. The physical observable is the frequency shift imparted to the probe beam as a manifestation of the angular Doppler effect. Our experimental results are confirmed by theoretical computations, which allow one to gain a deep p…

Laser control of photoinduced processes : alignment and reactivity

Laser control of photoinduced dynamics : Quantum gates

Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass

Recent research has been focused on the ability to manipulate a light beam in such a way to hide, namely to cloak, an event over a finite time or localization in space. The main idea is to create a hole or a gap in the spatial or time domain so as to allow for an object or data to be kept hidden for a while and then to be restored. By enlarging the field of applications of this concept to telecommunications, researchers have recently reported the possibility to hide transmitted data in an optical fibre. Here we report the first experimental demonstration of perpetual temporal spying and blinding process of optical data in fibre-optic transmission line based on polarization bypass. We succes…

Controle de l'orientation et de l'alignement moléculaire par un train d'impulsions soudaines

Les recents progres technologiques dans le domaine des Lasers permettent d'envisager le controle de nombreux processus quantiques jouant un role dans une variete de problemes s'etendant de la reactivite chimique a l'information quantique. Dans ce contexte, nous nous sommes interesses au controle de l'orientation ou de l'alignement moleculaire en utilisant un train d'impulsions soudaines. Nous avons defini des etats cibles qui maximisent a la fois l'orientation ou l'alignement et sa duree dans le temps et montre comment atteindre ces etats a l'aide de strategie systematique ou optimisee.

Discrete-valued-pulse optimal control algorithms: Application to spin systems

International audience; 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 generalizations 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.

Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat i…

Geometric Optimal Control of Simple Quantum Systems

International audience